From 48c946a2b88f9ce91bf8ea920777d5e9cabb64dd Mon Sep 17 00:00:00 2001 From: anjohan Date: Mon, 10 Jun 2024 19:20:06 +0000 Subject: [PATCH] deploy: 113b370c7cb33669754ab8c3759bd42755170cfa --- flare/bffs/gp/calculator.html | 49 +- flare/bffs/gp/gp.html | 361 +++++++ flare/bffs/gp/gp_algebra.html | 315 +++++- flare/bffs/gp/predict.html | 176 +++- flare/bffs/mgp/mgp.html | 129 +++ flare/bffs/mgp/splines_methods.html | 90 +- flare/bffs/sgp/calculator.html | 24 +- flare/bffs/sgp/sgp.html | 46 + flare/descriptors/env.html | 144 ++- flare/flare.html | 5 +- flare/io/otf_parser.html | 126 ++- flare/io/output.html | 220 ++++- flare/kernels/cutoffs.html | 115 ++- flare/kernels/helper.html | 157 ++- flare/kernels/mc_sephyps.html | 1074 +++++++++++++++++++- flare/kernels/mc_simple.html | 1425 ++++++++++++++++++++++++++- flare/kernels/sc.html | 1156 +++++++++++++++++++++- flare/learners/gp_from_aimd.html | 73 +- flare/learners/learners.html | 5 +- flare/learners/otf.html | 166 +++- flare/learners/utils.html | 151 ++- flare/md/fake.html | 73 ++ flare/md/lammps.html | 156 ++- flare/md/nosehoover.html | 42 +- flare/utils/env_getarray.html | 160 ++- flare/utils/mask_helper.html | 414 +++++++- flare/utils/utils.html | 13 + genindex.html | 1045 +++++++++++++++++++- index.html | 5 +- objects.inv | Bin 16595 -> 23111 bytes py-modindex.html | 269 +++++ searchindex.js | 2 +- 32 files changed, 8129 insertions(+), 57 deletions(-) create mode 100644 py-modindex.html diff --git a/flare/bffs/gp/calculator.html b/flare/bffs/gp/calculator.html index f80b09195..aa5fc9ff1 100644 --- a/flare/bffs/gp/calculator.html +++ b/flare/bffs/gp/calculator.html @@ -102,8 +102,53 @@
-
-

FLARE ASE Calculator

+
+

FLARE ASE Calculator

+

FLARE_Calculator is a calculator compatible with ASE. +You can build up ASE Atoms for your atomic structure, and use get_forces, +get_potential_energy as general ASE Calculators, and use it in +ASE Molecular Dynamics and our ASE OTF training module. For the usage +users can refer to ASE Calculator module +and ASE Calculator tutorial.

+
+
+class flare.bffs.gp.calculator.FLARE_Calculator(*args: Any, **kwargs: Any)
+

Build FLARE as an ASE Calculator, which is compatible with ASE Atoms and +Molecular Dynamics. +:Parameters: * gp_model (GaussianProcess) – FLARE’s Gaussian process object

+
+
    +

  • mgp_model (MappedGaussianProcess) – FLARE’s Mapped Gaussian Process +object. None by default. MGP will only be used if use_mapping +is set to True.

    • +

  • par (Bool) – set to True if parallelize the prediction. False by +default.

    • +

  • use_mapping (Bool) – set to True if use MGP for prediction. False +by default.

    • +
+
+
+
+calculate(atoms=None, properties=None, system_changes=ase.calculators.calculator.all_changes)
+
+
Calculate properties including: energy, local energies, forces,

stress, uncertainties.

+
+
+
+
Parameters
+

atoms (FLARE_Atoms) – FLARE_Atoms object

+
+
+
+ +
+
+implemented_properties: List[str] = ['energy', 'forces', 'stress', 'stds']
+

Properties calculator can handle (energy, forces, …)

+
+ +
+
diff --git a/flare/bffs/gp/gp.html b/flare/bffs/gp/gp.html index 3ccad79a6..4e41ce47c 100644 --- a/flare/bffs/gp/gp.html +++ b/flare/bffs/gp/gp.html @@ -110,6 +110,367 @@

Gaussian Process Force FieldsFLARE ASE Calculator

+
+
+class flare.bffs.gp.gp.GaussianProcess(kernels: List[str] = None, component: str = 'mc', hyps: ndarray = None, cutoffs: dict = None, hyps_mask: dict = None, hyp_labels: List = None, opt_algorithm: str = 'L-BFGS-B', maxiter: int = 10, parallel: bool = False, per_atom_par: bool = True, n_cpus: int = 1, n_sample: int = 100, output: Output = None, name='default_gp', energy_noise: float = 0.01, **kwargs)
+

Gaussian process force field. Implementation is based on Algorithm 2.1 +(pg. 19) of “Gaussian Processes for Machine Learning” by Rasmussen and +Williams.

+

Methods within GaussianProcess allow you to make predictions on +AtomicEnvironment objects (see env.py) generated from +FLARE FLARE_Atoms (see ase/atoms.py), and after data points are added, +optimize hyperparameters based on available training data (train method).

+
+
Parameters
+
    +

  • kernels (list, optional) – Determine the type of kernels. Example: +[‘twbody’, ‘threebody’], [‘2’, ‘3’, ‘mb’], [‘2’]. Defaults to [ +‘twboody’, ‘threebody’]

    • +

  • component (str, optional) – Determine single- (“sc”) or multi- +component (“mc”) kernel to use. Defaults to “mc”

    • +

  • hyps (np.ndarray, optional) – Hyperparameters of the GP.

    • +

  • cutoffs (Dict, optional) – Cutoffs of the GP kernel. For simple hyper- +parameter setups, formatted like {“twobody”:7, “threebody”:4.5}, +etc.

    • +

  • hyp_labels (List, optional) – List of hyperparameter labels. Defaults +to None.

    • +

  • opt_algorithm (str, optional) – Hyperparameter optimization algorithm. +Defaults to ‘L-BFGS-B’.

    • +

  • maxiter (int, optional) – Maximum number of iterations of the +hyperparameter optimization algorithm. Defaults to 10.

    • +

  • parallel (bool, optional) – If True, the covariance matrix K of the GP is +computed in parallel. Defaults to False.

    • +

  • n_cpus (int, optional) – Number of cpus used for parallel +calculations. Defaults to 1 (serial)

    • +

  • n_sample (int, optional) – Size of submatrix to use when parallelizing +predictions.

    • +

  • output (Output, optional) – Output object used to dump hyperparameters +during optimization. Defaults to None.

    • +

  • hyps_mask (dict, optional) – hyps_mask can set up which hyper parameter +is used for what interaction. Details see kernels/mc_sephyps.py

    • +

  • name (str, optional) – Name for the GP instance which dictates global +memory access.

    • +
+
+
+
+
+add_one_env(env: AtomicEnvironment, force: Optional[numpy.ndarray] = None, train: bool = False, **kwargs)
+

Add a single local environment to the training set of the GP.

+
+
Parameters
+
    +

  • env (AtomicEnvironment) – Local environment to be added to the +training set of the GP.

    • +

  • force (np.ndarray) – Force on the central atom of the local +environment in the form of a 3-component Numpy array +containing the x, y, and z components.

    • +

  • train (bool) – If True, the GP is trained after the local +environment is added.

    • +
+
+
+
+ +
+
+adjust_cutoffs(new_cutoffs: Optional[Union[list, tuple, numpy.ndarray]] = None, reset_L_alpha=True, train=True, new_hyps_mask=None)
+

Loop through atomic environment objects stored in the training data, +and re-compute cutoffs for each. Useful if you want to gauge the +impact of cutoffs given a certain training set! Unless you know +exactly what you are doing for some development or test purpose, +it is highly suggested that you call set_L_alpha and +re-optimize your hyperparameters afterwards as is default here.

+

A helpful way to update the cutoffs and kernel for an extant +GP is to perform the following commands: +>> hyps_mask = pm.as_dict() +>> hyps = hyps_mask[‘hyps’] +>> cutoffs = hyps_mask[‘cutoffs’] +>> kernels = hyps_mask[‘kernels’] +>> gp_model.update_kernel(kernels, ‘mc’, hyps, cutoffs, hyps_mask)

+
+
Parameters
+
    +

  • reset_L_alpha –

    • +

  • train –

    • +

  • new_hyps_mask –

    • +

  • new_cutoffs –

    • +
+
+
Returns
+

+
+
+
+ +
+
+as_dict()
+

Dictionary representation of the GP model.

+
+ +
+
+static backward_arguments(kwargs, new_args={})
+

update the initialize arguments that were renamed

+
+ +
+
+static backward_attributes(dictionary)
+

add new attributes to old instance +or update attribute types

+
+ +
+
+check_L_alpha()
+

Check that the alpha vector is up to date with the training set. If +not, update_L_alpha is called.

+
+ +
+
+check_instantiation()
+

Runs a series of checks to ensure that the user has not supplied +contradictory arguments which will result in undefined behavior +with multiple hyperparameters. +:return:

+
+ +
+
+compute_matrices()
+

When covariance matrix is known, reconstruct other matrices. +Used in re-loading large GPs. +:return:

+
+ +
+
+static from_dict(dictionary)
+

Create GP object from dictionary representation.

+
+ +
+
+static from_file(filename: str, format: str = '')
+

One-line convenience method to load a GP from a file stored using +write_file

+
+
Parameters
+
    +

  • filename (str) – path to GP model

    • +

  • format (str) – json or pickle if format is not in filename

    • +
+
+
Returns
+

+
+
+
+ +
+
+property par
+

Backwards compability attribute +:return:

+
+ +
+
+predict(x_t: AtomicEnvironment, d: int) → [<class 'float'>, <class 'float'>]
+

Predict a force component of the central atom of a local environment.

+
+
Parameters
+
    +

  • x_t (AtomicEnvironment) – Input local environment.

    • +

  • d (int) – Force component to be predicted (1 is x, 2 is y, and +3 is z).

    • +
+
+
Returns
+

Mean and epistemic variance of the prediction.

+
+
Return type
+

(float, float)

+
+
+
+ +
+
+predict_efs(x_t: AtomicEnvironment)
+

Predict the local energy, forces, and partial stresses of an +atomic environment and their predictive variances.

+
+ +
+
+predict_force_xyz(x_t: AtomicEnvironment)
+

Simple wrapper to predict all three components of a force in one go. +:param x_t: +:return:

+
+ +
+
+predict_local_energy(x_t: AtomicEnvironment) → float
+

Predict the local energy of a local environment.

+
+
Parameters
+

x_t (AtomicEnvironment) – Input local environment.

+
+
Returns
+

Local energy predicted by the GP.

+
+
Return type
+

float

+
+
+
+ +
+
+predict_local_energy_and_var(x_t: AtomicEnvironment)
+

Predict the local energy of a local environment and its +uncertainty.

+
+
Parameters
+

x_t (AtomicEnvironment) – Input local environment.

+
+
Returns
+

Mean and predictive variance predicted by the GP.

+
+
Return type
+

(float, float)

+
+
+
+ +
+
+remove_force_data(indexes: Union[int, List[int]], update_matrices: bool = True) → Tuple[List[FLARE_Atoms], List[ndarray]]
+

Remove force components from the model. Convenience function which +deletes individual data points.

+

Matrices should always be updated if you intend to use the GP to make +predictions afterwards. This might be time consuming for large GPs, +so, it is provided as an option, but, only do so with extreme caution. +(Undefined behavior may result if you try to make predictions and/or +add to the training set afterwards).

+

Returns training data which was removed akin to a pop method, in order +of lowest to highest index passed in.

+
+
Parameters
+
    +

  • indexes – Indexes of envs in training data to remove.

    • +

  • update_matrices – If false, will not update the GP’s matrices +afterwards (which can be time consuming for large models). +This should essentially always be true except for niche development +applications.

    • +
+
+
Returns
+

+
+
+
+ +
+
+set_L_alpha()
+

Invert the covariance matrix, setting L (a lower triangular +matrix s.t. L L^T = (K + sig_n^2 I)) and alpha, the inverse +covariance matrix multiplied by the vector of training labels. +The forces and variances are later obtained using alpha.

+
+ +
+
+train(logger_name: Optional[str] = None, custom_bounds=None, grad_tol: float = 0.0001, x_tol: float = 1e-05, line_steps: int = 20, print_progress: bool = False)
+

Train Gaussian Process model on training data. Tunes the +hyperparameters to maximize the likelihood, then computes L and alpha +(related to the covariance matrix of the training set).

+
+
Parameters
+
    +

  • logger (logging.logger) – logger object specifying where to write the +progress of the optimization.

    • +

  • custom_bounds (np.ndarray) – Custom bounds on the hyperparameters.

    • +

  • grad_tol (float) – Tolerance of the hyperparameter gradient that +determines when hyperparameter optimization is terminated.

    • +

  • x_tol (float) – Tolerance on the x values used to decide when +Nelder-Mead hyperparameter optimization is terminated.

    • +

  • line_steps (int) – Maximum number of line steps for L-BFGS +hyperparameter optimization. +:param logger_name: +:param print_progress:

    • +
+
+
+
+ +
+
+property training_statistics: dict
+

Return a dictionary with statistics about the current training data. +Useful for quickly summarizing info about the GP. +:return:

+
+ +
+
+update_L_alpha()
+

Update the GP’s L matrix and alpha vector without recalculating +the entire covariance matrix K.

+
+ +
+
+update_db(struc: FLARE_Atoms, forces: ndarray = None, custom_range: List[int] = (), energy: float = None, stress: ndarray = None)
+

Given a structure and forces, add local environments from the +structure to the training set of the GP. If energy is given, add the +entire structure to the training set.

+
+
Parameters
+
    +

  • struc (FLARE_Atoms) – Input structure. Local environments of atoms +in this structure will be added to the training set of the GP.

    • +

  • forces (np.ndarray) – Forces on atoms in the structure.

    • +

  • custom_range (List[int]) – Indices of atoms whose local +environments will be added to the training set of the GP.

    • +

  • energy (float) – Energy of the structure.

    • +

  • stress (np.ndarray) – Stress tensor of the structure. The stress +tensor components should be given in the following order: +xx, xy, xz, yy, yz, zz.

    • +
+
+
+
+ +
+
+write_model(name: str, format: Optional[str] = None, split_matrix_size_cutoff: int = 5000)
+

Write model in a variety of formats to a file for later re-use. +JSON files are open to visual inspection and are easier to use +across different versions of FLARE or GP implementations. However, +they are larger and loading them in takes longer (by setting up a +new GP from the specifications). Pickled files can be faster to +read & write, and they take up less memory.

+
+
Parameters
+
    +

  • name (str) – Output name.

    • +

  • format (str) – Output format.

    • +

  • split_matrix_size_cutoff (int) – If there are more than this

    • +

  • number of training points in the set, save the matrices seperately.

    • +
+
+
+
+ +
+ diff --git a/flare/bffs/gp/gp_algebra.html b/flare/bffs/gp/gp_algebra.html index 9ce267692..91fa608c2 100644 --- a/flare/bffs/gp/gp_algebra.html +++ b/flare/bffs/gp/gp_algebra.html @@ -102,8 +102,319 @@
-
-

Helper functions for GP

+
+

Helper functions for GP

+
+
+flare.bffs.gp.gp_algebra.efs_energy_vector(name, efs_energy_kernel, x, hyps, cutoffs=None, hyps_mask=None, n_cpus=1, n_sample=100)
+

Returns covariances between the local eneregy, force components, and +partial stresses of a test environment and the total energy labels in the +training set.

+
+ +
+
+flare.bffs.gp.gp_algebra.efs_force_vector(name, efs_force_kernel, x, hyps, cutoffs=None, hyps_mask=None, n_cpus=1, n_sample=100)
+

Returns covariances between the local eneregy, force components, and +partial stresses of a test environment and the force labels in the +training set.

+
+ +
+
+flare.bffs.gp.gp_algebra.energy_energy_vector(name, kernel, x, hyps, cutoffs=None, hyps_mask=None, n_cpus=1, n_sample=100)
+

Get a vector of covariances between the local energy of a test environment +and the total energy labels in the training set.

+
+ +
+
+flare.bffs.gp.gp_algebra.energy_energy_vector_unit(name, s, e, x, kernel, hyps, cutoffs=None, hyps_mask=None, d_1=None)
+

Gets part of the energy/energy vector.

+
+ +
+
+flare.bffs.gp.gp_algebra.energy_force_vector(name, kernel, x, hyps, cutoffs=None, hyps_mask=None, n_cpus=1, n_sample=100)
+

Get the vector of covariances between the local energy of a test +environment and the force labels in the training set.

+
+ +
+
+flare.bffs.gp.gp_algebra.energy_force_vector_unit(name, s, e, x, kernel, hyps, cutoffs=None, hyps_mask=None, d_1=None)
+

Gets part of the energy/force vector.

+
+ +
+
+flare.bffs.gp.gp_algebra.force_energy_vector(name, kernel, x, d_1, hyps, cutoffs=None, hyps_mask=None, n_cpus=1, n_sample=100)
+

Get a vector of covariances between a force component of a test environment +and the total energy labels in the training set.

+
+ +
+
+flare.bffs.gp.gp_algebra.force_energy_vector_unit(name, s, e, x, kernel, hyps, cutoffs, hyps_mask, d_1)
+

Gets part of the force/energy vector.

+
+ +
+
+flare.bffs.gp.gp_algebra.force_force_vector(name, kernel, x, d_1, hyps, cutoffs=None, hyps_mask=None, n_cpus=1, n_sample=100)
+

Get a vector of covariances between a force component of a test environment +and the force labels in the training set.

+
+ +
+
+flare.bffs.gp.gp_algebra.force_force_vector_unit(name, s, e, x, kernel, hyps, cutoffs, hyps_mask, d_1)
+

Gets part of the force/force vector.

+
+ +
+
+flare.bffs.gp.gp_algebra.get_distance_mat_pack(hyps: numpy.ndarray, name: str, s1: int, e1: int, s2: int, e2: int, same: bool, kernel, cutoffs, hyps_mask)
+

Compute covariance matrix element between set1 and set2 +:param hyps: list of hyper-parameters +:param name: name of the gp instance. +:param same: whether the row and column are the same +:param kernel: function object of the kernel +:param cutoffs: The cutoff values used for the atomic environments +:type cutoffs: list of 2 float numbers +:param hyps_mask: dictionary used for multi-group hyperparmeters +:return: covariance matrix

+
+ +
+
+flare.bffs.gp.gp_algebra.get_force_block(hyps: numpy.ndarray, name: str, kernel, cutoffs=None, hyps_mask=None, n_cpus=1, n_sample=100)
+

parallel version of get_ky_mat +:param hyps: list of hyper-parameters +:param name: name of the gp instance. +:param kernel: function object of the kernel +:param cutoffs: The cutoff values used for the atomic environments +:type cutoffs: list of 2 float numbers +:param hyps_mask: dictionary used for multi-group hyperparmeters

+
+
Returns
+

covariance matrix

+
+
+
+ +
+
+flare.bffs.gp.gp_algebra.get_force_block_pack(hyps: numpy.ndarray, name: str, s1: int, e1: int, s2: int, e2: int, same: bool, kernel, cutoffs, hyps_mask)
+

Compute covariance matrix element between set1 and set2 +:param hyps: list of hyper-parameters +:param name: name of the gp instance. +:param same: whether the row and column are the same +:param kernel: function object of the kernel +:param cutoffs: The cutoff values used for the atomic environments +:type cutoffs: list of 2 float numbers +:param hyps_mask: dictionary used for multi-group hyperparmeters

+
+
Returns
+

covariance matrix

+
+
+
+ +
+
+flare.bffs.gp.gp_algebra.get_ky_and_hyp(hyps: numpy.ndarray, name, kernel_grad, cutoffs=None, hyps_mask=None, n_cpus=1, n_sample=100)
+

parallel version of get_ky_and_hyp

+
+
Parameters
+
    +

  • hyps – list of hyper-parameters

    • +

  • name – name of the gp instance.

    • +

  • kernel_grad – function object of the kernel gradient

    • +

  • cutoffs (list of 2 float numbers) – The cutoff values used for the atomic environments

    • +

  • hyps_mask – dictionary used for multi-group hyperparmeters

    • +

  • n_cpus – number of cpus to use.

    • +

  • n_sample – the size of block for matrix to compute

    • +
+
+
Returns
+

hyp_mat, ky_mat

+
+
+
+ +
+
+flare.bffs.gp.gp_algebra.get_ky_and_hyp_pack(name, s1, e1, s2, e2, same: bool, hyps: numpy.ndarray, kernel_grad, cutoffs=None, hyps_mask=None)
+

computes a block of ky matrix and its derivative to hyper-parameter +If the cpu set up is None, it uses as much as posible cpus

+
+
Parameters
+
    +

  • hyps – list of hyper-parameters

    • +

  • name – name of the gp instance.

    • +

  • kernel_grad – function object of the kernel gradient

    • +

  • cutoffs (list of 2 float numbers) – The cutoff values used for the atomic environments

    • +

  • hyps_mask – dictionary used for multi-group hyperparmeters

    • +
+
+
Returns
+

hyp_mat, ky_mat

+
+
+
+ +
+
+flare.bffs.gp.gp_algebra.get_like_from_mats(ky_mat, l_mat, alpha, name)
+

compute the likelihood from the covariance matrix

+
+
Parameters
+

ky_mat – the covariance matrix

+
+
Returns
+

float, likelihood

+
+
+
+ +
+
+flare.bffs.gp.gp_algebra.get_like_grad_from_mats(ky_mat, hyp_mat, name)
+

compute the gradient of likelihood to hyper-parameters +from covariance matrix and its gradient

+
+
Parameters
+
    +

  • ky_mat (np.array) – covariance matrix

    • +

  • hyp_mat (np.array) – dky/d(hyper parameter) matrix

    • +

  • name – name of the gp instance.

    • +
+
+
Returns
+

float, list. the likelihood and its gradients

+
+
+
+ +
+
+flare.bffs.gp.gp_algebra.get_neg_like(hyps: numpy.ndarray, name: str, force_kernel, logger_name=None, cutoffs=None, hyps_mask=None, n_cpus=1, n_sample=100)
+

compute the log likelihood and its gradients +:param hyps: list of hyper-parameters +:type hyps: np.ndarray +:param name: name of the gp instance. +:param kernel_grad: function object of the kernel gradient +:param output: Output object for dumping every hyper-parameter

+
+

sets computed

+
+
+
Parameters
+
    +

  • cutoffs (list of 2 float numbers) – The cutoff values used for the atomic environments

    • +

  • hyps_mask – dictionary used for multi-group hyperparmeters

    • +

  • n_cpus – number of cpus to use.

    • +

  • n_sample – the size of block for matrix to compute

    • +
+
+
Returns
+

float, np.array

+
+
+
+ +
+
+flare.bffs.gp.gp_algebra.get_neg_like_grad(hyps: numpy.ndarray, name: str, kernel_grad, logger_name: Optional[str] = None, cutoffs=None, hyps_mask=None, n_cpus=1, n_sample=100)
+

compute the log likelihood and its gradients

+
+
Parameters
+
    +

  • hyps (np.ndarray) – list of hyper-parameters

    • +

  • name – name of the gp instance.

    • +

  • kernel_grad – function object of the kernel gradient

    • +

  • logger_name (str) – name of logger object for dumping every hyper-parameter +sets computed

    • +

  • cutoffs (list of 2 float numbers) – The cutoff values used for the atomic environments

    • +

  • hyps_mask – dictionary used for multi-group hyperparmeters

    • +

  • n_cpus – number of cpus to use.

    • +

  • n_sample – the size of block for matrix to compute

    • +
+
+
Returns
+

float, np.array

+
+
+
+ +
+
+flare.bffs.gp.gp_algebra.kernel_distance_mat(hyps: numpy.ndarray, name: str, kernel, cutoffs=None, hyps_mask=None, n_cpus=1, n_sample=100)
+

parallel version of get_ky_mat +:param hyps: list of hyper-parameters +:param name: name of the gp instance. +:param kernel: function object of the kernel +:param cutoffs: The cutoff values used for the atomic environments +:type cutoffs: list of 2 float numbers +:param hyps_mask: dictionary used for multi-group hyperparmeters +:return: covariance matrix

+
+ +
+
+flare.bffs.gp.gp_algebra.obtain_noise_len(hyps, hyps_mask)
+

obtain the noise parameter from hyps and mask

+
+ +
+
+flare.bffs.gp.gp_algebra.partition_force_energy_block(n_sample: int, size1: int, size2: int, n_cpus: int)
+

Special partition method for the force/energy block. Because the number +of environments in a structure can vary, we only split up the environment +list, which has length size1.

+

Note that two sizes need to be specified: the size of the envionment +list and the size of the structure list.

+
+
Parameters
+
    +

  • n_sample (int) – Number of environments per processor.

    • +

  • size1 (int) – Size of the environment list.

    • +

  • size2 (int) – Size of the structure list.

    • +

  • n_cpus (int) – Number of cpus.

    • +
+
+
+
+ +
+
+flare.bffs.gp.gp_algebra.partition_matrix(n_sample, size, n_cpus)
+

partition the training data for matrix calculation +the number of blocks are close to n_cpus +since mp.Process does not allow to change the thread number

+
+ +
+
+flare.bffs.gp.gp_algebra.partition_matrix_custom(n_sample: int, start1, end1, start2, end2, n_cpus)
+

Partition a specified portion of a matrix.

+
+ +
+
+flare.bffs.gp.gp_algebra.partition_vector(n_sample, size, n_cpus)
+

partition the training data for vector calculation +the number of blocks are the same as n_cpus +since mp.Process does not allow to change the thread number

+
+ +
+
+flare.bffs.gp.gp_algebra.queue_wrapper(result_queue, wid, func, args)
+

wrapper function for multiprocessing queue

+
+
diff --git a/flare/bffs/gp/predict.html b/flare/bffs/gp/predict.html index f69283467..cf450521d 100644 --- a/flare/bffs/gp/predict.html +++ b/flare/bffs/gp/predict.html @@ -102,8 +102,180 @@
-
-

Predict

+
+

Predict

+

Helper functions which obtain forces and energies +corresponding to atoms in structures. These functions automatically +cast atoms into their respective atomic environments.

+
+
+flare.bffs.gp.predict.predict_on_atom(param: Tuple[FLARE_Atoms, int, GaussianProcess])
+

Return the forces/std. dev. uncertainty associated with an individual atom +in a structure, without necessarily having cast it to a chemical +environment. In order to work with other functions, +all arguments are passed in as a tuple.

+
+
Parameters
+

param (Tuple(FLARE_Atoms, integer, GaussianProcess)) – tuple of FLARE FLARE_Atoms, atom index, and Gaussian Process +object

+
+
Returns
+

3-element force array and associated uncertainties

+
+
Return type
+

(np.ndarray, np.ndarray)

+
+
+
+ +
+
+flare.bffs.gp.predict.predict_on_atom_efs(param)
+

Predict the local energy, forces, and partial stresses and predictive +variances of a chemical environment.

+
+ +
+
+flare.bffs.gp.predict.predict_on_atom_en(param: ~typing.Tuple[~flare.atoms.FLARE_Atoms, int, ~flare.bffs.gp.gp.GaussianProcess]) -> ('np.ndarray', 'np.ndarray', <class 'float'>)
+

Return the forces/std. dev. uncertainty / energy associated with an +individual atom in a structure, without necessarily having cast it to a +chemical environment. In order to work with other functions, +all arguments are passed in as a tuple.

+
+
Parameters
+

param (Tuple(FLARE_Atoms, integer, GaussianProcess)) – tuple of FLARE FLARE_Atoms, atom index, and Gaussian Process +object

+
+
Returns
+

3-element force array, associated uncertainties, and local energy

+
+
Return type
+

(np.ndarray, np.ndarray, float)

+
+
+
+ +
+
+flare.bffs.gp.predict.predict_on_atom_en_std(param)
+

Predict local energy and predictive std of a chemical environment.

+
+ +
+
+flare.bffs.gp.predict.predict_on_structure(structure: FLARE_Atoms, gp: GaussianProcess, n_cpus: Optional[int] = None, write_to_structure: bool = True, selective_atoms: Optional[List[int]] = None, skipped_atom_value=0)
+

Return the forces/std. dev. uncertainty associated with each +individual atom in a structure. Forces are stored directly to the +structure and are also returned.

+
+
Parameters
+
    +

  • structure – FLARE structure to obtain forces for, with N atoms

    • +

  • gp – Gaussian Process model

    • +

  • write_to_structure – Write results to structure’s forces, +std attributes

    • +

  • selective_atoms – Only predict on these atoms; e.g. [0,1,2] will +only predict and return for those atoms

    • +

  • skipped_atom_value – What value to use for atoms that are skipped. +Defaults to 0 but other options could be e.g. NaN. Will NOT +write this to the structure if write_to_structure is True.

    • +
+
+
Returns
+

N x 3 numpy array of foces, Nx3 numpy array of uncertainties

+
+
Return type
+

(np.ndarray, np.ndarray)

+
+
+
+ +
+
+flare.bffs.gp.predict.predict_on_structure_en(structure: FLARE_Atoms, gp: GaussianProcess, n_cpus: Optional[int] = None, write_to_structure: bool = True, selective_atoms: Optional[List[int]] = None, skipped_atom_value=0)
+

Return the forces/std. dev. uncertainty / local energy associated with each +individual atom in a structure. Forces are stored directly to the +structure and are also returned.

+
+
Parameters
+
    +

  • structure – FLARE structure to obtain forces for, with N atoms

    • +

  • gp – Gaussian Process model

    • +

  • n_cpus – Dummy parameter passed as an argument to allow for +flexibility when the callable may or may not be parallelized

    • +
+
+
Returns
+

N x 3 array of forces, N x 3 array of uncertainties, +N-length array of energies

+
+
Return type
+

(np.ndarray, np.ndarray, np.ndarray)

+
+
+
+ +
+
+flare.bffs.gp.predict.predict_on_structure_mgp(structure: FLARE_Atoms, mgp: MappedGaussianProcess, output=None, output_name=None, n_cpus: Optional[int] = None, write_to_structure: bool = True, selective_atoms: Optional[List[int]] = None, skipped_atom_value: Union[float, int] = 0, energy: bool = False) → Union[Tuple[numpy.ndarray, numpy.ndarray, float], Tuple[numpy.ndarray, numpy.ndarray]]
+

Assign forces to structure based on an mgp

+
+ +
+
+flare.bffs.gp.predict.predict_on_structure_par(structure: FLARE_Atoms, gp: GaussianProcess, n_cpus: Optional[int] = None, write_to_structure: bool = True, selective_atoms: Optional[List[int]] = None, skipped_atom_value=0)
+

Return the forces/std. dev. uncertainty associated with each +individual atom in a structure. Forces are stored directly to the +structure and are also returned.

+
+
Parameters
+
    +

  • structure – FLARE structure to obtain forces for, with N atoms

    • +

  • gp – Gaussian Process model

    • +

  • n_cpus – Number of cores to parallelize over

    • +

  • write_to_structure – Write results to structure’s forces, +std attributes

    • +

  • selective_atoms – Only predict on these atoms; e.g. [0,1,2] will +only predict and return for those atoms

    • +

  • skipped_atom_value – What value to use for atoms that are skipped. +Defaults to 0 but other options could be e.g. NaN. Will NOT +write this to the structure if write_to_structure is True.

    • +
+
+
Returns
+

N x 3 array of forces, N x 3 array of uncertainties

+
+
Return type
+

(np.ndarray, np.ndarray)

+
+
+
+ +
+
+flare.bffs.gp.predict.predict_on_structure_par_en(structure: FLARE_Atoms, gp: GaussianProcess, n_cpus: Optional[int] = None, write_to_structure: bool = True, selective_atoms: Optional[List[int]] = None, skipped_atom_value=0)
+

Return the forces/std. dev. uncertainty / local energy associated with each +individual atom in a structure, parallelized over atoms. Forces are +stored directly to the structure and are also returned.

+
+
Parameters
+
    +

  • structure – FLARE structure to obtain forces for, with N atoms

    • +

  • gp – Gaussian Process model

    • +

  • n_cpus – Number of cores to parallelize over

    • +
+
+
Returns
+

N x 3 array of forces, N x 3 array of uncertainties, +N-length array of energies

+
+
Return type
+

(np.ndarray, np.ndarray, np.ndarray)

+
+
+
+
diff --git a/flare/bffs/mgp/mgp.html b/flare/bffs/mgp/mgp.html index a0e66006a..bb6f6901a 100644 --- a/flare/bffs/mgp/mgp.html +++ b/flare/bffs/mgp/mgp.html @@ -113,6 +113,135 @@

Mapped Gaussian Process

+

MappedGaussianProcess uses splines to build up interpolationfunction of the low-dimensional decomposition of Gaussian Process, with little loss of accuracy. Refer to Xie et al., Vandermause et al., Glielmo et al.

+
+
+class flare.bffs.mgp.mgp.MappedGaussianProcess(grid_params: dict, unique_species: list = [], GP: Optional[GaussianProcess] = None, var_map: Optional[str] = None, container_only: bool = True, lmp_file_name: str = 'lmp', n_cpus: Optional[int] = None, n_sample: int = 10)
+

Build Mapped Gaussian Process (MGP) +and automatically save coefficients for LAMMPS pair style.

+
+
Parameters
+
    +

  • grid_params (dict) – Parameters for the mapping itself, such as +grid size of spline fit, etc. As described below.

    • +

  • unique_species (dict) – List of all the (unique) species included during +the training that need to be mapped

    • +

  • GP (GaussianProcess) – None or a GaussianProcess object. If a GP is input, +and container_only is False, automatically build a mapping corresponding +to the GaussianProcess.

    • +

  • var_map (str) – if None: only build mapping for mean (force). If ‘pca’, then +use PCA to map the variance, based on grid_params[‘xxbody’][‘svd_rank’]. +If ‘simple’, then only map the diagonal of covariance, and predict the +upper bound of variance. The ‘pca’ mode is much heavier in terms of +memory, but its prediction is much closer to GP variance.

    • +

  • container_only (bool) – if True: only build splines container +(with no coefficients); if False: Attempt to build map immediately

    • +

  • lmp_file_name (str) – LAMMPS coefficient file name

    • +

  • n_cpus (int) – Default None. Set to the number of cores needed for +parallelization. Used in the construction of the map.

    • +

  • n_sample (int) – Default 10. The batch size for building map. Not used now.

    • +
+
+
+

Examples:

+
>>> # build 2 + 3 body map
+>>> grid_params = {'twobody': {'grid_num': [64]},
+...                'threebody': {'grid_num': [64, 64, 64]}}
+
+
+

For grid_params, the following keys and values are allowed

+
+
Parameters
+
    +

  • ‘twobody’ (dict, optional) – if 2-body is present, set as a dictionary +of parameters for 2-body mapping. Parameters see below.

    • +

  • ‘threebody’ (dict, optional) – if 3-body is present, set as a dictionary +of parameters for 3-body mapping. Parameters see below.

    • +

  • ‘load_grid’ (str, optional) – Default None. the path to the directory +where the previously generated grids (grid_*.npy) are stored. +If no path is specified, MGP will construct grids from scratch.

    • +

  • ‘lower_bound_relax’ (float, optional) – Default 0.1. if ‘lower_bound’ is +set to ‘auto’ this value will be used as a relaxation of lower +bound. (see below the description of ‘lower_bound’)

    • +
+
+
+

For two/three body parameter dictionary, the following keys and values are allowed

+
+
Parameters
+
    +

  • ‘grid_num’ (list) – a list of integers, the number of grid points for +interpolation. The larger the number, the better the approximation +of MGP is compared with GP.

    • +

  • ‘lower_bound’ (str or list, optional) – Default ‘auto’, the lower bound +of the spline interpolation will be searched. First, search the +training set of GP and find the minimal interatomic distance r_min. +Then, the lower_bound = r_min - lower_bound_relax. The user +can set their own lower_bound, of the same shape as ‘grid_num’. +E.g. for threebody, the customized lower bound can be set as +[1.2, 1.2, 1.2].

    • +

  • ‘upper_bound’ (str or list, optional) – Default ‘auto’, the upper bound +of the spline interpolation will be the cutoffs of GP. The user +can set their own upper_bound, of the same shape as ‘grid_num’. +E.g. for threebody, the customized lower bound can be set as +[3.5, 3.5, 3.5].

    • +

  • ‘svd_rank’ (int, optional) – Default ‘auto’. If the variance mapping is +needed, it is set as the rank of the mapping. ‘auto’ uses full +rank, which is the smaller one between the total number of grid +points and training set size. i.e. +full_rank = min(np.prod(grid_num), 3 * N_train)

    • +
+
+
+
+
+as_dict() → dict
+

Dictionary representation of the MGP model.

+
+ +
+
+static from_dict(dictionary: dict) → MappedGaussianProcess
+

Create MGP object from dictionary representation.

+
+ +
+
+predict(atom_env: ~flare.descriptors.env.AtomicEnvironment) -> ('ndarray', 'ndarray', 'ndarray', <class 'float'>)
+

predict force, variance, stress and local energy for given +atomic environment

+
+
Parameters
+

atom_env – atomic environment (with a center atom and its neighbors)

+
+
Returns
+

3d array of atomic force +variance: 3d array of the predictive variance +stress: 6d array of the virial stress +energy: the local energy (atomic energy)

+
+
Return type
+

force

+
+
+
+ +
+
+write_lmp_file(lammps_name: str, write_var: bool = False)
+

write the coefficients to a file that can be used by lammps pair style

+
+ +
+
+write_model(name: str, format: str = 'json')
+

Write everything necessary to re-load and re-use the model +:param model_name: +:return:

+
+ +
+
diff --git a/flare/bffs/mgp/splines_methods.html b/flare/bffs/mgp/splines_methods.html index 1a14a8ebc..c0bb6011c 100644 --- a/flare/bffs/mgp/splines_methods.html +++ b/flare/bffs/mgp/splines_methods.html @@ -101,8 +101,94 @@
-
-

Splines Methods

+
+

Splines Methods

+

Cubic spline functions used for interpolation.

+
+
+class flare.bffs.mgp.splines_methods.CubicSpline(a, b, orders, values=None)
+

Forked from Github repository: https://github.com/EconForge/interpolation.py. High-level API for cubic splines. Class representing a cubic spline interpolator on a regular cartesian grid.

+

Creates a cubic spline interpolator on a regular cartesian grid.

+
+
Parameters
+
    +

  • a (numpy array of size d (float)) – Lower bounds of the cartesian grid.

    • +

  • b (numpy array of size d (float)) – Upper bounds of the cartesian grid.

    • +

  • orders (numpy array of size d (int)) – Number of nodes along each dimension (=(n1,…,nd) )

    • +
+
+
Other Parameters
+

values (numpy array (float)) – (optional, (n1 x … x nd) array). Values on the nodes of the function to interpolate.

+
+
+
+
+property grid
+

Cartesian enumeration of all nodes.

+
+ +
+
+interpolate(points, values=None, with_derivatives=False)
+

Interpolate spline at a list of points.

+
+
Parameters
+
    +

  • points – (array-like) list of point where the spline is evaluated.

    • +

  • values – (optional) container for inplace computation.

    • +
+
+
Return values
+

(array-like) list of point where the spline is evaluated.

+
+
+
+ +
+
+set_values(values)
+

Set values on the nodes for the function to interpolate.

+
+ +
+ +
+
+class flare.bffs.mgp.splines_methods.PCASplines(l_bounds, u_bounds, orders, svd_rank)
+

Build splines for PCA decomposition, mainly used for the mapping of the variance

+
+
Parameters
+
    +

  • l_bounds (numpy array) – lower bound for the interpolation. E.g. 1-d for two-body, 3-d for three-body.

    • +

  • u_bounds (numpy array) – upper bound for the interpolation.

    • +

  • orders (numpy array) – grid numbers in each dimension. E.g, 1-d for two-body, 3-d for three-body, should be positive integers.

    • +

  • svd_rank (int) – rank for decomposition of variance matrix, also equal to the number of mappings constructed for mapping variance. For two-body svd_rank<=min(grid_num, train_size*3), for three-body svd_rank<=min(grid_num_in_cube, train_size*3)

    • +
+
+
+
+ +
+
+flare.bffs.mgp.splines_methods.vec_eval_cubic_spline(a, b, orders, coefs, points, values=None)
+

Forked from Github repository: https://github.com/EconForge/interpolation.py. Evaluates a cubic spline at many points

+
+
Parameters
+
    +

  • a (numpy array of size d (float)) – Lower bounds of the cartesian grid.

    • +

  • b (numpy array of size d (float)) – Upper bounds of the cartesian grid.

    • +

  • orders (numpy array of size d (int)) – Number of nodes along each dimension (=(n1,…,nd) )

    • +

  • coefs (array of dimension d, and size (n1+2, ..., nd+2)) – Filtered coefficients.

    • +

  • point (array of size N x d) – List of points where the splines must be interpolated.

    • +

  • values (array of size N) – (optional) If not None, contains the result.

    • +
+
+
Return value
+

Interpolated values. values[i] contains spline evaluated at point points[i,:].

+
+
+
+
diff --git a/flare/bffs/sgp/calculator.html b/flare/bffs/sgp/calculator.html index 0668860c6..546342552 100644 --- a/flare/bffs/sgp/calculator.html +++ b/flare/bffs/sgp/calculator.html @@ -100,8 +100,28 @@
-
-

ASE Calculator of Sparse GP

+
+

ASE Calculator of Sparse GP

+
+
+class flare.bffs.sgp.calculator.SGP_Calculator(sgp_model, use_mapping=False)
+
+
+calculate(atoms=None, properties=None, system_changes=['positions', 'numbers', 'cell', 'pbc', 'initial_charges', 'initial_magmoms'])
+
+
Calculate properties including: energy, local energies, forces,

stress, uncertainties.

+
+
+
+ +
+
+implemented_properties: List[str] = ['energy', 'forces', 'stress', 'stds']
+

Properties calculator can handle (energy, forces, …)

+
+ +
+
diff --git a/flare/bffs/sgp/sgp.html b/flare/bffs/sgp/sgp.html index ff3a6b21e..6dc0f4913 100644 --- a/flare/bffs/sgp/sgp.html +++ b/flare/bffs/sgp/sgp.html @@ -106,6 +106,52 @@

Sparse Gaussian Process Force FieldsASE Calculator of Sparse GP

+
+
+class flare.bffs.sgp.sparse_gp.SGP_Wrapper(kernels: List, descriptor_calculators: List, cutoff: float, sigma_e: float, sigma_f: float, sigma_s: float, species_map: dict, variance_type: str = 'SOR', single_atom_energies: Optional[dict] = None, energy_training=True, force_training=True, stress_training=True, max_iterations=10, opt_method='BFGS', bounds=None)
+

Wrapper class used to make the C++ sparse GP object compatible with +OTF. Methods and properties are designed to mirror the GP class.

+
+
+static from_dict(in_dict)
+

Need an initialized GP

+
+ +
+
+write_model(name: str)
+

Write to .json file

+
+ +
+ +
+
+flare.bffs.sgp.sparse_gp.compute_negative_likelihood(hyperparameters, sparse_gp, print_vals=False)
+

Compute the negative log likelihood and gradient with respect to the +hyperparameters.

+
+ +
+
+flare.bffs.sgp.sparse_gp.compute_negative_likelihood_grad(hyperparameters, sparse_gp, print_vals=False)
+

Compute the negative log likelihood and gradient with respect to the +hyperparameters.

+
+ +
+
+flare.bffs.sgp.sparse_gp.compute_negative_likelihood_grad_stable(hyperparameters, sparse_gp, precomputed=False)
+

Compute the negative log likelihood and gradient with respect to the +hyperparameters.

+
+ +
+
+flare.bffs.sgp.sparse_gp.optimize_hyperparameters(sparse_gp, display_results=False, gradient_tolerance=0.0001, max_iterations=10, bounds=None, method='BFGS')
+

Optimize the hyperparameters of a sparse GP model.

+
+
diff --git a/flare/descriptors/env.html b/flare/descriptors/env.html index 0d1997b33..6c5d3b22b 100644 --- a/flare/descriptors/env.html +++ b/flare/descriptors/env.html @@ -94,8 +94,148 @@
-
-

Atomic Environments

+
+

Atomic Environments

+

The AtomicEnvironment object stores information about the local +environment of an atom. AtomicEnvironment objects are inputs to the +2-, 3-, and 2+3-body kernels.

+
+
+class flare.descriptors.env.AtomicEnvironment(structure: FLARE_Atoms, atom: int, cutoffs, cutoffs_mask=None)
+

Contains information about the local environment of an atom, +including arrays of pair and triplet distances and the chemical +species of atoms in the environment.

+
+
Parameters
+
    +

  • structure (FLARE_Atoms) – structure of atoms.

    • +

  • atom (int) – Index of the atom in the structure.

    • +

  • cutoffs (np.ndarray) – 2- and 3-body cutoff radii. 2-body if one cutoff is +given, 2+3-body if two are passed.

    • +

  • cutoffs_mask (dict) – a dictionary to store multiple cutoffs if neede +it should be exactly the same as the hyps mask

    • +
+
+
+

The cutoffs_mask allows the user to define multiple cutoffs for different +bonds, triples, and many body interaction. This dictionary should be +consistent with the hyps_mask used in the GuassianProcess object.

+
    +
  • +
    species_mask: 118-long integer array descirbing which elements belong to

    like groups for determining which bond hyperparameters to use. +For instance, [0,0,1,1,0 …] assigns H to group 0, He and +Li to group 1, and Be to group 0 (the 0th register is ignored).

    +
    +
    +
    • +
  • +
    nspecie: Integer, number of different species groups (equal to number of

    unique values in species_mask).

    +
    +
    +
    • +
  • +
    ntwobody: Integer, number of different hyperparameter/cutoff sets to

    associate with different 2-body pairings of atoms in groups defined in +species_mask.

    +
    +
    +
    • +
  • +
    twobody_mask: Array of length nspecie^2, which describes the cutoff to

    associate with different pairings of species types. For example, if +there are atoms of type 0 and 1, then twobody_mask defines which cutoff +to use for parings [0-0, 0-1, 1-0, 1-1]: if we wanted cutoff0 for +0-0 parings and set 1 for 0-1 and 1-1 pairings, then we would make +twobody_mask [0, 1, 1, 1].

    +
    +
    +
    • +
  • +
    twobody_cutoff_list: Array of length ntwobody, which stores the cutoff

    used for different types of bonds defined in twobody_mask

    +
    +
    +
    • +
  • +
    ncut3b: Integer, number of different cutoffs sets to associate

    with different 3-body pariings of atoms in groups defined in +species_mask.

    +
    +
    +
    • +
  • +
    cut3b_mask: Array of length nspecie^2, which describes the cutoff to

    associate with different bond types in triplets. For example, in a +triplet (C, O, H) , there are three cutoffs. Cutoffs for CH bond, CO +bond and OH bond. If C and O are associate with atom group 1 in +species_mask and H are associate with group 0 in species_mask, the +cut3b_mask[1*nspecie+0] determines the C/O-H bond cutoff, and +cut3b_mask[1*nspecie+1] determines the C-O bond cutoff. If we want the +former one to use the 1st cutoff in threebody_cutoff_list and the later +to use the 2nd cutoff in threebody_cutoff_list, the cut3b_mask should +be [0, 0, 0, 1].

    +
    +
    +
    • +
  • +
    threebody_cutoff_list: Array of length ncut3b, which stores the cutoff

    used for different types of bonds in triplets.

    +
    +
    +
    • +
  • +
    nmanybody: Integer, number of different cutoffs set to associate with

    different coordination numbers.

    +
    +
    +
    • +

  • manybody_mask: Similar to twobody_mask and cut3b_mask.

    • +
  • +
    manybody_cutoff_list: Array of length nmanybody, stores the cutoff used

    for different many body terms

    +
    +
    +
    • +
+

Examples can be found at the end of in tests/test_env.py

+
+
+as_dict(include_structure: bool = False)
+

Returns Atomic Environment object as a dictionary for serialization +purposes. Optional to not include the structure to avoid redundant +information. +:return:

+
+ +
+
+as_str() → str
+

Returns string dictionary serialization cast as string.

+
+
Returns
+

output of as_dict method cast as string

+
+
Return type
+

str

+
+
+
+ +
+
+static from_dict(dictionary)
+

Loads in atomic environment object from a dictionary which was +serialized by the to_dict method.

+
+
Parameters
+

dictionary – Dictionary describing atomic environment.

+
+
+
+ +
+
+static from_file(file_name: str, format: str = '') → Union[flare.env.AtomicEnvironment, List[flare.env.AtomicEnvironment]]
+

Load an atomic environment from a file or a series of atomic environments +:param file_name: +:param format: +:return:

+
+ +
+
diff --git a/flare/flare.html b/flare/flare.html index 8edb9812e..3fbe898b0 100644 --- a/flare/flare.html +++ b/flare/flare.html @@ -114,7 +114,10 @@

Python Code DocumentationBayesian Active Learning diff --git a/flare/io/otf_parser.html b/flare/io/otf_parser.html index c72480078..cfc7f529a 100644 --- a/flare/io/otf_parser.html +++ b/flare/io/otf_parser.html @@ -95,8 +95,130 @@
-
-

OTF Parser

+
+

OTF Parser

+
+
+class flare.io.otf_parser.OtfAnalysis(filename, calculate_energy=False)
+

Parse the OTF log file to get trajectory, training data, +thermostat, and build GP model.

+
+
Parameters
+
    +

  • filename (str) – name of the OTF log file.

    • +

  • calculate_energy (bool) – if the potential energy is computed and +needs to be parsed, then set to True. Default False.

    • +
+
+
+
+
+make_gp(cell=None, call_no=None, hyps=None, init_gp=None, hyp_no=None, **kwargs)
+

Build GP model from the training frames parsed from the log file. +The cell, hyps and gp can be reset with customized values.

+
+
Parameters
+
    +

  • cell (np.ndarray) – Default None to use the cell from the log file. +A customized cell can be input as a 3x3 numpy array.

    • +

  • call_no (int) – Default None to use all the DFT frames as training +data for building GP. If not None, then the frames 0 to call_no +will be added to GP.

    • +

  • hyps (np.ndarray) – Default None to use the hyperparameters from the +log file. Customized hyps can be input as an array.

    • +

  • init_gp (GaussianProcess) – Default to None to use no initial settings +or training data. an initial GP can be used, and then the +frames parsed in the log file will add to the initial GP. Then the +final GP uses the hyps and kernels of init_gp, and consists of +training data from init_gp and the data from the log file. +NOTE: if a log file from restarted OTF is parsed, then an initial +GP needs to be parsed from the prior log file as the init_gp of the +restarted log file.

    • +

  • hyp_no (int) – Default None to use the final optimized hyperparameters to +build GP. If not None, then use the hyps from the `hyp_no`th +optimization step.

    • +

  • kwargs – if a new GP setting is needed without inputing init_gp, the GP +initial args can be input as kwargs.

    • +
+
+
+
+ +
+
+output_md_structures()
+

Returns structure objects corresponding to the MD frames of an OTF run. +:return:

+
+ +
+
+parse_pos_otf(blocks)
+

Exclusively parses MD run information +:param filename: +:return:

+
+ +
+
+to_xyz(xyz_file)
+

Convert OTF trajectory from log file to .xyz file. +:Parameters: xyz_file (str) – the file name of the .xyz file to output

+
+
Returns
+

A list of ASE Atoms objects.

+
+
+
+ +
+ +
+
+flare.io.otf_parser.append_atom_lists(species_list: List[str], position_list: List[ndarray], force_list: List[ndarray], uncertainty_list: List[ndarray], velocity_list: List[ndarray], lines: List[str], index: int, noa: int, dft_call: bool, noh: int) → None
+

Update lists containing atom information at each snapshot.

+
+ +
+
+flare.io.otf_parser.extract_gp_info(block, mae_list, maf_list, atoms_list, hyps_list, noh)
+

Exclusively parses DFT run information +:param filename: +:return:

+
+ +
+
+flare.io.otf_parser.parse_frame_line(frame_line)
+

parse a line in otf output. +:param frame_line: frame line to be parsed +:type frame_line: string +:return: species, position, force, uncertainty, and velocity of atom +:rtype: list, np.arrays

+
+ +
+
+flare.io.otf_parser.parse_header_information(lines) → dict
+

Get information about the run from the header of the file +:param outfile: +:return:

+
+ +
+
+flare.io.otf_parser.parse_snapshot(lines, index, noa, dft_call, noh)
+

Parses snapshot of otf output file.

+
+ +
+
+flare.io.otf_parser.strip_and_split(line)
+

Helper function which saves a few lines of code elsewhere +:param line: +:return:

+
+
diff --git a/flare/io/output.html b/flare/io/output.html index b2a8b9a6c..2e945c0c1 100644 --- a/flare/io/output.html +++ b/flare/io/output.html @@ -95,8 +95,224 @@
-
-

Output

+
+

Output

+

Class which contains various methods to print the output of different +ways of using FLARE, such as training a GP from an AIMD run, +or running an MD simulation updated on-the-fly.

+
+
+class flare.io.output.Output(basename: str = 'otf_run', verbose: str = 'INFO', print_as_xyz: bool = False, always_flush: bool = False)
+

This is an I/O class that hosts the log files for OTF and Trajectories +class. It is also used in get_neg_like_grad and get_neg_likelihood in +gp_algebra to print intermediate results.

+

It opens and print files with the basename prefix and different +suffixes corresponding to different kinds of output data.

+
+
Parameters
+
    +

  • basename (str, optional) – Base output file name, suffixes will be added

    • +

  • verbose (str, optional) – print level. The same as logging level. It can be +CRITICAL, ERROR, WARNING, INFO, DEBUG, NOTSET

    • +

  • always_flush – Always write to file instantly

    • +
+
+
+
+
+conclude_run(extra_strings: Optional[List[str]] = None)
+

destruction function that closes all files

+
+ +
+
+open_new_log(filetype: str, suffix: str, verbose='info')
+

Open files. If files with the same +name are exist, they are backed up with a suffix “-bak”.

+
+
Parameters
+
    +

  • filetype – the key name for logging

    • +

  • suffix – the suffix of the file to be opened

    • +

  • verbose – the verbose level for the logger

    • +
+
+
+
+ +
+
+write_gp_dft_comparison(curr_step, frame, start_time, dft_forces, dft_energy, error, local_energies=None, KE=None, mgp=False, cell=None, stress=None)
+

Write the comparison to logfile.

+
+
Parameters
+
    +

  • curr_step – current timestep

    • +

  • frame – FLARE_Atoms object that contains the current GP calculation +results.

    • +

  • start_time – start time for time profiling

    • +

  • dft_forces – list of forces computed by DFT

    • +

  • dft_energy – total energy computed by DFT

    • +

  • error – list of force differences between DFT and GP prediction

    • +

  • local_energies – local atomic energy

    • +

  • KE – total kinetic energy

    • +

  • cell – print the unit cell of the structure

    • +

  • stress – print the stress acting on the cell

    • +
+
+
Returns
+

+
+
+
+ +
+
+write_header(gp_str: str, dt: Optional[float] = None, Nsteps: Optional[int] = None, structure=None, std_tolerance: Optional[Union[float, int]] = None, optional: Optional[dict] = None)
+

TO DO: this should be replace by the string method of GP and OTF, GPFA

+

Write header to the log function. Designed for Trajectory Trainer and +OTF runs and can take flexible input for both.

+
+
Parameters
+
    +

  • gp_str – string representation of the GP

    • +

  • dt – timestep for OTF MD

    • +

  • Nsteps – total number of steps for OTF MD

    • +

  • structure – initial structure

    • +

  • std_tolerance – tolarence for active learning

    • +

  • optional – a dictionary of all the other parameters

    • +
+
+
+
+ +
+
+write_hyps(hyp_labels, hyps, start_time, like, like_grad, name='log', hyps_mask=None)
+

write hyperparameters to logfile

+
+
Parameters
+
    +

  • name –

    • +

  • hyp_labels – labels for hyper-parameters. can be None

    • +

  • hyps – list of hyper-parameters

    • +

  • start_time – start time for time profiling

    • +

  • like – likelihood

    • +

  • like_grad – gradient of likelihood

    • +
+
+
Returns
+

+
+
+
+ +
+
+write_md_config(dt, curr_step, structure, temperature, KE, start_time, dft_step, velocities)
+

write md configuration in log file

+
+
Parameters
+
    +

  • dt – timestemp of OTF MD

    • +

  • curr_step – current timestep of OTF MD

    • +

  • structure – atomic structure

    • +

  • temperature – current temperature

    • +

  • KE – current total kinetic energy

    • +

  • local_energies – local energy

    • +

  • start_time – starting time for time profiling

    • +

  • dft_step – # of DFT calls

    • +

  • velocities – list of velocities

    • +
+
+
Returns
+

+
+
+
+ +
+
+write_to_log(logstring: str, name: str = 'log', flush: bool = False)
+

Write any string to logfile

+
+
Parameters
+
    +

  • logstring – the string to write

    • +

  • name – the key name of the file to logger named ‘log’

    • +

  • flush – whether it should be flushed

    • +
+
+
+
+ +
+
+write_xyz_config(curr_step, structure, forces: Optional[numpy.array] = None, stds: Optional[numpy.array] = None, dft_forces: Optional[numpy.array] = None, dft_energy=0, predict_energy=nan, target_atoms=None)
+

write atomic configuration in xyz file

+
+
Parameters
+
    +

  • curr_step – Int, number of frames to note in the comment line

    • +

  • structure – FLARE_Atoms, contain positions and forces

    • +

  • forces – Optional list of forces to xyz file

    • +

  • stds – Optional list of uncertanties to xyz file

    • +

  • dft_forces – Optional second list of forces (e.g. DFT forces)

    • +
+
+
Returns
+

+
+
+
+ +
+ +
+
+flare.io.output.add_file(logger: Logger, filename: str, verbose: str = 'info')
+

set up file handler to the logger with handlers

+
+
Parameters
+
    +

  • logger – the logger

    • +

  • filename (str) – name of the logfile

    • +

  • verbose (str) – verbose level

    • +
+
+
+
+ +
+
+flare.io.output.add_stream(logger: Logger, verbose: str = 'info')
+

set up screen sctream handler to the logger with handlers

+
+
Parameters
+
    +

  • logger – the logger

    • +

  • verbose (str) – verbose level

    • +
+
+
+
+ +
+
+flare.io.output.set_logger(name: str, stream: bool, fileout_name: Optional[str] = None, verbose: str = 'info')
+

set up a logger with handlers

+
+
Parameters
+
    +

  • name (str) – unique name of the logger in logging module

    • +

  • stream (bool) – if True, set up a screen output

    • +

  • fileout_name (str) – name for log file

    • +

  • verbose (str) – verbose level

    • +
+
+
+
+
diff --git a/flare/kernels/cutoffs.html b/flare/kernels/cutoffs.html index 035f410c2..fcfb2b84a 100644 --- a/flare/kernels/cutoffs.html +++ b/flare/kernels/cutoffs.html @@ -98,8 +98,119 @@
-
-

Cutoff Functions

+
+

Cutoff Functions

+

The cutoffs module gives a few different options for smoothly sending the GP +kernel to zero near the boundary of the cutoff sphere.

+
+
+flare.kernels.cutoffs.cosine_cutoff(r_cut: float, ri: float, ci: float, d: float = 1)
+

A cosine cutoff that returns 1 up to r_cut - d, and assigns a cosine +envelope to values of r between r_cut - d and r_cut. Based on Eq. 24 of +Albert P. Bartók and Gábor Csányi. “Gaussian approximation potentials: A +brief tutorial introduction.” International Journal of Quantum Chemistry +115.16 (2015): 1051-1057.

+
+
Parameters
+
    +

  • r_cut (float) – Cutoff value (in angstrom).

    • +

  • ri (float) – Interatomic distance.

    • +

  • ci (float) – Cartesian coordinate divided by the distance.

    • +
+
+
Returns
+

Cutoff value and its derivative.

+
+
Return type
+

(float, float)

+
+
+
+ +
+
+flare.kernels.cutoffs.cubic_cutoff(r_cut: float, ri: float, ci: float)
+

A cubic cutoff that goes to zero smoothly at the cutoff boundary.

+
+
Parameters
+
    +

  • r_cut (float) – Cutoff value (in angstrom).

    • +

  • ri (float) – Interatomic distance.

    • +

  • ci (float) – Cartesian coordinate divided by the distance.

    • +
+
+
Returns
+

Cutoff value and its derivative.

+
+
Return type
+

(float, float)

+
+
+
+ +
+
+flare.kernels.cutoffs.hard_cutoff(r_cut: float, ri: float, ci: float)
+

A hard cutoff that assigns a value of 1 to all interatomic distances.

+
+
Parameters
+
    +

  • r_cut (float) – Cutoff value (in angstrom).

    • +

  • ri (float) – Interatomic distance.

    • +

  • ci (float) – Cartesian coordinate divided by the distance.

    • +
+
+
Returns
+

Cutoff value and its derivative.

+
+
Return type
+

(float, float)

+
+
+
+ +
+
+flare.kernels.cutoffs.quadratic_cutoff(r_cut: float, ri: float, ci: float)
+

A quadratic cutoff that goes to zero smoothly at the cutoff boundary.

+
+
Parameters
+
    +

  • r_cut (float) – Cutoff value (in angstrom).

    • +

  • ri (float) – Interatomic distance.

    • +

  • ci (float) – Cartesian coordinate divided by the distance.

    • +
+
+
Returns
+

Cutoff value and its derivative.

+
+
Return type
+

(float, float)

+
+
+
+ +
+
+flare.kernels.cutoffs.quadratic_cutoff_bound(r_cut: float, ri: float, ci: float)
+

A quadratic cutoff that goes to zero smoothly at the cutoff boundary.

+
+
Parameters
+
    +

  • r_cut (float) – Cutoff value (in angstrom).

    • +

  • ri (float) – Interatomic distance.

    • +

  • ci (float) – Cartesian coordinate divided by the distance.

    • +
+
+
Returns
+

Cutoff value and its derivative.

+
+
Return type
+

(float, float)

+
+
+
+
diff --git a/flare/kernels/helper.html b/flare/kernels/helper.html index f896c5e38..d58e9d2fd 100644 --- a/flare/kernels/helper.html +++ b/flare/kernels/helper.html @@ -98,8 +98,161 @@
-
-

Helper Functions

+
+

Helper Functions

+
+
+flare.kernels.kernels.coordination_number(rij, cij, r_cut, cutoff_func)
+
+
Pairwise contribution to many-body descriptor based on number of

atoms in the environment

+
+
+
+
Parameters
+
    +

  • rij (float) – distance between atoms i and j

    • +

  • cij (float) – Component of versor of rij along given direction

    • +

  • r_cut (float) – cutoff hyperparameter

    • +

  • cutoff_func (callable) – cutoff function

    • +
+
+
Returns
+

the value of the pairwise many-body contribution +float: the value of the derivative of the pairwise many-body +contribution w.r.t. the central atom displacement

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.kernels.force_helper(A, B, C, D, fi, fj, fdi, fdj, ls1, ls2, ls3, sig2)
+

Helper function for computing the force/force kernel between two +pairs or triplets of atoms of the same type.

+

See Table IV of the SI of the FLARE paper for definitions of intermediate +quantities.

+
+
Returns
+

+
Force/force kernel between two pairs or triplets of atoms of

the same type.

+
+
+

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.kernels.k_sq_exp_dev(q1, q2, sig, ls)
+

First Gradient of generic squared exponential kernel on two many body functions

+
+
Parameters
+
    +

  • q1 (float) – the many body descriptor of the first local environment

    • +

  • q2 (float) – the many body descriptor of the second local environment

    • +

  • sig (float) – amplitude hyperparameter

    • +

  • ls2 (float) – squared lenghtscale hyperparameter

    • +
+
+
Returns
+

the value of the derivative of the squared exponential kernel

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.kernels.k_sq_exp_double_dev(q1, q2, sig, ls)
+

Second Gradient of generic squared exponential kernel on two many body functions

+
+
Parameters
+
    +

  • q1 (float) – the many body descriptor of the first local environment

    • +

  • q2 (float) – the many body descriptor of the second local environment

    • +

  • sig (float) – amplitude hyperparameter

    • +

  • ls2 (float) – squared lenghtscale hyperparameter

    • +
+
+
Returns
+

the value of the double derivative of the squared exponential kernel

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.kernels.mb_grad_helper_ls(q1, q2, qi, qj, sig, ls)
+

Helper function for many body gradient collecting all the derivatives +of the force-force many body kernel w.r.t. ls

+
+ +
+
+flare.kernels.kernels.mb_grad_helper_ls_(qdiffsq, sig, ls)
+

Derivative of a many body force-force kernel w.r.t. ls

+
+ +
+
+flare.kernels.kernels.q_value(distances, r_cut, cutoff_func, q_func=numba.njit)
+

Compute value of many-body descriptor based on distances of atoms +in the local many-body environment.

+
+
Parameters
+
    +

  • distances (np.ndarray) – distances between atoms i and j

    • +

  • r_cut (float) – cutoff hyperparameter

    • +

  • cutoff_func (callable) – cutoff function

    • +

  • q_func (callable) – many-body pairwise descrptor function

    • +
+
+
Returns
+

the value of the many-body descriptor

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.kernels.q_value_mc(distances, r_cut, ref_species, species, cutoff_func, q_func=numba.njit)
+

Compute value of many-body many components descriptor based +on distances of atoms in the local many-body environment.

+
+
Parameters
+
    +

  • distances (np.ndarray) – distances between atoms i and j

    • +

  • r_cut (float) – cutoff hyperparameter

    • +

  • ref_species (int) – species to consider to compute the contribution

    • +

  • species (np.ndarray) – atomic species of neighbours

    • +

  • cutoff_func (callable) – cutoff function

    • +

  • q_func (callable) – many-body pairwise descrptor function

    • +
+
+
Returns
+

the value of the many-body descriptor

+
+
Return type
+

float

+
+
+
+
diff --git a/flare/kernels/mc_sephyps.html b/flare/kernels/mc_sephyps.html index 8df4b6215..032009bc8 100644 --- a/flare/kernels/mc_sephyps.html +++ b/flare/kernels/mc_sephyps.html @@ -98,8 +98,1078 @@
-
-

Multi-element Kernels (Separate Parameters)

+
+

Multi-element Kernels (Separate Parameters)

+

Multicomponent kernels (simple) restrict all signal variance and length scale of hyperparameters +to a single value. The kernels in this module allow you to have different sets of hyperparameters +and cutoffs for different interactions, and have flexible groupings of elements. It also allows +you to do partial hyper-parameter training, keeping some components fixed.

+

To use this set of kernels, we need a hyps_mask dictionary for GaussianProcess, MappedGaussianProcess, +and AtomicEnvironment (if you also set up different cutoffs). A simple example is shown below.

+

Examples

+
>>> from flare.util.parameter_helper import ParameterHelper
+>>> from flare.bffs.gp import GaussianProcess
+
+
+
>>> pm = ParameterHelper(species=['O', 'C', 'H'],
+...                      kernels={'twobody':[['*', '*'], ['O','O']],
+...                               'threebody':[['*', '*', '*'], ['O','O', 'O']]},
+...                      parameters={'twobody0':[1, 0.5, 1], 'twobody1':[2, 0.2, 2],
+...                            'triplet0':[1, 0.5], 'triplet1':[2, 0.2],
+...                            'cutoff_twobody':2, 'cutoff_threebody':1, 'noise': 0.05},
+...                      constraints={'twobody0':[False, True]})
+>>> hyps_mask = pm1.as_dict()
+>>> hyps = hyps_mask.pop('hyps')
+>>> cutoffs = hyps_mask.pop('cutoffs')
+>>> hyp_labels = hyps_mask.pop('hyp_labels')
+>>> kernels = hyps_mask['kernels']
+>>> gp_model = GaussianProcess(kernels=kernels,
+...                            hyps=hyps, cutoffs=cutoffs,
+...                            hyp_labels=hyp_labels,
+...                            parallel=True, per_atom_par=False,
+...                            n_cpus=n_cpus,
+...                            multihyps=True, hyps_mask=hm)
+
+
+

In the example above, Parameters class generates the arrays needed +for these kernels and store all the grouping and mapping information in the +hyps_mask dictionary. It stores following keys and values:

+
    +
  • +
    spec_mask: 118-long integer array descirbing which elements belong to

    like groups for determining which bond hyperparameters to use. For +instance, [0,0,1,1,0 …] assigns H to group 0, He and Li to group 1, +and Be to group 0 (the 0th register is ignored).

    +
    +
    +
    • +
  • +
    nspec: Integer, number of different species groups (equal to number of

    unique values in spec_mask).

    +
    +
    +
    • +
  • +
    nbond: Integer, number of different hyperparameter sets to associate with

    different 2-body pairings of atoms in groups defined in spec_mask.

    +
    +
    +
    • +
  • +
    bond_mask: Array of length nspec^2, which describes the hyperparameter sets to

    associate with different pairings of species types. For example, if there +are atoms of type 0 and 1, then bond_mask defines which hyperparameters +to use for parings [0-0, 0-1, 1-0, 1-1]: if we wanted hyperparameter set 0 for +0-0 parings and set 1 for 0-1 and 1-1 pairings, then we would make +bond_mask [0, 1, 1, 1].

    +
    +
    +
    • +
  • +
    ntriplet: Integer, number of different hyperparameter sets to associate

    with different 3-body pariings of atoms in groups defined in spec_mask.

    +
    +
    +
    • +
  • +
    triplet_mask: Similar to bond mask: Triplet pairings of type 0 and 1 atoms

    would go {0-0-0, 0-0-1, 0-1-0, 0-1-1, 1-0-0, 1-0-1, 1-1-0, 1-1-1}, +and if we wanted hyp. set 0 for triplets with only atoms of type 0 +and hyp. set 1 for all the rest, then the triplet_mask array would +read [0,1,1,1,1,1,1,1]. The user should make sure that the mask has +a permutational symmetry.

    +
    +
    +
    • +
  • +
    cutoff_2b: Array of length nbond, which stores the cutoff used for different

    types of bonds defined in bond_mask

    +
    +
    +
    • +
  • +
    ncut3b: Integer, number of different cutoffs sets to associate

    with different 3-body pariings of atoms in groups defined in spec_mask.

    +
    +
    +
    • +
  • +
    cut3b_mask: Array of length nspec^2, which describes the cutoff to

    associate with different bond types in triplets. For example, in a triplet +(C, O, H) , there are three cutoffs. Cutoffs for CH bond, CO bond and OH bond. +If C and O are associate with atom group 1 in spec_mask and H are associate with +group 0 in spec_mask, the cut3b_mask[1*nspec+0] determines the C/O-H bond cutoff, +and cut3b_mask[1*nspec+1] determines the C-O bond cutoff. If we want the +former one to use the 1st cutoff in cutoff_3b and the later to use the 2nd cutoff +in cutoff_3b, the cut3b_mask should be [0, 0, 0, 1]

    +
    +
    +
    • +
  • +
    cutoff_3b: Array of length ncut3b, which stores the cutoff used for different

    types of bonds in triplets.

    +
    +
    +
    • +
  • +
    nmbInteger, number of different cutoffs set to associate with different coordination

    numbers

    +
    +
    +
    • +

  • mb_mask: similar to bond_mask and cut3b_mask.

    • +

  • cutoff_mb: Array of length nmb, stores the cutoff used for different many body terms

    • +
+

For selective optimization. one can define ‘map’, ‘train_noise’ and ‘original’ +to identify which element to be optimized. All three have to be defined. +train_noise = Bool (True/False), whether the noise parameter can be optimized +original: np.array. Full set of initial values for hyperparmeters +map: np.array, array to map the hyper parameter back to the full set. +map[i]=j means the i-th element in hyps should be the j-th element in +hyps_mask[‘original’]

+

For example, the full set of hyper parmeters +may include [ls21, ls22, sig21, sig22, ls3 +sg3, noise] but suppose you wanted only the set 21 optimized. +The full set of hyperparameters is defined in ‘original’; include all those +you want to leave static, and set initial guesses for those you want to vary. +Have the ‘map’ list contain the indices of the hyperparameters in ‘original’ +that correspond to the hyperparameters you want to vary. +Have a hyps list which contain those which you want to vary. Below, +ls21, ls22 etc… represent floating-point variables which correspond +to the initial guesses / static values. +You would then pass in:

+

hyps = [ls21, sig21] +hyps_mask = { …, ‘train_noise’: False, ‘map’:[0, 2],

+
+

‘original’: [ls21, ls22, sig21, sig22, ls3, sg3, noise]}

+
+

the hyps argument should only contain the values that need to be optimized. +If you want noise to be trained as well include noise as the +final hyperparameter value in hyps.

+
+
+flare.kernels.mc_sephyps.many_body_mc(env1, env2, d1, d2, cutoff_2b, cutoff_3b, cutoff_mb, nspec, spec_mask, nbond, bond_mask, ntriplet, triplet_mask, ncut3b, cut3b_mask, nmb, mb_mask, sig2, ls2, sig3, ls3, sigm, lsm, cutoff_func=numba.njit)
+

many-body multi-element kernel between two force components.

+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – First local environment.

    • +

  • env2 (AtomicEnvironment) – Second local environment.

    • +

  • d1 (int) – Force component of the first environment.

    • +

  • d2 (int) – Force component of the second environment.

    • +

  • cutoff_2b – dummy

    • +

  • cutoff_3b – dummy

    • +

  • cutoff_mb (float, np.ndarray) – cutoff(s) for coordination-based manybody interaction

    • +

  • nspec (int) – number of different species groups

    • +

  • spec_mask (np.ndarray) – 118-long integer array that determines specie group

    • +

  • nbond – dummy

    • +

  • bond_mask – dummy

    • +

  • ntriplet – dummy

    • +

  • triplet_mask – dummy

    • +

  • ncut3b – dummy

    • +

  • cut3b_mask – dummy

    • +

  • nmb (int) – number of different hyperparameter sets to associate with manybody pairings

    • +

  • mb_mask (np.ndarray) – nspec^2 long integer array

    • +

  • sig2 – dummy

    • +

  • ls2 – dummy

    • +

  • sig3 – dummy

    • +

  • ls3 – dummy

    • +

  • sigm (np.ndarray) – signal variances associates with manybody term

    • +

  • lsm (np.ndarray) – length scales associates with manybody term

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

Value of the 2+3+many-body kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.mc_sephyps.many_body_mc_en(env1, env2, cutoff_2b, cutoff_3b, cutoff_mb, nspec, spec_mask, nbond, bond_mask, ntriplet, triplet_mask, ncut3b, cut3b_mask, nmb, mb_mask, sig2, ls2, sig3, ls3, sigm, lsm, cutoff_func=numba.njit)
+

many-body multi-element kernel between two local energies.

+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – First local environment.

    • +

  • env2 (AtomicEnvironment) – Second local environment.

    • +

  • hyps (np.ndarray) – Hyperparameters of the kernel function (sig, ls).

    • +

  • cutoffs (np.ndarray) – One-element array containing the 2-body +cutoff.

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

Value of the 2-body force/energy kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.mc_sephyps.many_body_mc_force_en(env1, env2, d1, cutoff_2b, cutoff_3b, cutoff_mb, nspec, spec_mask, nbond, bond_mask, ntriplet, triplet_mask, ncut3b, cut3b_mask, nmb, mb_mask, sig2, ls2, sig3, ls3, sigm, lsm, cutoff_func=numba.njit)
+

many-body single-element kernel between two local energies.

+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – First local environment.

    • +

  • env2 (AtomicEnvironment) – Second local environment.

    • +

  • hyps (np.ndarray) – Hyperparameters of the kernel function (sig, ls).

    • +

  • cutoffs (np.ndarray) – Two-element array containing the 2-, 3-, and +many-body cutoffs.

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

Value of the many-body force/energy kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.mc_sephyps.many_body_mc_grad(env1, env2, d1, d2, cutoff_2b, cutoff_3b, cutoff_mb, nspec, spec_mask, nbond, bond_mask, ntriplet, triplet_mask, ncut3b, cut3b_mask, nmb, mb_mask, sig2, ls2, sig3, ls3, sigm, lsm, cutoff_func=numba.njit)
+

manybody multi-element kernel between two force components and its +gradient with respect to the hyperparameters.

+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – First local environment.

    • +

  • env2 (AtomicEnvironment) – Second local environment.

    • +

  • d1 (int) – Force component of the first environment.

    • +

  • d2 (int) – Force component of the second environment.

    • +

  • cutoff_2b – dummy

    • +

  • cutoff_3b – dummy

    • +

  • cutoff_mb (float, np.ndarray) – cutoff(s) for coordination-based manybody interaction

    • +

  • nspec (int) – number of different species groups

    • +

  • spec_mask (np.ndarray) – 118-long integer array that determines specie group

    • +

  • nbond – dummy

    • +

  • bond_mask – dummy

    • +

  • ntriplet – dummy

    • +

  • triplet_mask – dummy

    • +

  • ncut3b – dummy

    • +

  • cut3b_mask – dummy

    • +

  • nmb (int) – number of different hyperparameter sets to associate with manybody pairings

    • +

  • mb_mask (np.ndarray) – nspec^2 long integer array

    • +

  • sig2 – dummy

    • +

  • ls2 – dummy

    • +

  • sig3 – dummy

    • +

  • ls3 – dummy

    • +

  • sigm (np.ndarray) – signal variances associates with manybody term

    • +

  • lsm (np.ndarray) – length scales associates with manybody term

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

Value of the 2+3+manybody kernel and its gradient +with respect to the hyperparameters.

+
+
Return type
+

(float, np.ndarray)

+
+
+
+ +
+
+flare.kernels.mc_sephyps.three_body_mc(env1, env2, d1, d2, cutoff_2b, cutoff_3b, cutoff_mb, nspec, spec_mask, nbond, bond_mask, ntriplet, triplet_mask, ncut3b, cut3b_mask, nmb, mb_mask, sig2, ls2, sig3, ls3, sigm, lsm, cutoff_func=numba.njit)
+

3-body multi-element kernel between two force components.

+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – First local environment.

    • +

  • env2 (AtomicEnvironment) – Second local environment.

    • +

  • d1 (int) – Force component of the first environment.

    • +

  • d2 (int) – Force component of the second environment.

    • +

  • cutoff_2b – dummy

    • +

  • cutoff_3b (float, np.ndarray) – cutoff(s) for three-body interaction

    • +

  • nspec (int) – number of different species groups

    • +

  • spec_mask (np.ndarray) – 118-long integer array that determines specie group

    • +

  • nbond – dummy

    • +

  • bond_mask – dummy

    • +

  • ntriplet (int) – number of different hyperparameter sets to associate with 3-body pairings

    • +

  • triplet_mask (np.ndarray) – nspec^3 long integer array

    • +

  • ncut3b (int) – number of different 3-body cutoff sets to associate with 3-body pairings

    • +

  • cut3b_mask (np.ndarray) – nspec^2 long integer array

    • +

  • sig2 – dummy

    • +

  • ls2 – dummy

    • +

  • sig3 (np.ndarray) – signal variances associates with three-body term

    • +

  • ls3 (np.ndarray) – length scales associates with three-body term

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

Value of the 2+3-body force/force kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.mc_sephyps.three_body_mc_en(env1, env2, cutoff_2b, cutoff_3b, cutoff_mb, nspec, spec_mask, nbond, bond_mask, ntriplet, triplet_mask, ncut3b, cut3b_mask, nmb, mb_mask, sig2, ls2, sig3, ls3, sigm, lsm, cutoff_func=numba.njit)
+

3-body multi-element kernel between two local energies

+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – First local environment.

    • +

  • env2 (AtomicEnvironment) – Second local environment.

    • +

  • d1 (int) – Force component of the first environment.

    • +

  • d2 (int) – Force component of the second environment.

    • +

  • cutoff_2b – dummy

    • +

  • cutoff_3b (float, np.ndarray) – cutoff(s) for three-body interaction

    • +

  • nspec (int) – number of different species groups

    • +

  • spec_mask (np.ndarray) – 118-long integer array that determines specie group

    • +

  • nbond – dummy

    • +

  • bond_mask – dummy

    • +

  • ntriplet (int) – number of different hyperparameter sets to associate with 3-body pairings

    • +

  • triplet_mask (np.ndarray) – nspec^3 long integer array

    • +

  • ncut3b (int) – number of different 3-body cutoff sets to associate with 3-body pairings

    • +

  • cut3b_mask (np.ndarray) – nspec^2 long integer array

    • +

  • sig2 – dummy

    • +

  • ls2 – dummy

    • +

  • sig3 (np.ndarray) – signal variances associates with three-body term

    • +

  • ls3 (np.ndarray) – length scales associates with three-body term

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

Value of the 2+3-body energy/energy kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.mc_sephyps.three_body_mc_force_en(env1, env2, d1, cutoff_2b, cutoff_3b, cutoff_mb, nspec, spec_mask, nbond, bond_mask, ntriplet, triplet_mask, ncut3b, cut3b_mask, nmb, mb_mask, sig2, ls2, sig3, ls3, sigm, lsm, cutoff_func=numba.njit)
+

3-body multi-element kernel between a force component and local energies

+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – First local environment.

    • +

  • env2 (AtomicEnvironment) – Second local environment.

    • +

  • d1 (int) – Force component of the first environment.

    • +

  • d2 (int) – Force component of the second environment.

    • +

  • cutoff_2b – dummy

    • +

  • cutoff_3b (float, np.ndarray) – cutoff(s) for three-body interaction

    • +

  • nspec (int) – number of different species groups

    • +

  • spec_mask (np.ndarray) – 118-long integer array that determines specie group

    • +

  • nbond – dummy

    • +

  • bond_mask – dummy

    • +

  • ntriplet (int) – number of different hyperparameter sets to associate with 3-body pairings

    • +

  • triplet_mask (np.ndarray) – nspec^3 long integer array

    • +

  • ncut3b (int) – number of different 3-body cutoff sets to associate with 3-body pairings

    • +

  • cut3b_mask (np.ndarray) – nspec^2 long integer array

    • +

  • sig2 – dummy

    • +

  • ls2 – dummy

    • +

  • sig3 (np.ndarray) – signal variances associates with three-body term

    • +

  • ls3 (np.ndarray) – length scales associates with three-body term

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

Value of the 2+3-body force/energy kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.mc_sephyps.three_body_mc_force_en_jit(bond_array_1, c1, etypes1, bond_array_2, c2, etypes2, cross_bond_inds_1, cross_bond_inds_2, cross_bond_dists_1, cross_bond_dists_2, triplets_1, triplets_2, d1, sig, ls, r_cut, cutoff_func, nspec, spec_mask, triplet_mask, cut3b_mask)
+

Kernel for 3-body force/energy comparisons.

+
+ +
+
+flare.kernels.mc_sephyps.three_body_mc_grad(env1, env2, d1, d2, cutoff_2b, cutoff_3b, cutoff_mb, nspec, spec_mask, nbond, bond_mask, ntriplet, triplet_mask, ncut3b, cut3b_mask, nmb, mb_mask, sig2, ls2, sig3, ls3, sigm, lsm, cutoff_func=numba.njit)
+

3-body multi-element kernel between two force components and its +gradient with respect to the hyperparameters.

+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – First local environment.

    • +

  • env2 (AtomicEnvironment) – Second local environment.

    • +

  • d1 (int) – Force component of the first environment.

    • +

  • d2 (int) – Force component of the second environment.

    • +

  • cutoff_2b – dummy

    • +

  • cutoff_3b (float, np.ndarray) – cutoff(s) for three-body interaction

    • +

  • nspec (int) – number of different species groups

    • +

  • spec_mask (np.ndarray) – 118-long integer array that determines specie group

    • +

  • nbond – dummy

    • +

  • bond_mask – dummy

    • +

  • ntriplet (int) – number of different hyperparameter sets to associate with 3-body pairings

    • +

  • triplet_mask (np.ndarray) – nspec^3 long integer array

    • +

  • ncut3b (int) – number of different 3-body cutoff sets to associate with 3-body pairings

    • +

  • cut3b_mask (np.ndarray) – nspec^2 long integer array

    • +

  • sig2 – dummy

    • +

  • ls2 – dummy

    • +

  • sig3 (np.ndarray) – signal variances associates with three-body term

    • +

  • ls3 (np.ndarray) – length scales associates with three-body term

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

Value of the 2+3+manybody kernel and its gradient +with respect to the hyperparameters.

+
+
Return type
+

(float, np.ndarray)

+
+
+
+ +
+
+flare.kernels.mc_sephyps.three_body_mc_grad_jit(bond_array_1, c1, etypes1, bond_array_2, c2, etypes2, cross_bond_inds_1, cross_bond_inds_2, cross_bond_dists_1, cross_bond_dists_2, triplets_1, triplets_2, d1, d2, sig, ls, r_cut, cutoff_func, nspec, spec_mask, ntriplet, triplet_mask, cut3b_mask)
+

Kernel gradient for 3-body force comparisons.

+
+ +
+
+flare.kernels.mc_sephyps.two_body_mc(env1, env2, d1, d2, cutoff_2b, cutoff_3b, cutoff_mb, nspec, spec_mask, nbond, bond_mask, ntriplet, triplet_mask, ncut3b, cut3b_mask, nmb, mb_mask, sig2, ls2, sig3, ls3, sigm, lsm, cutoff_func=numba.njit)
+

2-body multi-element kernel between two force components.

+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – First local environment.

    • +

  • env2 (AtomicEnvironment) – Second local environment.

    • +

  • d1 (int) – Force component of the first environment.

    • +

  • d2 (int) – Force component of the second environment.

    • +

  • cutoff_2b (float, np.ndarray) – cutoff(s) for two-body interaction

    • +

  • cutoff_3b – dummy

    • +

  • nspec (int) – number of different species groups

    • +

  • spec_mask (np.ndarray) – 118-long integer array that determines specie group

    • +

  • nbond (int) – number of different hyperparameter sets to associate with two-body pairings

    • +

  • bond_mask (np.ndarray) – nspec^2 long integer array

    • +

  • ntriplet – dummy

    • +

  • triplet_mask – dummy

    • +

  • ncut3b – dummy

    • +

  • cut3b_mask – dummy

    • +

  • sig2 – dummy

    • +

  • ls2 – dummy

    • +

  • sig3 – dummy

    • +

  • ls3 – dummy

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

Value of the 2-body force/force kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.mc_sephyps.two_body_mc_en(env1, env2, cutoff_2b, cutoff_3b, cutoff_mb, nspec, spec_mask, nbond, bond_mask, ntriplet, triplet_mask, ncut3b, cut3b_mask, nmb, mb_mask, sig2, ls2, sig3, ls3, sigm, lsm, cutoff_func=numba.njit)
+

2-body multi-element kernel between two local energies

+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – First local environment.

    • +

  • env2 (AtomicEnvironment) – Second local environment.

    • +

  • d1 (int) – Force component of the first environment.

    • +

  • d2 (int) – Force component of the second environment.

    • +

  • cutoff_2b (float, np.ndarray) – cutoff(s) for two-body interaction

    • +

  • cutoff_3b – dummy

    • +

  • nspec (int) – number of different species groups

    • +

  • spec_mask (np.ndarray) – 118-long integer array that determines specie group

    • +

  • nbond (int) – number of different hyperparameter sets to associate with two-body pairings

    • +

  • bond_mask (np.ndarray) – nspec^2 long integer array

    • +

  • ntriplet – dummy

    • +

  • triplet_mask – dummy

    • +

  • ncut3b – dummy

    • +

  • cut3b_mask – dummy

    • +

  • sig2 – dummy

    • +

  • ls2 – dummy

    • +

  • sig3 – dummy

    • +

  • ls3 – dummy

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

Value of the 2-body energy/energy kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.mc_sephyps.two_body_mc_en_jit(bond_array_1, c1, etypes1, bond_array_2, c2, etypes2, sig, ls, r_cut, cutoff_func, nspec, spec_mask, bond_mask)
+

Multicomponent two-body energy/energy kernel accelerated with +Numba’s njit decorator.

+
+ +
+
+flare.kernels.mc_sephyps.two_body_mc_force_en(env1, env2, d1, cutoff_2b, cutoff_3b, cutoff_mb, nspec, spec_mask, nbond, bond_mask, ntriplet, triplet_mask, ncut3b, cut3b_mask, nmb, mb_mask, sig2, ls2, sig3, ls3, sigm, lsm, cutoff_func=numba.njit)
+

2-body multi-element kernel between a force components and local energy

+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – First local environment.

    • +

  • env2 (AtomicEnvironment) – Second local environment.

    • +

  • d1 (int) – Force component of the first environment.

    • +

  • d2 (int) – Force component of the second environment.

    • +

  • cutoff_2b (float, np.ndarray) – cutoff(s) for two-body interaction

    • +

  • cutoff_3b – dummy

    • +

  • nspec (int) – number of different species groups

    • +

  • spec_mask (np.ndarray) – 118-long integer array that determines specie group

    • +

  • nbond (int) – number of different hyperparameter sets to associate with two-body pairings

    • +

  • bond_mask (np.ndarray) – nspec^2 long integer array

    • +

  • ntriplet – dummy

    • +

  • triplet_mask – dummy

    • +

  • ncut3b – dummy

    • +

  • cut3b_mask – dummy

    • +

  • sig2 – dummy

    • +

  • ls2 – dummy

    • +

  • sig3 – dummy

    • +

  • ls3 – dummy

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

Value of the 2-body force/energy kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.mc_sephyps.two_body_mc_force_en_jit(bond_array_1, c1, etypes1, bond_array_2, c2, etypes2, d1, sig, ls, r_cut, cutoff_func, nspec, spec_mask, bond_mask)
+

Multicomponent two-body force/energy kernel accelerated with +Numba’s njit decorator.

+
+ +
+
+flare.kernels.mc_sephyps.two_body_mc_grad(env1, env2, d1, d2, cutoff_2b, cutoff_3b, cutoff_mb, nspec, spec_mask, nbond, bond_mask, ntriplet, triplet_mask, ncut3b, cut3b_mask, nmb, mb_mask, sig2, ls2, sig3, ls3, sigm, lsm, cutoff_func=numba.njit)
+

2-body multi-element kernel between two force components and its +gradient with respect to the hyperparameters.

+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – First local environment.

    • +

  • env2 (AtomicEnvironment) – Second local environment.

    • +

  • d1 (int) – Force component of the first environment.

    • +

  • d2 (int) – Force component of the second environment.

    • +

  • cutoff_2b (float, np.ndarray) – cutoff(s) for two-body interaction

    • +

  • cutoff_3b – dummy

    • +

  • nspec (int) – number of different species groups

    • +

  • spec_mask (np.ndarray) – 118-long integer array that determines specie group

    • +

  • nbond (int) – number of different hyperparameter sets to associate with two-body pairings

    • +

  • bond_mask (np.ndarray) – nspec^2 long integer array

    • +

  • ntriplet – dummy

    • +

  • triplet_mask – dummy

    • +

  • ncut3b – dummy

    • +

  • cut3b_mask – dummy

    • +

  • sig2 (np.ndarray) – signal variances associates with two-body term

    • +

  • ls2 (np.ndarray) – length scales associates with two-body term

    • +

  • sig3 – dummy

    • +

  • ls3 – dummy

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

Value of the 2-body kernel and its gradient +with respect to the hyperparameters.

+
+
Return type
+

(float, np.ndarray)

+
+
+
+ +
+
+flare.kernels.mc_sephyps.two_body_mc_grad_jit(bond_array_1, c1, etypes1, bond_array_2, c2, etypes2, d1, d2, sig, ls, r_cut, cutoff_func, nspec, spec_mask, nbond, bond_mask)
+

Multicomponent two-body force/force kernel gradient accelerated with +Numba’s njit decorator.

+
+ +
+
+flare.kernels.mc_sephyps.two_body_mc_jit(bond_array_1, c1, etypes1, bond_array_2, c2, etypes2, d1, d2, sig, ls, r_cut, cutoff_func, nspec, spec_mask, bond_mask)
+

Multicomponent two-body force/force kernel accelerated with Numba’s +njit decorator. +Loops over bonds in two environments and adds to the kernel if bonds are +of the same type.

+
+ +
+
+flare.kernels.mc_sephyps.two_plus_three_body_mc(env1, env2, d1, d2, cutoff_2b, cutoff_3b, cutoff_mb, nspec, spec_mask, nbond, bond_mask, ntriplet, triplet_mask, ncut3b, cut3b_mask, nmb, mb_mask, sig2, ls2, sig3, ls3, sigm, lsm, cutoff_func=numba.njit)
+

2+3-body multi-element kernel between two force components.

+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – First local environment.

    • +

  • env2 (AtomicEnvironment) – Second local environment.

    • +

  • d1 (int) – Force component of the first environment.

    • +

  • d2 (int) – Force component of the second environment.

    • +

  • cutoff_2b (float, np.ndarray) – cutoff(s) for two-body interaction

    • +

  • cutoff_3b (float, np.ndarray) – cutoff(s) for three-body interaction

    • +

  • cutoff_mb (float, np.ndarray) – cutoff(s) for coordination-based manybody interaction

    • +

  • nspec (int) – number of different species groups

    • +

  • spec_mask (np.ndarray) – 118-long integer array that determines specie group

    • +

  • nbond (int) – number of different hyperparameter sets to associate with two-body pairings

    • +

  • bond_mask (np.ndarray) – nspec^2 long integer array

    • +

  • ntriplet (int) – number of different hyperparameter sets to associate with 3-body pairings

    • +

  • triplet_mask (np.ndarray) – nspec^3 long integer array

    • +

  • ncut3b (int) – number of different 3-body cutoff sets to associate with 3-body pairings

    • +

  • cut3b_mask (np.ndarray) – nspec^2 long integer array

    • +

  • sig2 (np.ndarray) – signal variances associates with two-body term

    • +

  • ls2 (np.ndarray) – length scales associates with two-body term

    • +

  • sig3 (np.ndarray) – signal variances associates with three-body term

    • +

  • ls3 (np.ndarray) – length scales associates with three-body term

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

Value of the 2+3-body force/force kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.mc_sephyps.two_plus_three_body_mc_grad(env1, env2, d1, d2, cutoff_2b, cutoff_3b, cutoff_mb, nspec, spec_mask, nbond, bond_mask, ntriplet, triplet_mask, ncut3b, cut3b_mask, nmb, mb_mask, sig2, ls2, sig3, ls3, sigm, lsm, cutoff_func=numba.njit)
+

2+3-body multi-element kernel between two force components and its +gradient with respect to the hyperparameters.

+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – First local environment.

    • +

  • env2 (AtomicEnvironment) – Second local environment.

    • +

  • d1 (int) – Force component of the first environment.

    • +

  • d2 (int) – Force component of the second environment.

    • +

  • cutoff_2b (float, np.ndarray) – cutoff(s) for two-body interaction

    • +

  • cutoff_3b (float, np.ndarray) – cutoff(s) for three-body interaction

    • +

  • nspec (int) – number of different species groups

    • +

  • spec_mask (np.ndarray) – 118-long integer array that determines specie group

    • +

  • nbond (int) – number of different hyperparameter sets to associate with two-body pairings

    • +

  • bond_mask (np.ndarray) – nspec^2 long integer array

    • +

  • ntriplet (int) – number of different hyperparameter sets to associate with 3-body pairings

    • +

  • triplet_mask (np.ndarray) – nspec^3 long integer array

    • +

  • ncut3b (int) – number of different 3-body cutoff sets to associate with 3-body pairings

    • +

  • cut3b_mask (np.ndarray) – nspec^2 long integer array

    • +

  • sig2 (np.ndarray) – signal variances associates with two-body term

    • +

  • ls2 (np.ndarray) – length scales associates with two-body term

    • +

  • sig3 (np.ndarray) – signal variances associates with three-body term

    • +

  • ls3 (np.ndarray) – length scales associates with three-body term

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

Value of the 2+3-body kernel and its gradient +with respect to the hyperparameters.

+
+
Return type
+

(float, np.ndarray)

+
+
+
+ +
+
+flare.kernels.mc_sephyps.two_plus_three_mc_en(env1, env2, cutoff_2b, cutoff_3b, cutoff_mb, nspec, spec_mask, nbond, bond_mask, ntriplet, triplet_mask, ncut3b, cut3b_mask, nmb, mb_mask, sig2, ls2, sig3, ls3, sigm, lsm, cutoff_func=numba.njit)
+

2+3-body multi-element kernel between two local energies

+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – First local environment.

    • +

  • env2 (AtomicEnvironment) – Second local environment.

    • +

  • d1 (int) – Force component of the first environment.

    • +

  • d2 (int) – Force component of the second environment.

    • +

  • cutoff_2b (float, np.ndarray) – cutoff(s) for two-body interaction

    • +

  • cutoff_3b (float, np.ndarray) – cutoff(s) for three-body interaction

    • +

  • cutoff_mb (float, np.ndarray) – cutoff(s) for coordination-based manybody interaction

    • +

  • nspec (int) – number of different species groups

    • +

  • spec_mask (np.ndarray) – 118-long integer array that determines specie group

    • +

  • nbond (int) – number of different hyperparameter sets to associate with two-body pairings

    • +

  • bond_mask (np.ndarray) – nspec^2 long integer array

    • +

  • ntriplet (int) – number of different hyperparameter sets to associate with 3-body pairings

    • +

  • triplet_mask (np.ndarray) – nspec^3 long integer array

    • +

  • ncut3b (int) – number of different 3-body cutoff sets to associate with 3-body pairings

    • +

  • cut3b_mask (np.ndarray) – nspec^2 long integer array

    • +

  • sig2 (np.ndarray) – signal variances associates with two-body term

    • +

  • ls2 (np.ndarray) – length scales associates with two-body term

    • +

  • sig3 (np.ndarray) – signal variances associates with three-body term

    • +

  • ls3 (np.ndarray) – length scales associates with three-body term

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

Value of the 2+3-body energy/energy kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.mc_sephyps.two_plus_three_mc_force_en(env1, env2, d1, cutoff_2b, cutoff_3b, cutoff_mb, nspec, spec_mask, nbond, bond_mask, ntriplet, triplet_mask, ncut3b, cut3b_mask, nmb, mb_mask, sig2, ls2, sig3, ls3, sigm, lsm, cutoff_func=numba.njit)
+

2+3-body multi-element kernel between force and local energy

+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – First local environment.

    • +

  • env2 (AtomicEnvironment) – Second local environment.

    • +

  • d1 (int) – Force component of the first environment.

    • +

  • d2 (int) – Force component of the second environment.

    • +

  • cutoff_2b (float, np.ndarray) – cutoff(s) for two-body interaction

    • +

  • cutoff_3b (float, np.ndarray) – cutoff(s) for three-body interaction

    • +

  • cutoff_mb (float, np.ndarray) – cutoff(s) for coordination-based manybody interaction

    • +

  • nspec (int) – number of different species groups

    • +

  • spec_mask (np.ndarray) – 118-long integer array that determines specie group

    • +

  • nbond (int) – number of different hyperparameter sets to associate with two-body pairings

    • +

  • bond_mask (np.ndarray) – nspec^2 long integer array

    • +

  • ntriplet (int) – number of different hyperparameter sets to associate with 3-body pairings

    • +

  • triplet_mask (np.ndarray) – nspec^3 long integer array

    • +

  • ncut3b (int) – number of different 3-body cutoff sets to associate with 3-body pairings

    • +

  • cut3b_mask (np.ndarray) – nspec^2 long integer array

    • +

  • sig2 (np.ndarray) – signal variances associates with two-body term

    • +

  • ls2 (np.ndarray) – length scales associates with two-body term

    • +

  • sig3 (np.ndarray) – signal variances associates with three-body term

    • +

  • ls3 (np.ndarray) – length scales associates with three-body term

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

Value of the 2+3-body force/energy kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.mc_sephyps.two_three_many_body_mc(env1, env2, d1, d2, cutoff_2b, cutoff_3b, cutoff_mb, nspec, spec_mask, nbond, bond_mask, ntriplet, triplet_mask, ncut3b, cut3b_mask, nmb, mb_mask, sig2, ls2, sig3, ls3, sigm, lsm, cutoff_func=numba.njit)
+

2+3+manybody multi-element kernel between two force components.

+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – First local environment.

    • +

  • env2 (AtomicEnvironment) – Second local environment.

    • +

  • d1 (int) – Force component of the first environment.

    • +

  • d2 (int) – Force component of the second environment.

    • +

  • cutoff_2b (float, np.ndarray) – cutoff(s) for two-body interaction

    • +

  • cutoff_3b (float, np.ndarray) – cutoff(s) for three-body interaction

    • +

  • cutoff_mb (float, np.ndarray) – cutoff(s) for coordination-based manybody interaction

    • +

  • nspec (int) – number of different species groups

    • +

  • spec_mask (np.ndarray) – 118-long integer array that determines specie group

    • +

  • nbond (int) – number of different hyperparameter sets to associate with two-body pairings

    • +

  • bond_mask (np.ndarray) – nspec^2 long integer array

    • +

  • ntriplet (int) – number of different hyperparameter sets to associate with 3-body pairings

    • +

  • triplet_mask (np.ndarray) – nspec^3 long integer array

    • +

  • ncut3b (int) – number of different 3-body cutoff sets to associate with 3-body pairings

    • +

  • cut3b_mask (np.ndarray) – nspec^2 long integer array

    • +

  • nmb (int) – number of different hyperparameter sets to associate with manybody pairings

    • +

  • mb_mask (np.ndarray) – nspec^2 long integer array

    • +

  • sig2 (np.ndarray) – signal variances associates with two-body term

    • +

  • ls2 (np.ndarray) – length scales associates with two-body term

    • +

  • sig3 (np.ndarray) – signal variances associates with three-body term

    • +

  • ls3 (np.ndarray) – length scales associates with three-body term

    • +

  • sigm (np.ndarray) – signal variances associates with manybody term

    • +

  • lsm (np.ndarray) – length scales associates with manybody term

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

Value of the 2+3+many-body kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.mc_sephyps.two_three_many_body_mc_grad(env1, env2, d1, d2, cutoff_2b, cutoff_3b, cutoff_mb, nspec, spec_mask, nbond, bond_mask, ntriplet, triplet_mask, ncut3b, cut3b_mask, nmb, mb_mask, sig2, ls2, sig3, ls3, sigm, lsm, cutoff_func=numba.njit)
+

2+3+manybody multi-element kernel between two force components and its +gradient with respect to the hyperparameters.

+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – First local environment.

    • +

  • env2 (AtomicEnvironment) – Second local environment.

    • +

  • d1 (int) – Force component of the first environment.

    • +

  • d2 (int) – Force component of the second environment.

    • +

  • cutoff_2b (float, np.ndarray) – cutoff(s) for two-body interaction

    • +

  • cutoff_3b (float, np.ndarray) – cutoff(s) for three-body interaction

    • +

  • cutoff_mb (float, np.ndarray) – cutoff(s) for coordination-based manybody interaction

    • +

  • nspec (int) – number of different species groups

    • +

  • spec_mask (np.ndarray) – 118-long integer array that determines specie group

    • +

  • nbond (int) – number of different hyperparameter sets to associate with two-body pairings

    • +

  • bond_mask (np.ndarray) – nspec^2 long integer array

    • +

  • ntriplet (int) – number of different hyperparameter sets to associate with 3-body pairings

    • +

  • triplet_mask (np.ndarray) – nspec^3 long integer array

    • +

  • ncut3b (int) – number of different 3-body cutoff sets to associate with 3-body pairings

    • +

  • cut3b_mask (np.ndarray) – nspec^2 long integer array

    • +

  • nmb (int) – number of different hyperparameter sets to associate with manybody pairings

    • +

  • mb_mask (np.ndarray) – nspec^2 long integer array

    • +

  • sig2 (np.ndarray) – signal variances associates with two-body term

    • +

  • ls2 (np.ndarray) – length scales associates with two-body term

    • +

  • sig3 (np.ndarray) – signal variances associates with three-body term

    • +

  • ls3 (np.ndarray) – length scales associates with three-body term

    • +

  • sigm (np.ndarray) – signal variances associates with manybody term

    • +

  • lsm (np.ndarray) – length scales associates with manybody term

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

Value of the 2+3+manybody kernel and its gradient +with respect to the hyperparameters.

+
+
Return type
+

(float, np.ndarray)

+
+
+
+ +
+
+flare.kernels.mc_sephyps.two_three_many_mc_en(env1, env2, cutoff_2b, cutoff_3b, cutoff_mb, nspec, spec_mask, nbond, bond_mask, ntriplet, triplet_mask, ncut3b, cut3b_mask, nmb, mb_mask, sig2, ls2, sig3, ls3, sigm, lsm, cutoff_func=numba.njit)
+

2+3+many-body multi-element kernel between two local energies.

+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – First local environment.

    • +

  • env2 (AtomicEnvironment) – Second local environment.

    • +

  • d1 (int) – Force component of the first environment.

    • +

  • d2 (int) – Force component of the second environment.

    • +

  • cutoff_2b (float, np.ndarray) – cutoff(s) for two-body interaction

    • +

  • cutoff_3b (float, np.ndarray) – cutoff(s) for three-body interaction

    • +

  • cutoff_mb (float, np.ndarray) – cutoff(s) for coordination-based manybody interaction

    • +

  • nspec (int) – number of different species groups

    • +

  • spec_mask (np.ndarray) – 118-long integer array that determines specie group

    • +

  • nbond (int) – number of different hyperparameter sets to associate with two-body pairings

    • +

  • bond_mask (np.ndarray) – nspec^2 long integer array

    • +

  • ntriplet (int) – number of different hyperparameter sets to associate with 3-body pairings

    • +

  • triplet_mask (np.ndarray) – nspec^3 long integer array

    • +

  • ncut3b (int) – number of different 3-body cutoff sets to associate with 3-body pairings

    • +

  • cut3b_mask (np.ndarray) – nspec^2 long integer array

    • +

  • nmb (int) – number of different hyperparameter sets to associate with manybody pairings

    • +

  • mb_mask (np.ndarray) – nspec^2 long integer array

    • +

  • sig2 (np.ndarray) – signal variances associates with two-body term

    • +

  • ls2 (np.ndarray) – length scales associates with two-body term

    • +

  • sig3 (np.ndarray) – signal variances associates with three-body term

    • +

  • ls3 (np.ndarray) – length scales associates with three-body term

    • +

  • sigm (np.ndarray) – signal variances associates with manybody term

    • +

  • lsm (np.ndarray) – length scales associates with manybody term

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

Value of the 2+3+many-body energy/energy kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.mc_sephyps.two_three_many_mc_force_en(env1, env2, d1, cutoff_2b, cutoff_3b, cutoff_mb, nspec, spec_mask, nbond, bond_mask, ntriplet, triplet_mask, ncut3b, cut3b_mask, nmb, mb_mask, sig2, ls2, sig3, ls3, sigm, lsm, cutoff_func=numba.njit)
+

2+3+manybody multi-element kernel between a force component and a local +energy.

+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – First local environment.

    • +

  • env2 (AtomicEnvironment) – Second local environment.

    • +

  • d1 (int) – Force component of the first environment.

    • +

  • d2 (int) – Force component of the second environment.

    • +

  • cutoff_2b (float, np.ndarray) – cutoff(s) for two-body interaction

    • +

  • cutoff_3b (float, np.ndarray) – cutoff(s) for three-body interaction

    • +

  • cutoff_mb (float, np.ndarray) – cutoff(s) for coordination-based manybody interaction

    • +

  • nspec (int) – number of different species groups

    • +

  • spec_mask (np.ndarray) – 118-long integer array that determines specie group

    • +

  • nbond (int) – number of different hyperparameter sets to associate with two-body pairings

    • +

  • bond_mask (np.ndarray) – nspec^2 long integer array

    • +

  • ntriplet (int) – number of different hyperparameter sets to associate with 3-body pairings

    • +

  • triplet_mask (np.ndarray) – nspec^3 long integer array

    • +

  • ncut3b (int) – number of different 3-body cutoff sets to associate with 3-body pairings

    • +

  • cut3b_mask (np.ndarray) – nspec^2 long integer array

    • +

  • nmb (int) – number of different hyperparameter sets to associate with manybody pairings

    • +

  • mb_mask (np.ndarray) – nspec^2 long integer array

    • +

  • sig2 (np.ndarray) – signal variances associates with two-body term

    • +

  • ls2 (np.ndarray) – length scales associates with two-body term

    • +

  • sig3 (np.ndarray) – signal variances associates with three-body term

    • +

  • ls3 (np.ndarray) – length scales associates with three-body term

    • +

  • sigm (np.ndarray) – signal variances associates with manybody term

    • +

  • lsm (np.ndarray) – length scales associates with manybody term

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

Value of the 2+3+many-body force/energy kernel.

+
+
Return type
+

float

+
+
+
+ +

Implementation of three-body kernels using different cutoffs.

+

The kernels are slightly slower.

+
+
+flare.kernels.mc_3b_sepcut.three_body_mc_force_en_sepcut_jit(bond_array_1, c1, etypes1, bond_array_2, c2, etypes2, cross_bond_inds_1, cross_bond_inds_2, cross_bond_dists_1, cross_bond_dists_2, triplets_1, triplets_2, d1, sig, ls, r_cut, cutoff_func, nspec, spec_mask, triplet_mask, cut3b_mask)
+

Kernel for 3-body force/energy comparisons.

+
+ +
+
+flare.kernels.mc_3b_sepcut.three_body_mc_grad_sepcut_jit(bond_array_1, c1, etypes1, bond_array_2, c2, etypes2, cross_bond_inds_1, cross_bond_inds_2, cross_bond_dists_1, cross_bond_dists_2, triplets_1, triplets_2, d1, d2, sig, ls, r_cut, cutoff_func, nspec, spec_mask, ntriplet, triplet_mask, cut3b_mask)
+

Kernel gradient for 3-body force comparisons.

+
+ +

Implementation of three-body kernels using different cutoffs.

+

The kernels are slightly slower.

+
+
+flare.kernels.mc_mb_sepcut.many_body_mc_en_sepcut_jit(q_array_1, q_array_2, c1, c2, species1, species2, sig, ls, nspec, spec_mask, mb_mask)
+

many-body many-element kernel between energy components accelerated +with Numba.

+
+
Parameters
+
    +

  • bond_array_1 (np.ndarray) – many-body bond array of the first local +environment.

    • +

  • bond_array_2 (np.ndarray) – many-body bond array of the second local +environment.

    • +

  • c1 (int) – atomic species of the central atom in env 1

    • +

  • c2 (int) – atomic species of the central atom in env 2

    • +

  • etypes1 (np.ndarray) – atomic species of atoms in env 1

    • +

  • etypes2 (np.ndarray) – atomic species of atoms in env 2

    • +

  • species1 (np.ndarray) – all the atomic species present in trajectory 1

    • +

  • species2 (np.ndarray) – all the atomic species present in trajectory 2

    • +

  • sig (float) – many-body signal variance hyperparameter.

    • +

  • ls (float) – many-body length scale hyperparameter.

    • +

  • r_cut (float) – many-body cutoff radius.

    • +

  • cutoff_func (Callable) – Cutoff function.

    • +
+
+
Returns
+

Value of the many-body kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.mc_mb_sepcut.many_body_mc_force_en_sepcut_jit(q_array_1, q_array_2, q_neigh_array_1, q_neigh_grads_1, c1, c2, etypes1, species1, species2, d1, sig, ls, nspec, spec_mask, mb_mask)
+

many-body many-element kernel between force and energy components accelerated +with Numba.

+
+
Parameters
+
    +

  • To be complete

    • +

  • c1 (int) – atomic species of the central atom in env 1

    • +

  • c2 (int) – atomic species of the central atom in env 2

    • +

  • etypes1 (np.ndarray) – atomic species of atoms in env 1

    • +

  • species1 (np.ndarray) – all the atomic species present in trajectory 1

    • +

  • species2 (np.ndarray) – all the atomic species present in trajectory 2

    • +

  • d1 (int) – Force component of the first environment.

    • +

  • sig (float) – many-body signal variance hyperparameter.

    • +

  • ls (float) – many-body length scale hyperparameter.

    • +
+
+
Returns
+

Value of the many-body kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.mc_mb_sepcut.many_body_mc_grad_sepcut_jit(q_array_1, q_array_2, q_neigh_array_1, q_neigh_array_2, q_neigh_grads_1, q_neigh_grads_2, c1, c2, etypes1, etypes2, species1, species2, d1, d2, sig, ls, nspec, spec_mask, nmb, mb_mask)
+

gradient of many-body multi-element kernel between two force components +w.r.t. the hyperparameters, accelerated with Numba.

+
+
Parameters
+
    +

  • c1 (int) – atomic species of the central atom in env 1

    • +

  • c2 (int) – atomic species of the central atom in env 2

    • +

  • etypes1 (np.ndarray) – atomic species of atoms in env 1

    • +

  • etypes2 (np.ndarray) – atomic species of atoms in env 2

    • +

  • species1 (np.ndarray) – all the atomic species present in trajectory 1

    • +

  • species2 (np.ndarray) – all the atomic species present in trajectory 2

    • +

  • d1 (int) – Force component of the first environment.

    • +

  • d2 (int) – Force component of the second environment.

    • +

  • sig (float) – many-body signal variance hyperparameter.

    • +

  • ls (float) – many-body length scale hyperparameter.

    • +
+
+
Returns
+

Value of the many-body kernel and its gradient w.r.t. sig and ls

+
+
Return type
+

array

+
+
+
+ +
+
+flare.kernels.mc_mb_sepcut.many_body_mc_sepcut_jit(q_array_1, q_array_2, q_neigh_array_1, q_neigh_array_2, q_neigh_grads_1, q_neigh_grads_2, c1, c2, etypes1, etypes2, species1, species2, d1, d2, sig, ls, nspec, spec_mask, mb_mask)
+

many-body multi-element kernel between two force components accelerated +with Numba.

+
+
Parameters
+
    +

  • c1 (int) – atomic species of the central atom in env 1

    • +

  • c2 (int) – atomic species of the central atom in env 2

    • +

  • etypes1 (np.ndarray) – atomic species of atoms in env 1

    • +

  • etypes2 (np.ndarray) – atomic species of atoms in env 2

    • +

  • species1 (np.ndarray) – all the atomic species present in trajectory 1

    • +

  • species2 (np.ndarray) – all the atomic species present in trajectory 2

    • +

  • d1 (int) – Force component of the first environment.

    • +

  • d2 (int) – Force component of the second environment.

    • +

  • sig (float) – many-body signal variance hyperparameter.

    • +

  • ls (float) – many-body length scale hyperparameter.

    • +
+
+
Returns
+

Value of the many-body kernel.

+
+
Return type
+

float

+
+
+
+
diff --git a/flare/kernels/mc_simple.html b/flare/kernels/mc_simple.html index a3418fd7f..388b6b16b 100644 --- a/flare/kernels/mc_simple.html +++ b/flare/kernels/mc_simple.html @@ -98,8 +98,1429 @@
-
-

Multi-element Kernels (simple)

+
+

Multi-element Kernels (simple)

+

Multi-element 2-, 3-, and 2+3-body kernels that restrict all signal +variance hyperparameters to a single value.

+
+
+flare.kernels.mc_simple.many_body_mc(env1: AtomicEnvironment, env2: AtomicEnvironment, d1: int, d2: int, hyps: ndarray, cutoffs: ndarray, cutoff_func: Callable = numba.njit) → float
+

many-body multi-element kernel between two force components.

+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – First local environment.

    • +

  • env2 (AtomicEnvironment) – Second local environment.

    • +

  • d1 (int) – Force component of the first environment.

    • +

  • d2 (int) – Force component of the second environment.

    • +

  • hyps (np.ndarray) – Hyperparameters of the kernel function (sig, ls).

    • +

  • cutoffs (np.ndarray) – Two-element array containing the 2- and 3-body +cutoffs.

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

Value of the 3-body kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.mc_simple.many_body_mc_en(env1: AtomicEnvironment, env2: AtomicEnvironment, hyps: ndarray, cutoffs: ndarray, cutoff_func: Callable = numba.njit) → float
+

many-body multi-element kernel between two local energies.

+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – First local environment.

    • +

  • env2 (AtomicEnvironment) – Second local environment.

    • +

  • hyps (np.ndarray) – Hyperparameters of the kernel function (sig, ls).

    • +

  • cutoffs (np.ndarray) – One-element array containing the 2-body +cutoff.

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

Value of the 2-body force/energy kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.mc_simple.many_body_mc_en_jit(q_array_1, q_array_2, c1, c2, species1, species2, sig, ls)
+

many-body many-element kernel between energy components accelerated +with Numba.

+
+
Parameters
+
    +

  • bond_array_1 (np.ndarray) – many-body bond array of the first local +environment.

    • +

  • bond_array_2 (np.ndarray) – many-body bond array of the second local +environment.

    • +

  • c1 (int) – atomic species of the central atom in env 1

    • +

  • c2 (int) – atomic species of the central atom in env 2

    • +

  • etypes1 (np.ndarray) – atomic species of atoms in env 1

    • +

  • etypes2 (np.ndarray) – atomic species of atoms in env 2

    • +

  • species1 (np.ndarray) – all the atomic species present in trajectory 1

    • +

  • species2 (np.ndarray) – all the atomic species present in trajectory 2

    • +

  • sig (float) – many-body signal variance hyperparameter.

    • +

  • ls (float) – many-body length scale hyperparameter.

    • +

  • r_cut (float) – many-body cutoff radius.

    • +

  • cutoff_func (Callable) – Cutoff function.

    • +
+
+
Returns
+

Value of the many-body kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.mc_simple.many_body_mc_force_en(env1, env2, d1, hyps, cutoffs, cutoff_func=numba.njit)
+

many-body single-element kernel between two local energies.

+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – First local environment.

    • +

  • env2 (AtomicEnvironment) – Second local environment.

    • +

  • hyps (np.ndarray) – Hyperparameters of the kernel function (sig, ls).

    • +

  • cutoffs (np.ndarray) – Two-element array containing the 2-, 3-, and +many-body cutoffs.

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

Value of the many-body force/energy kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.mc_simple.many_body_mc_force_en_jit(q_array_1, q_array_2, q_neigh_array_1, q_neigh_grads_1, c1, c2, etypes1, species1, species2, d1, sig, ls)
+

many-body many-element kernel between force and energy components accelerated +with Numba.

+
+
Parameters
+
    +

  • c1 (int) – atomic species of the central atom in env 1

    • +

  • c2 (int) – atomic species of the central atom in env 2

    • +

  • etypes1 (np.ndarray) – atomic species of atoms in env 1

    • +

  • species1 (np.ndarray) – all the atomic species present in trajectory 1

    • +

  • species2 (np.ndarray) – all the atomic species present in trajectory 2

    • +

  • d1 (int) – Force component of the first environment.

    • +

  • sig (float) – many-body signal variance hyperparameter.

    • +

  • ls (float) – many-body length scale hyperparameter.

    • +
+
+
Returns
+

Value of the many-body kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.mc_simple.many_body_mc_grad(env1: AtomicEnvironment, env2: AtomicEnvironment, d1: int, d2: int, hyps: ndarray, cutoffs: ndarray, cutoff_func: Callable = numba.njit) → float
+

gradient manybody-body multi-element kernel between two force +components.

+
+ +
+
+flare.kernels.mc_simple.many_body_mc_grad_jit(q_array_1, q_array_2, q_neigh_array_1, q_neigh_array_2, q_neigh_grads_1, q_neigh_grads_2, c1, c2, etypes1, etypes2, species1, species2, d1, d2, sig, ls)
+

gradient of many-body multi-element kernel between two force components +w.r.t. the hyperparameters, accelerated with Numba.

+
+
Parameters
+
    +

  • bond_array_1 (np.ndarray) – many-body bond array of the first local +environment.

    • +

  • bond_array_2 (np.ndarray) – many-body bond array of the second local +environment.

    • +

  • neigh_dists_1 (np.ndarray) – matrix padded with zero values of distances +of neighbours for the atoms in the first local environment.

    • +

  • neigh_dists_2 (np.ndarray) – matrix padded with zero values of distances +of neighbours for the atoms in the second local environment.

    • +

  • num_neigh_1 (np.ndarray) – number of neighbours of each atom in the +first local environment

    • +

  • num_neigh_2 (np.ndarray) – number of neighbours of each atom in the +second local environment

    • +

  • c1 (int) – atomic species of the central atom in env 1

    • +

  • c2 (int) – atomic species of the central atom in env 2

    • +

  • etypes1 (np.ndarray) – atomic species of atoms in env 1

    • +

  • etypes2 (np.ndarray) – atomic species of atoms in env 2

    • +

  • etypes_neigh_1 (np.ndarray) – atomic species of atoms in the +neighbourhoods of atoms in env 1

    • +

  • etypes_neigh_2 (np.ndarray) – atomic species of atoms in the +neighbourhoods of atoms in env 2

    • +

  • species1 (np.ndarray) – all the atomic species present in trajectory 1

    • +

  • species2 (np.ndarray) – all the atomic species present in trajectory 2

    • +

  • d1 (int) – Force component of the first environment.

    • +

  • d2 (int) – Force component of the second environment.

    • +

  • sig (float) – many-body signal variance hyperparameter.

    • +

  • ls (float) – many-body length scale hyperparameter.

    • +

  • r_cut (float) – many-body cutoff radius.

    • +

  • cutoff_func (Callable) – Cutoff function.

    • +
+
+
Returns
+

Value of the many-body kernel and its gradient w.r.t. sig and ls

+
+
Return type
+

array

+
+
+
+ +
+
+flare.kernels.mc_simple.many_body_mc_jit(q_array_1, q_array_2, q_neigh_array_1, q_neigh_array_2, q_neigh_grads_1, q_neigh_grads_2, c1, c2, etypes1, etypes2, species1, species2, d1, d2, sig, ls)
+

many-body multi-element kernel between two force components accelerated +with Numba.

+
+
Parameters
+
    +

  • bond_array_1 (np.ndarray) – many-body bond array of the first local +environment.

    • +

  • bond_array_2 (np.ndarray) – many-body bond array of the second local +environment.

    • +

  • neigh_dists_1 (np.ndarray) – matrix padded with zero values of distances +of neighbours for the atoms in the first local environment.

    • +

  • neigh_dists_2 (np.ndarray) – matrix padded with zero values of distances +of neighbours for the atoms in the second local environment.

    • +

  • num_neigh_1 (np.ndarray) – number of neighbours of each atom in the +first local environment

    • +

  • num_neigh_2 (np.ndarray) – number of neighbours of each atom in the +second local environment

    • +

  • c1 (int) – atomic species of the central atom in env 1

    • +

  • c2 (int) – atomic species of the central atom in env 2

    • +

  • etypes1 (np.ndarray) – atomic species of atoms in env 1

    • +

  • etypes2 (np.ndarray) – atomic species of atoms in env 2

    • +

  • etypes_neigh_1 (np.ndarray) – atomic species of atoms in the +neighbourhoods of atoms in env 1

    • +

  • etypes_neigh_2 (np.ndarray) – atomic species of atoms in the +neighbourhoods of atoms in env 2

    • +

  • species1 (np.ndarray) – all the atomic species present in trajectory 1

    • +

  • species2 (np.ndarray) – all the atomic species present in trajectory 2

    • +

  • d1 (int) – Force component of the first environment.

    • +

  • d2 (int) – Force component of the second environment.

    • +

  • sig (float) – many-body signal variance hyperparameter.

    • +

  • ls (float) – many-body length scale hyperparameter.

    • +

  • cutoff_func (Callable) – Cutoff function.

    • +
+
+
Returns
+

Value of the many-body kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.mc_simple.three_body_mc(env1: AtomicEnvironment, env2: AtomicEnvironment, d1: int, d2: int, hyps: ndarray, cutoffs: ndarray, cutoff_func: Callable = numba.njit) → float
+

3-body multi-element kernel between two force components.

+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – First local environment.

    • +

  • env2 (AtomicEnvironment) – Second local environment.

    • +

  • d1 (int) – Force component of the first environment.

    • +

  • d2 (int) – Force component of the second environment.

    • +

  • hyps (np.ndarray) – Hyperparameters of the kernel function (sig, ls).

    • +

  • cutoffs (np.ndarray) – Two-element array containing the 2- and 3-body +cutoffs.

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

Value of the 3-body kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.mc_simple.three_body_mc_en(env1: AtomicEnvironment, env2: AtomicEnvironment, hyps: ndarray, cutoffs: ndarray, cutoff_func: Callable = numba.njit) → float
+

3-body multi-element kernel between two local energies.

+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – First local environment.

    • +

  • env2 (AtomicEnvironment) – Second local environment.

    • +

  • hyps (np.ndarray) – Hyperparameters of the kernel function (sig, ls).

    • +

  • cutoffs (np.ndarray) – Two-element array containing the 2- and 3-body +cutoffs.

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

Value of the 3-body force/energy kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.mc_simple.three_body_mc_en_jit(bond_array_1, c1, etypes1, bond_array_2, c2, etypes2, cross_bond_inds_1, cross_bond_inds_2, cross_bond_dists_1, cross_bond_dists_2, triplets_1, triplets_2, sig, ls, r_cut, cutoff_func)
+

3-body multi-element kernel between two local energies accelerated +with Numba.

+
+
Parameters
+
    +

  • bond_array_1 (np.ndarray) – 3-body bond array of the first local +environment.

    • +

  • c1 (int) – Species of the central atom of the first local environment.

    • +

  • etypes1 (np.ndarray) – Species of atoms in the first local +environment.

    • +

  • bond_array_2 (np.ndarray) – 3-body bond array of the second local +environment.

    • +

  • c2 (int) – Species of the central atom of the second local environment.

    • +

  • etypes2 (np.ndarray) – Species of atoms in the second local +environment.

    • +

  • cross_bond_inds_1 (np.ndarray) – Two dimensional array whose row m +contains the indices of atoms n > m in the first local +environment that are within a distance r_cut of both atom n and +the central atom.

    • +

  • cross_bond_inds_2 (np.ndarray) – Two dimensional array whose row m +contains the indices of atoms n > m in the second local +environment that are within a distance r_cut of both atom n and +the central atom.

    • +

  • cross_bond_dists_1 (np.ndarray) – Two dimensional array whose row m +contains the distances from atom m of atoms n > m in the first +local environment that are within a distance r_cut of both atom +n and the central atom.

    • +

  • cross_bond_dists_2 (np.ndarray) – Two dimensional array whose row m +contains the distances from atom m of atoms n > m in the second +local environment that are within a distance r_cut of both atom +n and the central atom.

    • +

  • triplets_1 (np.ndarray) – One dimensional array of integers whose entry +m is the number of atoms in the first local environment that are +within a distance r_cut of atom m.

    • +

  • triplets_2 (np.ndarray) – One dimensional array of integers whose entry +m is the number of atoms in the second local environment that are +within a distance r_cut of atom m.

    • +

  • sig (float) – 3-body signal variance hyperparameter.

    • +

  • ls (float) – 3-body length scale hyperparameter.

    • +

  • r_cut (float) – 3-body cutoff radius.

    • +

  • cutoff_func (Callable) – Cutoff function.

    • +
+
+
Returns
+

Value of the 3-body local energy kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.mc_simple.three_body_mc_force_en(env1: AtomicEnvironment, env2: AtomicEnvironment, d1: int, hyps: ndarray, cutoffs: ndarray, cutoff_func: Callable = numba.njit) → float
+

3-body multi-element kernel between a force component and a local +energy.

+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – Local environment associated with the +force component.

    • +

  • env2 (AtomicEnvironment) – Local environment associated with the +local energy.

    • +

  • d1 (int) – Force component of the first environment.

    • +

  • hyps (np.ndarray) – Hyperparameters of the kernel function (sig, ls).

    • +

  • cutoffs (np.ndarray) – Two-element array containing the 2- and 3-body +cutoffs.

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

Value of the 3-body force/energy kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.mc_simple.three_body_mc_force_en_jit(bond_array_1, c1, etypes1, bond_array_2, c2, etypes2, cross_bond_inds_1, cross_bond_inds_2, cross_bond_dists_1, cross_bond_dists_2, triplets_1, triplets_2, d1, sig, ls, r_cut, cutoff_func)
+

3-body multi-element kernel between a force component and a local +energy accelerated with Numba.

+
+
Parameters
+
    +

  • bond_array_1 (np.ndarray) – 3-body bond array of the first local +environment.

    • +

  • c1 (int) – Species of the central atom of the first local environment.

    • +

  • etypes1 (np.ndarray) – Species of atoms in the first local +environment.

    • +

  • bond_array_2 (np.ndarray) – 3-body bond array of the second local +environment.

    • +

  • c2 (int) – Species of the central atom of the second local environment.

    • +

  • etypes2 (np.ndarray) – Species of atoms in the second local +environment.

    • +

  • cross_bond_inds_1 (np.ndarray) – Two dimensional array whose row m +contains the indices of atoms n > m in the first local +environment that are within a distance r_cut of both atom n and +the central atom.

    • +

  • cross_bond_inds_2 (np.ndarray) – Two dimensional array whose row m +contains the indices of atoms n > m in the second local +environment that are within a distance r_cut of both atom n and +the central atom.

    • +

  • cross_bond_dists_1 (np.ndarray) – Two dimensional array whose row m +contains the distances from atom m of atoms n > m in the first +local environment that are within a distance r_cut of both atom +n and the central atom.

    • +

  • cross_bond_dists_2 (np.ndarray) – Two dimensional array whose row m +contains the distances from atom m of atoms n > m in the second +local environment that are within a distance r_cut of both atom +n and the central atom.

    • +

  • triplets_1 (np.ndarray) – One dimensional array of integers whose entry +m is the number of atoms in the first local environment that are +within a distance r_cut of atom m.

    • +

  • triplets_2 (np.ndarray) – One dimensional array of integers whose entry +m is the number of atoms in the second local environment that are +within a distance r_cut of atom m.

    • +

  • d1 (int) – Force component of the first environment (1=x, 2=y, 3=z).

    • +

  • sig (float) – 3-body signal variance hyperparameter.

    • +

  • ls (float) – 3-body length scale hyperparameter.

    • +

  • r_cut (float) – 3-body cutoff radius.

    • +

  • cutoff_func (Callable) – Cutoff function.

    • +
+
+
Returns
+

Value of the 3-body force/energy kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.mc_simple.three_body_mc_grad(env1: AtomicEnvironment, env2: AtomicEnvironment, d1: int, d2: int, hyps: ndarray, cutoffs: ndarray, cutoff_func: Callable = numba.njit)
+

3-body multi-element kernel between two force components and its +gradient with respect to the hyperparameters.

+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – First local environment.

    • +

  • env2 (AtomicEnvironment) – Second local environment.

    • +

  • d1 (int) – Force component of the first environment.

    • +

  • d2 (int) – Force component of the second environment.

    • +

  • hyps (np.ndarray) – Hyperparameters of the kernel function (sig, ls).

    • +

  • cutoffs (np.ndarray) – Two-element array containing the 2- and 3-body +cutoffs.

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

Value of the 3-body kernel and its gradient with respect to the +hyperparameters.

+
+
Return type
+

(float, np.ndarray)

+
+
+
+ +
+
+flare.kernels.mc_simple.three_body_mc_grad_jit(bond_array_1, c1, etypes1, bond_array_2, c2, etypes2, cross_bond_inds_1, cross_bond_inds_2, cross_bond_dists_1, cross_bond_dists_2, triplets_1, triplets_2, d1, d2, sig, ls, r_cut, cutoff_func)
+

3-body multi-element kernel between two force components and its +gradient with respect to the hyperparameters.

+
+
Parameters
+
    +

  • bond_array_1 (np.ndarray) – 3-body bond array of the first local +environment.

    • +

  • c1 (int) – Species of the central atom of the first local environment.

    • +

  • etypes1 (np.ndarray) – Species of atoms in the first local +environment.

    • +

  • bond_array_2 (np.ndarray) – 3-body bond array of the second local +environment.

    • +

  • c2 (int) – Species of the central atom of the second local environment.

    • +

  • etypes2 (np.ndarray) – Species of atoms in the second local +environment.

    • +

  • cross_bond_inds_1 (np.ndarray) – Two dimensional array whose row m +contains the indices of atoms n > m in the first local +environment that are within a distance r_cut of both atom n and +the central atom.

    • +

  • cross_bond_inds_2 (np.ndarray) – Two dimensional array whose row m +contains the indices of atoms n > m in the second local +environment that are within a distance r_cut of both atom n and +the central atom.

    • +

  • cross_bond_dists_1 (np.ndarray) – Two dimensional array whose row m +contains the distances from atom m of atoms n > m in the first +local environment that are within a distance r_cut of both atom +n and the central atom.

    • +

  • cross_bond_dists_2 (np.ndarray) – Two dimensional array whose row m +contains the distances from atom m of atoms n > m in the second +local environment that are within a distance r_cut of both atom +n and the central atom.

    • +

  • triplets_1 (np.ndarray) – One dimensional array of integers whose entry +m is the number of atoms in the first local environment that are +within a distance r_cut of atom m.

    • +

  • triplets_2 (np.ndarray) – One dimensional array of integers whose entry +m is the number of atoms in the second local environment that are +within a distance r_cut of atom m.

    • +

  • d1 (int) – Force component of the first environment.

    • +

  • d2 (int) – Force component of the second environment.

    • +

  • sig (float) – 3-body signal variance hyperparameter.

    • +

  • ls (float) – 3-body length scale hyperparameter.

    • +

  • r_cut (float) – 3-body cutoff radius.

    • +

  • cutoff_func (Callable) – Cutoff function.

    • +
+
+
Returns
+

Value of the 3-body kernel and its gradient with respect to the +hyperparameters.

+
+
Return type
+

(float, float)

+
+
+
+ +
+
+flare.kernels.mc_simple.three_body_mc_jit(bond_array_1, c1, etypes1, bond_array_2, c2, etypes2, cross_bond_inds_1, cross_bond_inds_2, cross_bond_dists_1, cross_bond_dists_2, triplets_1, triplets_2, d1, d2, sig, ls, r_cut, cutoff_func)
+

3-body multi-element kernel between two force components accelerated +with Numba.

+
+
Parameters
+
    +

  • bond_array_1 (np.ndarray) – 3-body bond array of the first local +environment.

    • +

  • c1 (int) – Species of the central atom of the first local environment.

    • +

  • etypes1 (np.ndarray) – Species of atoms in the first local +environment.

    • +

  • bond_array_2 (np.ndarray) – 3-body bond array of the second local +environment.

    • +

  • c2 (int) – Species of the central atom of the second local environment.

    • +

  • etypes2 (np.ndarray) – Species of atoms in the second local +environment.

    • +

  • cross_bond_inds_1 (np.ndarray) – Two dimensional array whose row m +contains the indices of atoms n > m in the first local +environment that are within a distance r_cut of both atom n and +the central atom.

    • +

  • cross_bond_inds_2 (np.ndarray) – Two dimensional array whose row m +contains the indices of atoms n > m in the second local +environment that are within a distance r_cut of both atom n and +the central atom.

    • +

  • cross_bond_dists_1 (np.ndarray) – Two dimensional array whose row m +contains the distances from atom m of atoms n > m in the first +local environment that are within a distance r_cut of both atom +n and the central atom.

    • +

  • cross_bond_dists_2 (np.ndarray) – Two dimensional array whose row m +contains the distances from atom m of atoms n > m in the second +local environment that are within a distance r_cut of both atom +n and the central atom.

    • +

  • triplets_1 (np.ndarray) – One dimensional array of integers whose entry +m is the number of atoms in the first local environment that are +within a distance r_cut of atom m.

    • +

  • triplets_2 (np.ndarray) – One dimensional array of integers whose entry +m is the number of atoms in the second local environment that are +within a distance r_cut of atom m.

    • +

  • d1 (int) – Force component of the first environment.

    • +

  • d2 (int) – Force component of the second environment.

    • +

  • sig (float) – 3-body signal variance hyperparameter.

    • +

  • ls (float) – 3-body length scale hyperparameter.

    • +

  • r_cut (float) – 3-body cutoff radius.

    • +

  • cutoff_func (Callable) – Cutoff function.

    • +
+
+
Returns
+

Value of the 3-body kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.mc_simple.three_body_se_jit(bond_array_1, c1, etypes1, bond_array_2, c2, etypes2, cross_bond_inds_1, cross_bond_inds_2, cross_bond_dists_1, cross_bond_dists_2, triplets_1, triplets_2, sig, ls, r_cut, cutoff_func)
+

3-body multi-element kernel between a force component and a local +energy accelerated with Numba.

+
+
Parameters
+
    +

  • bond_array_1 (np.ndarray) – 3-body bond array of the first local +environment.

    • +

  • c1 (int) – Species of the central atom of the first local environment.

    • +

  • etypes1 (np.ndarray) – Species of atoms in the first local +environment.

    • +

  • bond_array_2 (np.ndarray) – 3-body bond array of the second local +environment.

    • +

  • c2 (int) – Species of the central atom of the second local environment.

    • +

  • etypes2 (np.ndarray) – Species of atoms in the second local +environment.

    • +

  • cross_bond_inds_1 (np.ndarray) – Two dimensional array whose row m +contains the indices of atoms n > m in the first local +environment that are within a distance r_cut of both atom n and +the central atom.

    • +

  • cross_bond_inds_2 (np.ndarray) – Two dimensional array whose row m +contains the indices of atoms n > m in the second local +environment that are within a distance r_cut of both atom n and +the central atom.

    • +

  • cross_bond_dists_1 (np.ndarray) – Two dimensional array whose row m +contains the distances from atom m of atoms n > m in the first +local environment that are within a distance r_cut of both atom +n and the central atom.

    • +

  • cross_bond_dists_2 (np.ndarray) – Two dimensional array whose row m +contains the distances from atom m of atoms n > m in the second +local environment that are within a distance r_cut of both atom +n and the central atom.

    • +

  • triplets_1 (np.ndarray) – One dimensional array of integers whose entry +m is the number of atoms in the first local environment that are +within a distance r_cut of atom m.

    • +

  • triplets_2 (np.ndarray) – One dimensional array of integers whose entry +m is the number of atoms in the second local environment that are +within a distance r_cut of atom m.

    • +

  • sig (float) – 3-body signal variance hyperparameter.

    • +

  • ls (float) – 3-body length scale hyperparameter.

    • +

  • r_cut (float) – 3-body cutoff radius.

    • +

  • cutoff_func (Callable) – Cutoff function.

    • +
+
+
Returns
+

Value of the 3-body force/energy kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.mc_simple.three_body_sf_jit(bond_array_1, c1, etypes1, bond_array_2, c2, etypes2, cross_bond_inds_1, cross_bond_inds_2, cross_bond_dists_1, cross_bond_dists_2, triplets_1, triplets_2, sig, ls, r_cut, cutoff_func)
+

3-body multi-element kernel between two force components accelerated +with Numba.

+
+
Parameters
+
    +

  • bond_array_1 (np.ndarray) – 3-body bond array of the first local +environment.

    • +

  • c1 (int) – Species of the central atom of the first local environment.

    • +

  • etypes1 (np.ndarray) – Species of atoms in the first local +environment.

    • +

  • bond_array_2 (np.ndarray) – 3-body bond array of the second local +environment.

    • +

  • c2 (int) – Species of the central atom of the second local environment.

    • +

  • etypes2 (np.ndarray) – Species of atoms in the second local +environment.

    • +

  • cross_bond_inds_1 (np.ndarray) – Two dimensional array whose row m +contains the indices of atoms n > m in the first local +environment that are within a distance r_cut of both atom n and +the central atom.

    • +

  • cross_bond_inds_2 (np.ndarray) – Two dimensional array whose row m +contains the indices of atoms n > m in the second local +environment that are within a distance r_cut of both atom n and +the central atom.

    • +

  • cross_bond_dists_1 (np.ndarray) – Two dimensional array whose row m +contains the distances from atom m of atoms n > m in the first +local environment that are within a distance r_cut of both atom +n and the central atom.

    • +

  • cross_bond_dists_2 (np.ndarray) – Two dimensional array whose row m +contains the distances from atom m of atoms n > m in the second +local environment that are within a distance r_cut of both atom +n and the central atom.

    • +

  • triplets_1 (np.ndarray) – One dimensional array of integers whose entry +m is the number of atoms in the first local environment that are +within a distance r_cut of atom m.

    • +

  • triplets_2 (np.ndarray) – One dimensional array of integers whose entry +m is the number of atoms in the second local environment that are +within a distance r_cut of atom m.

    • +

  • sig (float) – 3-body signal variance hyperparameter.

    • +

  • ls (float) – 3-body length scale hyperparameter.

    • +

  • r_cut (float) – 3-body cutoff radius.

    • +

  • cutoff_func (Callable) – Cutoff function.

    • +
+
+
Returns
+

Value of the 3-body kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.mc_simple.three_body_ss_jit(bond_array_1, c1, etypes1, bond_array_2, c2, etypes2, cross_bond_inds_1, cross_bond_inds_2, cross_bond_dists_1, cross_bond_dists_2, triplets_1, triplets_2, sig, ls, r_cut, cutoff_func)
+

3-body multi-element kernel between two force components accelerated +with Numba.

+
+
Parameters
+
    +

  • bond_array_1 (np.ndarray) – 3-body bond array of the first local +environment.

    • +

  • c1 (int) – Species of the central atom of the first local environment.

    • +

  • etypes1 (np.ndarray) – Species of atoms in the first local +environment.

    • +

  • bond_array_2 (np.ndarray) – 3-body bond array of the second local +environment.

    • +

  • c2 (int) – Species of the central atom of the second local environment.

    • +

  • etypes2 (np.ndarray) – Species of atoms in the second local +environment.

    • +

  • cross_bond_inds_1 (np.ndarray) – Two dimensional array whose row m +contains the indices of atoms n > m in the first local +environment that are within a distance r_cut of both atom n and +the central atom.

    • +

  • cross_bond_inds_2 (np.ndarray) – Two dimensional array whose row m +contains the indices of atoms n > m in the second local +environment that are within a distance r_cut of both atom n and +the central atom.

    • +

  • cross_bond_dists_1 (np.ndarray) – Two dimensional array whose row m +contains the distances from atom m of atoms n > m in the first +local environment that are within a distance r_cut of both atom +n and the central atom.

    • +

  • cross_bond_dists_2 (np.ndarray) – Two dimensional array whose row m +contains the distances from atom m of atoms n > m in the second +local environment that are within a distance r_cut of both atom +n and the central atom.

    • +

  • triplets_1 (np.ndarray) – One dimensional array of integers whose entry +m is the number of atoms in the first local environment that are +within a distance r_cut of atom m.

    • +

  • triplets_2 (np.ndarray) – One dimensional array of integers whose entry +m is the number of atoms in the second local environment that are +within a distance r_cut of atom m.

    • +

  • sig (float) – 3-body signal variance hyperparameter.

    • +

  • ls (float) – 3-body length scale hyperparameter.

    • +

  • r_cut (float) – 3-body cutoff radius.

    • +

  • cutoff_func (Callable) – Cutoff function.

    • +
+
+
Returns
+

Value of the 3-body kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.mc_simple.two_body_mc(env1: AtomicEnvironment, env2: AtomicEnvironment, d1: int, d2: int, hyps: ndarray, cutoffs: ndarray, cutoff_func: Callable = numba.njit) → float
+

2-body multi-element kernel between two force components.

+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – First local environment.

    • +

  • env2 (AtomicEnvironment) – Second local environment.

    • +

  • d1 (int) – Force component of the first environment.

    • +

  • d2 (int) – Force component of the second environment.

    • +

  • hyps (np.ndarray) – Hyperparameters of the kernel function (sig, ls).

    • +

  • cutoffs (np.ndarray) – One-element array containing the 2-body +cutoff.

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

Value of the 2-body kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.mc_simple.two_body_mc_en(env1: AtomicEnvironment, env2: AtomicEnvironment, hyps: ndarray, cutoffs: ndarray, cutoff_func: Callable = numba.njit) → float
+

2-body multi-element kernel between two local energies.

+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – First local environment.

    • +

  • env2 (AtomicEnvironment) – Second local environment.

    • +

  • hyps (np.ndarray) – Hyperparameters of the kernel function (sig, ls).

    • +

  • cutoffs (np.ndarray) – One-element array containing the 2-body +cutoff.

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

Value of the 2-body force/energy kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.mc_simple.two_body_mc_en_jit(bond_array_1, c1, etypes1, bond_array_2, c2, etypes2, sig, ls, r_cut, cutoff_func)
+

2-body multi-element kernel between two local energies accelerated +with Numba.

+
+
Parameters
+
    +

  • bond_array_1 (np.ndarray) – 2-body bond array of the first local +environment.

    • +

  • c1 (int) – Species of the central atom of the first local environment.

    • +

  • etypes1 (np.ndarray) – Species of atoms in the first local +environment.

    • +

  • bond_array_2 (np.ndarray) – 2-body bond array of the second local +environment.

    • +

  • c2 (int) – Species of the central atom of the second local environment.

    • +

  • etypes2 (np.ndarray) – Species of atoms in the second local +environment.

    • +

  • sig (float) – 2-body signal variance hyperparameter.

    • +

  • ls (float) – 2-body length scale hyperparameter.

    • +

  • r_cut (float) – 2-body cutoff radius.

    • +

  • cutoff_func (Callable) – Cutoff function.

    • +
+
+
Returns
+

Value of the 2-body local energy kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.mc_simple.two_body_mc_force_en(env1: AtomicEnvironment, env2: AtomicEnvironment, d1: int, hyps: ndarray, cutoffs: ndarray, cutoff_func: Callable = numba.njit) → float
+

2-body multi-element kernel between a force component and a local +energy.

+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – Local environment associated with the +force component.

    • +

  • env2 (AtomicEnvironment) – Local environment associated with the +local energy.

    • +

  • d1 (int) – Force component of the first environment.

    • +

  • hyps (np.ndarray) – Hyperparameters of the kernel function (sig, ls).

    • +

  • cutoffs (np.ndarray) – One-element array containing the 2-body +cutoff.

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

Value of the 2-body force/energy kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.mc_simple.two_body_mc_force_en_jit(bond_array_1, c1, etypes1, bond_array_2, c2, etypes2, d1, sig, ls, r_cut, cutoff_func)
+

2-body multi-element kernel between a force component and a local +energy accelerated with Numba.

+
+
Parameters
+
    +

  • bond_array_1 (np.ndarray) – 2-body bond array of the first local +environment.

    • +

  • c1 (int) – Species of the central atom of the first local environment.

    • +

  • etypes1 (np.ndarray) – Species of atoms in the first local +environment.

    • +

  • bond_array_2 (np.ndarray) – 2-body bond array of the second local +environment.

    • +

  • c2 (int) – Species of the central atom of the second local environment.

    • +

  • etypes2 (np.ndarray) – Species of atoms in the second local +environment.

    • +

  • d1 (int) – Force component of the first environment (1=x, 2=y, 3=z).

    • +

  • sig (float) – 2-body signal variance hyperparameter.

    • +

  • ls (float) – 2-body length scale hyperparameter.

    • +

  • r_cut (float) – 2-body cutoff radius.

    • +

  • cutoff_func (Callable) – Cutoff function.

    • +
+
+
Returns
+

Value of the 2-body force/energy kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.mc_simple.two_body_mc_grad(env1: ~flare.descriptors.env.AtomicEnvironment, env2: ~flare.descriptors.env.AtomicEnvironment, d1: int, d2: int, hyps: ndarray, cutoffs: ndarray, cutoff_func: ~typing.Callable = numba.njit) -> (<class 'float'>, 'ndarray')
+

2-body multi-element kernel between two force components and its +gradient with respect to the hyperparameters.

+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – First local environment.

    • +

  • env2 (AtomicEnvironment) – Second local environment.

    • +

  • d1 (int) – Force component of the first environment.

    • +

  • d2 (int) – Force component of the second environment.

    • +

  • hyps (np.ndarray) – Hyperparameters of the kernel function (sig, ls).

    • +

  • cutoffs (np.ndarray) – One-element array containing the 2-body +cutoff.

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

Value of the 2-body kernel and its gradient with respect to the +hyperparameters.

+
+
Return type
+

(float, np.ndarray)

+
+
+
+ +
+
+flare.kernels.mc_simple.two_body_mc_grad_jit(bond_array_1, c1, etypes1, bond_array_2, c2, etypes2, d1, d2, sig, ls, r_cut, cutoff_func)
+

2-body multi-element kernel between two force components and its +gradient with respect to the hyperparameters.

+
+
Parameters
+
    +

  • bond_array_1 (np.ndarray) – 2-body bond array of the first local +environment.

    • +

  • c1 (int) – Species of the central atom of the first local environment.

    • +

  • etypes1 (np.ndarray) – Species of atoms in the first local +environment.

    • +

  • bond_array_2 (np.ndarray) – 2-body bond array of the second local +environment.

    • +

  • c2 (int) – Species of the central atom of the second local environment.

    • +

  • etypes2 (np.ndarray) – Species of atoms in the second local +environment.

    • +

  • d1 (int) – Force component of the first environment (1=x, 2=y, 3=z).

    • +

  • d2 (int) – Force component of the second environment (1=x, 2=y, 3=z).

    • +

  • sig (float) – 2-body signal variance hyperparameter.

    • +

  • ls (float) – 2-body length scale hyperparameter.

    • +

  • r_cut (float) – 2-body cutoff radius.

    • +

  • cutoff_func (Callable) – Cutoff function.

    • +
+
+
Returns
+

Value of the 2-body kernel and its gradient with respect to the +hyperparameters.

+
+
Return type
+

(float, float)

+
+
+
+ +
+
+flare.kernels.mc_simple.two_body_mc_jit(bond_array_1, c1, etypes1, bond_array_2, c2, etypes2, d1, d2, sig, ls, r_cut, cutoff_func)
+

2-body multi-element kernel between two force components accelerated +with Numba.

+
+
Parameters
+
    +

  • bond_array_1 (np.ndarray) – 2-body bond array of the first local +environment.

    • +

  • c1 (int) – Species of the central atom of the first local environment.

    • +

  • etypes1 (np.ndarray) – Species of atoms in the first local +environment.

    • +

  • bond_array_2 (np.ndarray) – 2-body bond array of the second local +environment.

    • +

  • c2 (int) – Species of the central atom of the second local environment.

    • +

  • etypes2 (np.ndarray) – Species of atoms in the second local +environment.

    • +

  • d1 (int) – Force component of the first environment (1=x, 2=y, 3=z).

    • +

  • d2 (int) – Force component of the second environment (1=x, 2=y, 3=z).

    • +

  • sig (float) – 2-body signal variance hyperparameter.

    • +

  • ls (float) – 2-body length scale hyperparameter.

    • +

  • r_cut (float) – 2-body cutoff radius.

    • +

  • cutoff_func (Callable) – Cutoff function.

    • +
+
+
Returns
+

Value of the 2-body kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.mc_simple.two_body_mc_stress_en_jit(bond_array_1, c1, etypes1, bond_array_2, c2, etypes2, d1, d2, sig, ls, r_cut, cutoff_func)
+

2-body multi-element kernel between a partial stress component and a +local energy accelerated with Numba.

+
+
Parameters
+
    +

  • bond_array_1 (np.ndarray) – 2-body bond array of the first local +environment.

    • +

  • c1 (int) – Species of the central atom of the first local environment.

    • +

  • etypes1 (np.ndarray) – Species of atoms in the first local +environment.

    • +

  • bond_array_2 (np.ndarray) – 2-body bond array of the second local +environment.

    • +

  • c2 (int) – Species of the central atom of the second local environment.

    • +

  • etypes2 (np.ndarray) – Species of atoms in the second local +environment.

    • +

  • d1 (int) – First stress component of the first environment (1=x, 2=y, +3=z).

    • +

  • d2 (int) – Second stress component of the first environment (1=x, 2=y, +3=z).

    • +

  • sig (float) – 2-body signal variance hyperparameter.

    • +

  • ls (float) – 2-body length scale hyperparameter.

    • +

  • r_cut (float) – 2-body cutoff radius.

    • +

  • cutoff_func (Callable) – Cutoff function.

    • +
+
+
Returns
+

Value of the 2-body partial-stress/energy kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.mc_simple.two_body_mc_stress_force_jit(bond_array_1, c1, etypes1, bond_array_2, c2, etypes2, d1, d2, d3, sig, ls, r_cut, cutoff_func)
+

2-body multi-element kernel between two force components accelerated +with Numba.

+
+
Parameters
+
    +

  • bond_array_1 (np.ndarray) – 2-body bond array of the first local +environment.

    • +

  • c1 (int) – Species of the central atom of the first local environment.

    • +

  • etypes1 (np.ndarray) – Species of atoms in the first local +environment.

    • +

  • bond_array_2 (np.ndarray) – 2-body bond array of the second local +environment.

    • +

  • c2 (int) – Species of the central atom of the second local environment.

    • +

  • etypes2 (np.ndarray) – Species of atoms in the second local +environment.

    • +

  • d1 (int) – First stress component of the first environment (1=x, 2=y, +3=z).

    • +

  • d2 (int) – Second stress component of the first environment (1=x, 2=y, +3=z).

    • +

  • d3 (int) – Force component of the second environment (1=x, 2=y, 3=z).

    • +

  • sig (float) – 2-body signal variance hyperparameter.

    • +

  • ls (float) – 2-body length scale hyperparameter.

    • +

  • r_cut (float) – 2-body cutoff radius.

    • +

  • cutoff_func (Callable) – Cutoff function.

    • +
+
+
Returns
+

Value of the 2-body kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.mc_simple.two_body_mc_stress_stress_jit(bond_array_1, c1, etypes1, bond_array_2, c2, etypes2, d1, d2, d3, d4, sig, ls, r_cut, cutoff_func)
+
+
2-body multi-element kernel between two partial stress components

accelerated with Numba.

+
+
+
+
Parameters
+
    +

  • bond_array_1 (np.ndarray) – 2-body bond array of the first local +environment.

    • +

  • c1 (int) – Species of the central atom of the first local environment.

    • +

  • etypes1 (np.ndarray) – Species of atoms in the first local +environment.

    • +

  • bond_array_2 (np.ndarray) – 2-body bond array of the second local +environment.

    • +

  • c2 (int) – Species of the central atom of the second local environment.

    • +

  • etypes2 (np.ndarray) – Species of atoms in the second local +environment.

    • +

  • d1 (int) – First stress component of the first environment (1=x, 2=y, +3=z).

    • +

  • d2 (int) – Second stress component of the first environment (1=x, 2=y, +3=z).

    • +

  • d3 (int) – First stress component of the second environment (1=x, 2=y, +3=z).

    • +

  • d4 (int) – Second stress component of the second environment (1=x, 2=y, +3=z).

    • +

  • sig (float) – 2-body signal variance hyperparameter.

    • +

  • ls (float) – 2-body length scale hyperparameter.

    • +

  • r_cut (float) – 2-body cutoff radius.

    • +

  • cutoff_func (Callable) – Cutoff function.

    • +
+
+
Returns
+

Value of the 2-body kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.mc_simple.two_plus_many_body_mc(env1: AtomicEnvironment, env2: AtomicEnvironment, d1: int, d2: int, hyps, cutoffs, cutoff_func=numba.njit)
+

2+many body kernel.

+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – First local environment.

    • +

  • env2 (AtomicEnvironment) – Second local environment.

    • +

  • d1 (int) – Force component of the first environment.

    • +

  • d2 (int) – Force component of the second environment.

    • +

  • hyps (np.ndarray) – Hyperparameters of the kernel function (sig2b, ls2b, +sigmb, lsmb, sig_n).

    • +

  • cutoffs (np.ndarray) – Two-element array containing the 2- and many-body +cutoffs.

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

Value of the 2+3+many-body kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.mc_simple.two_plus_many_body_mc_en(env1: AtomicEnvironment, env2: AtomicEnvironment, hyps, cutoffs, cutoff_func=numba.njit)
+

2+3+many-body single-element energy kernel.

+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – First local environment.

    • +

  • env2 (AtomicEnvironment) – Second local environment.

    • +

  • hyps (np.ndarray) – Hyperparameters of the kernel function (sig2b ls2b, +sigmb, lsmb, sig_n).

    • +

  • cutoffs (np.ndarray) – Two-element array containing the 2- and 3-body +cutoffs.

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

Value of the 2+3+many-body kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.mc_simple.two_plus_many_body_mc_force_en(env1: AtomicEnvironment, env2: AtomicEnvironment, d1: int, hyps, cutoffs, cutoff_func=numba.njit)
+
+
2+many-body multi-element kernel between two force and energy

components.

+
+
+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – First local environment.

    • +

  • env2 (AtomicEnvironment) – Second local environment.

    • +

  • d1 (int) – Force component of the first environment.

    • +

  • hyps (np.ndarray) – Hyperparameters of the kernel function (sig1, ls1, +sig2, ls2, sig3, ls3, sig_n).

    • +

  • cutoffs (np.ndarray) – Two-element array containing the 2- and 3-body +cutoffs.

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

Value of the 2+3+many-body kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.mc_simple.two_plus_many_body_mc_grad(env1: AtomicEnvironment, env2: AtomicEnvironment, d1: int, d2: int, hyps, cutoffs, cutoff_func=numba.njit)
+

2+many-body single-element kernel between two force components.

+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – First local environment.

    • +

  • env2 (AtomicEnvironment) – Second local environment.

    • +

  • d1 (int) – Force component of the first environment.

    • +

  • d2 (int) – Force component of the second environment.

    • +

  • hyps (np.ndarray) – Hyperparameters of the kernel function (sig1, ls1, +sig2, ls2, sig3, ls3, sig_n).

    • +

  • cutoffs (np.ndarray) – Two-element array containing the 2- and 3-body +cutoffs.

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

Value of the 2+3+many-body kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.mc_simple.two_plus_three_body_mc(env1: AtomicEnvironment, env2: AtomicEnvironment, d1: int, d2: int, hyps: ndarray, cutoffs: ndarray, cutoff_func: Callable = numba.njit) → float
+

2+3-body multi-element kernel between two force components.

+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – First local environment.

    • +

  • env2 (AtomicEnvironment) – Second local environment.

    • +

  • d1 (int) – Force component of the first environment.

    • +

  • d2 (int) – Force component of the second environment.

    • +

  • hyps (np.ndarray) – Hyperparameters of the kernel function (sig1, ls1, +sig2, ls2, sig_n).

    • +

  • cutoffs (np.ndarray) – Two-element array containing the 2- and 3-body +cutoffs.

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

Value of the 2+3-body kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.mc_simple.two_plus_three_body_mc_grad(env1: AtomicEnvironment, env2: AtomicEnvironment, d1: int, d2: int, hyps: ndarray, cutoffs: ndarray, cutoff_func: Callable = numba.njit)
+

2+3-body multi-element kernel between two force components and its +gradient with respect to the hyperparameters.

+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – First local environment.

    • +

  • env2 (AtomicEnvironment) – Second local environment.

    • +

  • d1 (int) – Force component of the first environment.

    • +

  • d2 (int) – Force component of the second environment.

    • +

  • hyps (np.ndarray) – Hyperparameters of the kernel function (sig1, ls1, +sig2, ls2, sig_n).

    • +

  • cutoffs (np.ndarray) – Two-element array containing the 2- and 3-body +cutoffs.

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

Value of the 2+3-body kernel and its gradient +with respect to the hyperparameters.

+
+
Return type
+

(float, np.ndarray)

+
+
+
+ +
+
+flare.kernels.mc_simple.two_plus_three_mc_en(env1: AtomicEnvironment, env2: AtomicEnvironment, hyps: ndarray, cutoffs: ndarray, cutoff_func: Callable = numba.njit) → float
+

2+3-body multi-element kernel between two local energies.

+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – First local environment.

    • +

  • env2 (AtomicEnvironment) – Second local environment.

    • +

  • hyps (np.ndarray) – Hyperparameters of the kernel function (sig1, ls1, +sig2, ls2).

    • +

  • cutoffs (np.ndarray) – Two-element array containing the 2- and 3-body +cutoffs.

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

Value of the 2+3-body energy/energy kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.mc_simple.two_plus_three_mc_force_en(env1: AtomicEnvironment, env2: AtomicEnvironment, d1: int, hyps: ndarray, cutoffs: ndarray, cutoff_func: Callable = numba.njit) → float
+

2+3-body multi-element kernel between a force component and a local +energy.

+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – Local environment associated with the +force component.

    • +

  • env2 (AtomicEnvironment) – Local environment associated with the +local energy.

    • +

  • d1 (int) – Force component of the first environment.

    • +

  • hyps (np.ndarray) – Hyperparameters of the kernel function (sig1, ls1, +sig2, ls2).

    • +

  • cutoffs (np.ndarray) – Two-element array containing the 2- and 3-body +cutoffs.

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

Value of the 2+3-body force/energy kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.mc_simple.two_plus_three_plus_many_body_mc(env1: AtomicEnvironment, env2: AtomicEnvironment, d1: int, d2: int, hyps, cutoffs, cutoff_func=numba.njit)
+

2+3-body single-element kernel between two force components.

+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – First local environment.

    • +

  • env2 (AtomicEnvironment) – Second local environment.

    • +

  • d1 (int) – Force component of the first environment.

    • +

  • d2 (int) – Force component of the second environment.

    • +

  • hyps (np.ndarray) – Hyperparameters of the kernel function (sig1, ls1, +sig2, ls2, sig3, ls3, sig_n).

    • +

  • cutoffs (np.ndarray) – Two-element array containing the 2- and 3-body +cutoffs.

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

Value of the 2+3+many-body kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.mc_simple.two_plus_three_plus_many_body_mc_en(env1: AtomicEnvironment, env2: AtomicEnvironment, hyps, cutoffs, cutoff_func=numba.njit)
+

2+3+many-body single-element energy kernel.

+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – First local environment.

    • +

  • env2 (AtomicEnvironment) – Second local environment.

    • +

  • hyps (np.ndarray) – Hyperparameters of the kernel function (sig1, ls1, +sig2, ls2, sig3, ls3, sig_n).

    • +

  • cutoffs (np.ndarray) – Two-element array containing the 2- and 3-body +cutoffs.

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

Value of the 2+3+many-body kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.mc_simple.two_plus_three_plus_many_body_mc_force_en(env1: AtomicEnvironment, env2: AtomicEnvironment, d1: int, hyps, cutoffs, cutoff_func=numba.njit)
+
+
2+3+many-body single-element kernel between two force and energy

components.

+
+
+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – First local environment.

    • +

  • env2 (AtomicEnvironment) – Second local environment.

    • +

  • d1 (int) – Force component of the first environment.

    • +

  • hyps (np.ndarray) – Hyperparameters of the kernel function (sig1, ls1, +sig2, ls2, sig3, ls3, sig_n).

    • +

  • cutoffs (np.ndarray) – Two-element array containing the 2- and 3-body +cutoffs.

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

Value of the 2+3+many-body kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.mc_simple.two_plus_three_plus_many_body_mc_grad(env1: AtomicEnvironment, env2: AtomicEnvironment, d1: int, d2: int, hyps, cutoffs, cutoff_func=numba.njit)
+

2+3+many-body single-element kernel between two force components.

+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – First local environment.

    • +

  • env2 (AtomicEnvironment) – Second local environment.

    • +

  • d1 (int) – Force component of the first environment.

    • +

  • d2 (int) – Force component of the second environment.

    • +

  • hyps (np.ndarray) – Hyperparameters of the kernel function (sig1, ls1, +sig2, ls2, sig3, ls3, sig_n).

    • +

  • cutoffs (np.ndarray) – Two-element array containing the 2- and 3-body +cutoffs.

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

Value of the 2+3+many-body kernel.

+
+
Return type
+

float

+
+
+
+
diff --git a/flare/kernels/sc.html b/flare/kernels/sc.html index b8efae4ce..a647bf435 100644 --- a/flare/kernels/sc.html +++ b/flare/kernels/sc.html @@ -98,8 +98,1160 @@
-
-

Single-element Kernels

+
+

Single-element Kernels

+

Single element 2-, 3-, and 2+3-body kernels. +The kernel functions to choose:

+
    +

  • Two body:

    +
    +
      +

    • two_body: force kernel

      • +

    • two_body_en: energy kernel

      • +

    • two_body_grad: gradient of kernel function

      • +

    • two_body_force_en: energy force kernel

      • +
    +
    +
    • +

  • Three body:

    +
    +
      +

    • three_body,

      • +

    • three_body_grad,

      • +

    • three_body_en,

      • +

    • three_body_force_en,

      • +
    +
    +
    • +

  • Two plus three body:

    +
    +
      +

    • two_plus_three_body,

      • +

    • two_plus_three_body_grad,

      • +

    • two_plus_three_en,

      • +

    • two_plus_three_force_en

      • +
    +
    +
    • +

  • Two plus many body:

    +
    +
      +

    • two_plus_many_body,

      • +

    • two_plus_many_body_grad,

      • +

    • two_plus_many_body_en,

      • +

    • two_plus_many_body_force_en

      • +
    +
    +
    • +

  • Two plus three plus many body:

    +
    +
      +

    • two_plus_three_plus_many_body,

      • +

    • two_plus_three_plus_many_body_grad,

      • +

    • two_plus_three_plus_many_body_en,

      • +

    • two_plus_three_plus_many_body_force_en

      • +
    +
    +
    • +
+

Example:

+
>>> gp_model = GaussianProcess(kernel_name='2b',
+                               <other arguments>)
+
+
+
+
+flare.kernels.sc.many_body(env1, env2, d1, d2, hyps, cutoffs, cutoff_func=numba.njit)
+

many-body single-element kernel between two forces.

+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – First local environment.

    • +

  • env2 (AtomicEnvironment) – Second local environment.

    • +

  • d1 (int) – Force component of the first environment.

    • +

  • d2 (int) – Force component of the second environment.

    • +

  • hyps (np.ndarray) – Hyperparameters of the kernel function (sig, ls).

    • +

  • cutoffs (np.ndarray) – Two-element array containing the 2-, 3-, and +many-body cutoffs.

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

Value of the many-body force/force kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.sc.many_body_en(env1, env2, hyps, cutoffs, cutoff_func=numba.njit)
+

many-body single-element kernel between two local energies.

+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – First local environment.

    • +

  • env2 (AtomicEnvironment) – Second local environment.

    • +

  • hyps (np.ndarray) – Hyperparameters of the kernel function (sig, ls).

    • +

  • cutoffs (np.ndarray) – Two-element array containing the 2-, 3-, and +many-body cutoffs.

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

Value of the many-body energy/energy kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.sc.many_body_en_jit(q_array_1, q_array_2, sig, ls)
+

many-body single-element energy kernel between accelerated +with Numba.

+
+
Parameters
+
    +

  • q_array_1 (np.ndarray) – coordination number of the 1st local +environment.

    • +

  • q_array_2 (np.ndarray) – coordination number of the 2nd local +environment.

    • +

  • sig (float) – many-body signal variance hyperparameter.

    • +

  • ls (float) – many-body length scale hyperparameter.

    • +
+
+
Returns
+

Value of the many-body kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.sc.many_body_force_en(env1, env2, d1, hyps, cutoffs, cutoff_func=numba.njit)
+

many-body single-element kernel between two local energies.

+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – First local environment.

    • +

  • env2 (AtomicEnvironment) – Second local environment.

    • +

  • hyps (np.ndarray) – Hyperparameters of the kernel function (sig, ls).

    • +

  • cutoffs (np.ndarray) – Two-element array containing the 2-, 3-, and +many-body cutoffs.

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

Value of the many-body force/energy kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.sc.many_body_force_en_jit(q_array_1, q_array_2, q_neigh_array_1, q_neigh_grads, d1, sig, ls)
+

many-body single-element kernel between force and energy components accelerated +with Numba.

+
+
Parameters
+
    +

  • bond_array_1 (np.ndarray) – many-body bond array of the first local +environment.

    • +

  • bond_array_2 (np.ndarray) – many-body bond array of the second local +environment.

    • +

  • neighbouring_dists_array_1 (np.ndarray) – matrix padded with zero values of distances +of neighbours for the atoms in the first local environment.

    • +

  • num_neighbours_1 (np.nsdarray) – number of neighbours of each atom in the first +local environment

    • +

  • d1 (int) – Force component of the first environment.

    • +

  • sig (float) – many-body signal variance hyperparameter.

    • +

  • ls (float) – many-body length scale hyperparameter.

    • +

  • r_cut (float) – many-body cutoff radius.

    • +

  • cutoff_func (Callable) – Cutoff function.

    • +
+
+
Returns
+

Value of the many-body kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.sc.many_body_grad(env1, env2, d1, d2, hyps, cutoffs, cutoff_func=numba.njit)
+

many-body single-element kernel between two force components and its +gradient with respect to the hyperparameters.

+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – First local environment.

    • +

  • env2 (AtomicEnvironment) – Second local environment.

    • +

  • d1 (int) – Force component of the first environment.

    • +

  • d2 (int) – Force component of the second environment.

    • +

  • hyps (np.ndarray) – Hyperparameters of the kernel function (sig, ls).

    • +

  • cutoffs (np.ndarray) – Two-element array containing the 2-, 3-, and +many-body cutoffs.

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

+
Value of the many-body kernel and its gradient

with respect to the hyperparameters.

+
+
+

+
+
Return type
+

(float, np.ndarray)

+
+
+
+ +
+
+flare.kernels.sc.many_body_grad_jit(q_array_1, q_array_2, q_neigh_array_1, q_neigh_array_2, q_neigh_grads_1, q_neigh_grads_2, d1, d2, sig, ls)
+

gradient of many-body single-element kernel between two force components +w.r.t. the hyperparameters, accelerated with Numba.

+
+
Parameters
+
    +

  • bond_array_1 (np.ndarray) – many-body bond array of the first local +environment.

    • +

  • bond_array_2 (np.ndarray) – many-body bond array of the second local +environment.

    • +

  • neighbouring_dists_array_1 (np.ndarray) – matrix padded with zero values of distances +of neighbours for the atoms in the first local environment.

    • +

  • neighbouring_dists_array_2 (np.ndarray) – matrix padded with zero values of distances +of neighbours for the atoms in the second local environment.

    • +

  • num_neighbours_1 (np.nsdarray) – number of neighbours of each atom in the first +local environment

    • +

  • num_neighbours_2 (np.ndarray) – number of neighbours of each atom in the second +local environment

    • +

  • d1 (int) – Force component of the first environment.

    • +

  • d2 (int) – Force component of the second environment.

    • +

  • sig (float) – many-body signal variance hyperparameter.

    • +

  • ls (float) – many-body length scale hyperparameter.

    • +

  • r_cut (float) – many-body cutoff radius.

    • +

  • cutoff_func (Callable) – Cutoff function.

    • +
+
+
Returns
+

Value of the many-body kernel and its gradient w.r.t. sig and ls

+
+
Return type
+

array

+
+
+
+ +
+
+flare.kernels.sc.many_body_jit(q_array_1, q_array_2, q_neigh_array_1, q_neigh_array_2, q_neigh_grads_1, q_neigh_grads_2, d1, d2, sig, ls)
+

many-body single-element kernel between two force components accelerated +with Numba.

+
+
Parameters
+
    +

  • bond_array_1 (np.ndarray) – many-body bond array of the first local +environment.

    • +

  • bond_array_2 (np.ndarray) – many-body bond array of the second local +environment.

    • +

  • neighbouring_dists_array_1 (np.ndarray) – matrix padded with zero values of distances +of neighbours for the atoms in the first local environment.

    • +

  • neighbouring_dists_array_2 (np.ndarray) – matrix padded with zero values of distances +of neighbours for the atoms in the second local environment.

    • +

  • num_neighbours_1 (np.nsdarray) – number of neighbours of each atom in the first +local environment

    • +

  • num_neighbours_2 (np.ndarray) – number of neighbours of each atom in the second +local environment

    • +

  • d1 (int) – Force component of the first environment.

    • +

  • d2 (int) – Force component of the second environment.

    • +

  • sig (float) – many-body signal variance hyperparameter.

    • +

  • ls (float) – many-body length scale hyperparameter.

    • +

  • r_cut (float) – many-body cutoff radius.

    • +

  • cutoff_func (Callable) – Cutoff function.

    • +
+
+
Returns
+

Value of the many-body kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.sc.three_body(env1, env2, d1, d2, hyps, cutoffs, cutoff_func=numba.njit)
+

3-body single-element kernel between two force components.

+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – First local environment.

    • +

  • env2 (AtomicEnvironment) – Second local environment.

    • +

  • d1 (int) – Force component of the first environment.

    • +

  • d2 (int) – Force component of the second environment.

    • +

  • hyps (np.ndarray) – Hyperparameters of the kernel function (sig, ls).

    • +

  • cutoffs (np.ndarray) – Two-element array containing the 2- and 3-body +cutoffs.

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

Value of the 3-body kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.sc.three_body_en(env1, env2, hyps, cutoffs, cutoff_func=numba.njit)
+

3-body single-element kernel between two local energies.

+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – First local environment.

    • +

  • env2 (AtomicEnvironment) – Second local environment.

    • +

  • hyps (np.ndarray) – Hyperparameters of the kernel function (sig, ls).

    • +

  • cutoffs (np.ndarray) – Two-element array containing the 2- and 3-body +cutoffs.

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

Value of the 3-body force/energy kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.sc.three_body_en_jit(bond_array_1, bond_array_2, cross_bond_inds_1, cross_bond_inds_2, cross_bond_dists_1, cross_bond_dists_2, triplets_1, triplets_2, sig, ls, r_cut, cutoff_func)
+

3-body single-element kernel between two local energies accelerated +with Numba.

+
+
Parameters
+
    +

  • bond_array_1 (np.ndarray) – 3-body bond array of the first local +environment.

    • +

  • bond_array_2 (np.ndarray) – 3-body bond array of the second local +environment.

    • +

  • cross_bond_inds_1 (np.ndarray) – Two dimensional array whose row m +contains the indices of atoms n > m in the first local +environment that are within a distance r_cut of both atom n and +the central atom.

    • +

  • cross_bond_inds_2 (np.ndarray) – Two dimensional array whose row m +contains the indices of atoms n > m in the second local +environment that are within a distance r_cut of both atom n and +the central atom.

    • +

  • cross_bond_dists_1 (np.ndarray) – Two dimensional array whose row m +contains the distances from atom m of atoms n > m in the first +local environment that are within a distance r_cut of both atom +n and the central atom.

    • +

  • cross_bond_dists_2 (np.ndarray) – Two dimensional array whose row m +contains the distances from atom m of atoms n > m in the second +local environment that are within a distance r_cut of both atom +n and the central atom.

    • +

  • triplets_1 (np.ndarray) – One dimensional array of integers whose entry +m is the number of atoms in the first local environment that are +within a distance r_cut of atom m.

    • +

  • triplets_2 (np.ndarray) – One dimensional array of integers whose entry +m is the number of atoms in the second local environment that are +within a distance r_cut of atom m.

    • +

  • sig (float) – 3-body signal variance hyperparameter.

    • +

  • ls (float) – 3-body length scale hyperparameter.

    • +

  • r_cut (float) – 3-body cutoff radius.

    • +

  • cutoff_func (Callable) – Cutoff function.

    • +
+
+
Returns
+

Value of the 3-body local energy kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.sc.three_body_force_en(env1, env2, d1, hyps, cutoffs, cutoff_func=numba.njit)
+

3-body single-element kernel between a force component and a local +energy.

+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – Local environment associated with the +force component.

    • +

  • env2 (AtomicEnvironment) – Local environment associated with the +local energy.

    • +

  • d1 (int) – Force component of the first environment.

    • +

  • hyps (np.ndarray) – Hyperparameters of the kernel function (sig, ls).

    • +

  • cutoffs (np.ndarray) – Two-element array containing the 2- and 3-body +cutoffs.

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

Value of the 3-body force/energy kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.sc.three_body_force_en_jit(bond_array_1, bond_array_2, cross_bond_inds_1, cross_bond_inds_2, cross_bond_dists_1, cross_bond_dists_2, triplets_1, triplets_2, d1, sig, ls, r_cut, cutoff_func)
+

3-body single-element kernel between a force component and a local +energy accelerated with Numba.

+
+
Parameters
+
    +

  • bond_array_1 (np.ndarray) – 3-body bond array of the first local +environment.

    • +

  • bond_array_2 (np.ndarray) – 3-body bond array of the second local +environment.

    • +

  • cross_bond_inds_1 (np.ndarray) – Two dimensional array whose row m +contains the indices of atoms n > m in the first local +environment that are within a distance r_cut of both atom n and +the central atom.

    • +

  • cross_bond_inds_2 (np.ndarray) – Two dimensional array whose row m +contains the indices of atoms n > m in the second local +environment that are within a distance r_cut of both atom n and +the central atom.

    • +

  • cross_bond_dists_1 (np.ndarray) – Two dimensional array whose row m +contains the distances from atom m of atoms n > m in the first +local environment that are within a distance r_cut of both atom +n and the central atom.

    • +

  • cross_bond_dists_2 (np.ndarray) – Two dimensional array whose row m +contains the distances from atom m of atoms n > m in the second +local environment that are within a distance r_cut of both atom +n and the central atom.

    • +

  • triplets_1 (np.ndarray) – One dimensional array of integers whose entry +m is the number of atoms in the first local environment that are +within a distance r_cut of atom m.

    • +

  • triplets_2 (np.ndarray) – One dimensional array of integers whose entry +m is the number of atoms in the second local environment that are +within a distance r_cut of atom m.

    • +

  • d1 (int) – Force component of the first environment (1=x, 2=y, 3=z).

    • +

  • sig (float) – 3-body signal variance hyperparameter.

    • +

  • ls (float) – 3-body length scale hyperparameter.

    • +

  • r_cut (float) – 3-body cutoff radius.

    • +

  • cutoff_func (Callable) – Cutoff function.

    • +
+
+
Returns
+

Value of the 3-body force/energy kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.sc.three_body_grad(env1, env2, d1, d2, hyps, cutoffs, cutoff_func=numba.njit)
+

3-body single-element kernel between two force components and its +gradient with respect to the hyperparameters.

+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – First local environment.

    • +

  • env2 (AtomicEnvironment) – Second local environment.

    • +

  • d1 (int) – Force component of the first environment.

    • +

  • d2 (int) – Force component of the second environment.

    • +

  • hyps (np.ndarray) – Hyperparameters of the kernel function (sig, ls).

    • +

  • cutoffs (np.ndarray) – Two-element array containing the 2- and 3-body +cutoffs.

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

+
Value of the 3-body kernel and its gradient

with respect to the hyperparameters.

+
+
+

+
+
Return type
+

(float, np.ndarray)

+
+
+
+ +
+
+flare.kernels.sc.three_body_grad_jit(bond_array_1, bond_array_2, cross_bond_inds_1, cross_bond_inds_2, cross_bond_dists_1, cross_bond_dists_2, triplets_1, triplets_2, d1, d2, sig, ls, r_cut, cutoff_func)
+

3-body single-element kernel between two force components and its +gradient with respect to the hyperparameters.

+
+
Parameters
+
    +

  • bond_array_1 (np.ndarray) – 3-body bond array of the first local +environment.

    • +

  • bond_array_2 (np.ndarray) – 3-body bond array of the second local +environment.

    • +

  • cross_bond_inds_1 (np.ndarray) – Two dimensional array whose row m +contains the indices of atoms n > m in the first local +environment that are within a distance r_cut of both atom n and +the central atom.

    • +

  • cross_bond_inds_2 (np.ndarray) – Two dimensional array whose row m +contains the indices of atoms n > m in the second local +environment that are within a distance r_cut of both atom n and +the central atom.

    • +

  • cross_bond_dists_1 (np.ndarray) – Two dimensional array whose row m +contains the distances from atom m of atoms n > m in the first +local environment that are within a distance r_cut of both atom +n and the central atom.

    • +

  • cross_bond_dists_2 (np.ndarray) – Two dimensional array whose row m +contains the distances from atom m of atoms n > m in the second +local environment that are within a distance r_cut of both atom +n and the central atom.

    • +

  • triplets_1 (np.ndarray) – One dimensional array of integers whose entry +m is the number of atoms in the first local environment that are +within a distance r_cut of atom m.

    • +

  • triplets_2 (np.ndarray) – One dimensional array of integers whose entry +m is the number of atoms in the second local environment that are +within a distance r_cut of atom m.

    • +

  • d1 (int) – Force component of the first environment.

    • +

  • d2 (int) – Force component of the second environment.

    • +

  • sig (float) – 3-body signal variance hyperparameter.

    • +

  • ls (float) – 3-body length scale hyperparameter.

    • +

  • r_cut (float) – 3-body cutoff radius.

    • +

  • cutoff_func (Callable) – Cutoff function.

    • +
+
+
Returns
+

Value of the 3-body kernel and its gradient with respect to the +hyperparameters.

+
+
Return type
+

(float, float)

+
+
+
+ +
+
+flare.kernels.sc.three_body_jit(bond_array_1, bond_array_2, cross_bond_inds_1, cross_bond_inds_2, cross_bond_dists_1, cross_bond_dists_2, triplets_1, triplets_2, d1, d2, sig, ls, r_cut, cutoff_func)
+

3-body single-element kernel between two force components accelerated +with Numba.

+
+
Parameters
+
    +

  • bond_array_1 (np.ndarray) – 3-body bond array of the first local +environment.

    • +

  • bond_array_2 (np.ndarray) – 3-body bond array of the second local +environment.

    • +

  • cross_bond_inds_1 (np.ndarray) – Two dimensional array whose row m +contains the indices of atoms n > m in the first local +environment that are within a distance r_cut of both atom n and +the central atom.

    • +

  • cross_bond_inds_2 (np.ndarray) – Two dimensional array whose row m +contains the indices of atoms n > m in the second local +environment that are within a distance r_cut of both atom n and +the central atom.

    • +

  • cross_bond_dists_1 (np.ndarray) – Two dimensional array whose row m +contains the distances from atom m of atoms n > m in the first +local environment that are within a distance r_cut of both atom +n and the central atom.

    • +

  • cross_bond_dists_2 (np.ndarray) – Two dimensional array whose row m +contains the distances from atom m of atoms n > m in the second +local environment that are within a distance r_cut of both atom +n and the central atom.

    • +

  • triplets_1 (np.ndarray) – One dimensional array of integers whose entry +m is the number of atoms in the first local environment that are +within a distance r_cut of atom m.

    • +

  • triplets_2 (np.ndarray) – One dimensional array of integers whose entry +m is the number of atoms in the second local environment that are +within a distance r_cut of atom m.

    • +

  • d1 (int) – Force component of the first environment.

    • +

  • d2 (int) – Force component of the second environment.

    • +

  • sig (float) – 3-body signal variance hyperparameter.

    • +

  • ls (float) – 3-body length scale hyperparameter.

    • +

  • r_cut (float) – 3-body cutoff radius.

    • +

  • cutoff_func (Callable) – Cutoff function.

    • +
+
+
Returns
+

Value of the 3-body kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.sc.two_body(env1, env2, d1, d2, hyps, cutoffs, cutoff_func=numba.njit)
+

2-body single-element kernel between two force components.

+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – First local environment.

    • +

  • env2 (AtomicEnvironment) – Second local environment.

    • +

  • d1 (int) – Force component of the first environment.

    • +

  • d2 (int) – Force component of the second environment.

    • +

  • hyps (np.ndarray) – Hyperparameters of the kernel function (sig, ls).

    • +

  • cutoffs (np.ndarray) – One-element array containing the 2-body +cutoff.

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

Value of the 2-body kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.sc.two_body_en(env1, env2, hyps, cutoffs, cutoff_func=numba.njit)
+

2-body single-element kernel between two local energies.

+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – First local environment.

    • +

  • env2 (AtomicEnvironment) – Second local environment.

    • +

  • hyps (np.ndarray) – Hyperparameters of the kernel function (sig, ls).

    • +

  • cutoffs (np.ndarray) – One-element array containing the 2-body +cutoff.

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

Value of the 2-body force/energy kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.sc.two_body_en_jit(bond_array_1, bond_array_2, sig, ls, r_cut, cutoff_func)
+

2-body single-element kernel between two local energies accelerated +with Numba.

+
+
Parameters
+
    +

  • bond_array_1 (np.ndarray) – 2-body bond array of the first local +environment.

    • +

  • bond_array_2 (np.ndarray) – 2-body bond array of the second local +environment.

    • +

  • sig (float) – 2-body signal variance hyperparameter.

    • +

  • ls (float) – 2-body length scale hyperparameter.

    • +

  • r_cut (float) – 2-body cutoff radius.

    • +

  • cutoff_func (Callable) – Cutoff function.

    • +
+
+
Returns
+

Value of the 2-body local energy kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.sc.two_body_force_en(env1, env2, d1, hyps, cutoffs, cutoff_func=numba.njit)
+

2-body single-element kernel between a force component and a local +energy.

+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – Local environment associated with the +force component.

    • +

  • env2 (AtomicEnvironment) – Local environment associated with the +local energy.

    • +

  • d1 (int) – Force component of the first environment.

    • +

  • hyps (np.ndarray) – Hyperparameters of the kernel function (sig, ls).

    • +

  • cutoffs (np.ndarray) – One-element array containing the 2-body +cutoff.

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

Value of the 2-body force/energy kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.sc.two_body_force_en_jit(bond_array_1, bond_array_2, d1, sig, ls, r_cut, cutoff_func)
+

2-body single-element kernel between a force component and a local +energy accelerated with Numba.

+
+
Parameters
+
    +

  • bond_array_1 (np.ndarray) – 2-body bond array of the first local +environment.

    • +

  • bond_array_2 (np.ndarray) – 2-body bond array of the second local +environment.

    • +

  • d1 (int) – Force component of the first environment (1=x, 2=y, 3=z).

    • +

  • sig (float) – 2-body signal variance hyperparameter.

    • +

  • ls (float) – 2-body length scale hyperparameter.

    • +

  • r_cut (float) – 2-body cutoff radius.

    • +

  • cutoff_func (Callable) – Cutoff function.

    • +
+
+
Returns
+

Value of the 2-body force/energy kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.sc.two_body_grad(env1, env2, d1, d2, hyps, cutoffs, cutoff_func=numba.njit)
+

2-body single-element kernel between two force components and its +gradient with respect to the hyperparameters.

+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – First local environment.

    • +

  • env2 (AtomicEnvironment) – Second local environment.

    • +

  • d1 (int) – Force component of the first environment.

    • +

  • d2 (int) – Force component of the second environment.

    • +

  • hyps (np.ndarray) – Hyperparameters of the kernel function (sig, ls).

    • +

  • cutoffs (np.ndarray) – One-element array containing the 2-body +cutoff.

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

+
Value of the 2-body kernel and its gradient

with respect to the hyperparameters.

+
+
+

+
+
Return type
+

(float, np.ndarray)

+
+
+
+ +
+
+flare.kernels.sc.two_body_grad_jit(bond_array_1, bond_array_2, d1, d2, sig, ls, r_cut, cutoff_func)
+

2-body single-element kernel between two force components and its +gradient with respect to the hyperparameters.

+
+
Parameters
+
    +

  • bond_array_1 (np.ndarray) – 2-body bond array of the first local +environment.

    • +

  • bond_array_2 (np.ndarray) – 2-body bond array of the second local +environment.

    • +

  • d1 (int) – Force component of the first environment (1=x, 2=y, 3=z).

    • +

  • d2 (int) – Force component of the second environment (1=x, 2=y, 3=z).

    • +

  • sig (float) – 2-body signal variance hyperparameter.

    • +

  • ls (float) – 2-body length scale hyperparameter.

    • +

  • r_cut (float) – 2-body cutoff radius.

    • +

  • cutoff_func (Callable) – Cutoff function.

    • +
+
+
Returns
+

Value of the 2-body kernel and its gradient with respect to the +hyperparameters.

+
+
Return type
+

(float, float)

+
+
+
+ +
+
+flare.kernels.sc.two_body_jit(bond_array_1, bond_array_2, d1, d2, sig, ls, r_cut, cutoff_func)
+

2-body single-element kernel between two force components accelerated +with Numba.

+
+
Parameters
+
    +

  • bond_array_1 (np.ndarray) – 2-body bond array of the first local +environment.

    • +

  • bond_array_2 (np.ndarray) – 2-body bond array of the second local +environment.

    • +

  • d1 (int) – Force component of the first environment (1=x, 2=y, 3=z).

    • +

  • d2 (int) – Force component of the second environment (1=x, 2=y, 3=z).

    • +

  • sig (float) – 2-body signal variance hyperparameter.

    • +

  • ls (float) – 2-body length scale hyperparameter.

    • +

  • r_cut (float) – 2-body cutoff radius.

    • +

  • cutoff_func (Callable) – Cutoff function.

    • +
+
+
Returns
+

Value of the 2-body kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.sc.two_plus_many_body(env1: AtomicEnvironment, env2: AtomicEnvironment, d1: int, d2: int, hyps, cutoffs, cutoff_func=numba.njit)
+

2+many-body single-element kernel between two force components.

+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – First local environment.

    • +

  • env2 (AtomicEnvironment) – Second local environment.

    • +

  • d1 (int) – Force component of the first environment.

    • +

  • d2 (int) – Force component of the second environment.

    • +

  • hyps (np.ndarray) – Hyperparameters of the kernel function (sig2b, ls2b, +sigmb, lsmb, sig_n).

    • +

  • cutoffs (np.ndarray) – Two-element array containing the 2- and 3-body +cutoffs.

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

Value of the 2+3+many-body kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.sc.two_plus_many_body_en(env1: AtomicEnvironment, env2: AtomicEnvironment, hyps, cutoffs, cutoff_func=numba.njit)
+

2+3+many-body single-element energy kernel.

+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – First local environment.

    • +

  • env2 (AtomicEnvironment) – Second local environment.

    • +

  • hyps (np.ndarray) – Hyperparameters of the kernel function (sig2, ls2, +sig3, ls3, sigm, lsm, sig_n).

    • +

  • cutoffs (np.ndarray) – Two-element array containing the 2- and 3-body +cutoffs.

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

Value of the 2+3+many-body kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.sc.two_plus_many_body_force_en(env1: AtomicEnvironment, env2: AtomicEnvironment, d1: int, hyps, cutoffs, cutoff_func=numba.njit)
+

2+3+many-body single-element kernel between two force and energy components.

+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – First local environment.

    • +

  • env2 (AtomicEnvironment) – Second local environment.

    • +

  • d1 (int) – Force component of the first environment.

    • +

  • hyps (np.ndarray) – Hyperparameters of the kernel function (sig2, ls2, +sig3, ls3, sigm, lsm, sig_n).

    • +

  • cutoffs (np.ndarray) – Two-element array containing the 2- and 3-body +cutoffs.

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

Value of the 2+3+many-body kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.sc.two_plus_many_body_grad(env1: AtomicEnvironment, env2: AtomicEnvironment, d1: int, d2: int, hyps, cutoffs, cutoff_func=numba.njit)
+

2+many-body single-element kernel between two force components.

+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – First local environment.

    • +

  • env2 (AtomicEnvironment) – Second local environment.

    • +

  • d1 (int) – Force component of the first environment.

    • +

  • d2 (int) – Force component of the second environment.

    • +

  • hyps (np.ndarray) – Hyperparameters of the kernel function (sig2b, ls2b, +sigmb, lsmb, sig_n).

    • +

  • cutoffs (np.ndarray) – Two-element array containing the 2- and 3-body +cutoffs.

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

Value of the 2+3+many-body kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.sc.two_plus_three_body(env1: AtomicEnvironment, env2: AtomicEnvironment, d1: int, d2: int, hyps, cutoffs, cutoff_func=numba.njit)
+

2+3-body single-element kernel between two force components.

+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – First local environment.

    • +

  • env2 (AtomicEnvironment) – Second local environment.

    • +

  • d1 (int) – Force component of the first environment.

    • +

  • d2 (int) – Force component of the second environment.

    • +

  • hyps (np.ndarray) – Hyperparameters of the kernel function (sig1, ls1, +sig2, ls2, sig_n).

    • +

  • cutoffs (np.ndarray) – Two-element array containing the 2- and 3-body +cutoffs.

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

Value of the 2+3-body kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.sc.two_plus_three_body_grad(env1, env2, d1, d2, hyps, cutoffs, cutoff_func=numba.njit)
+

2+3-body single-element kernel between two force components and its +gradient with respect to the hyperparameters.

+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – First local environment.

    • +

  • env2 (AtomicEnvironment) – Second local environment.

    • +

  • d1 (int) – Force component of the first environment.

    • +

  • d2 (int) – Force component of the second environment.

    • +

  • hyps (np.ndarray) – Hyperparameters of the kernel function (sig1, ls1, +sig2, ls2, sig_n).

    • +

  • cutoffs (np.ndarray) – Two-element array containing the 2- and 3-body +cutoffs.

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

+
Value of the 2+3-body kernel and its gradient

with respect to the hyperparameters.

+
+
+

+
+
Return type
+

(float, np.ndarray)

+
+
+
+ +
+
+flare.kernels.sc.two_plus_three_en(env1, env2, hyps, cutoffs, cutoff_func=numba.njit)
+

2+3-body single-element kernel between two local energies.

+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – First local environment.

    • +

  • env2 (AtomicEnvironment) – Second local environment.

    • +

  • hyps (np.ndarray) – Hyperparameters of the kernel function (sig1, ls1, +sig2, ls2).

    • +

  • cutoffs (np.ndarray) – Two-element array containing the 2- and 3-body +cutoffs.

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

Value of the 2+3-body force/energy kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.sc.two_plus_three_force_en(env1, env2, d1, hyps, cutoffs, cutoff_func=numba.njit)
+

2+3-body single-element kernel between a force component and a local +energy.

+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – Local environment associated with the +force component.

    • +

  • env2 (AtomicEnvironment) – Local environment associated with the +local energy.

    • +

  • d1 (int) – Force component of the first environment.

    • +

  • hyps (np.ndarray) – Hyperparameters of the kernel function (sig1, ls1, +sig2, ls2).

    • +

  • cutoffs (np.ndarray) – Two-element array containing the 2- and 3-body +cutoffs.

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

Value of the 2+3-body force/energy kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.sc.two_plus_three_plus_many_body(env1: AtomicEnvironment, env2: AtomicEnvironment, d1: int, d2: int, hyps, cutoffs, cutoff_func=numba.njit)
+

2+3-body single-element kernel between two force components.

+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – First local environment.

    • +

  • env2 (AtomicEnvironment) – Second local environment.

    • +

  • d1 (int) – Force component of the first environment.

    • +

  • d2 (int) – Force component of the second environment.

    • +

  • hyps (np.ndarray) – Hyperparameters of the kernel function (sig2, ls2, +sig3, ls3, sigm, lsm, sig_n).

    • +

  • cutoffs (np.ndarray) – Two-element array containing the 2- and 3-body +cutoffs.

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

Value of the 2+3+many-body kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.sc.two_plus_three_plus_many_body_en(env1: AtomicEnvironment, env2: AtomicEnvironment, hyps, cutoffs, cutoff_func=numba.njit)
+

2+3+many-body single-element energy kernel.

+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – First local environment.

    • +

  • env2 (AtomicEnvironment) – Second local environment.

    • +

  • hyps (np.ndarray) – Hyperparameters of the kernel function (sig2, ls2, +sig3, ls3, sigm, lsm, sig_n).

    • +

  • cutoffs (np.ndarray) – Two-element array containing the 2- and 3-body +cutoffs.

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

Value of the 2+3+many-body kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.sc.two_plus_three_plus_many_body_force_en(env1: AtomicEnvironment, env2: AtomicEnvironment, d1: int, hyps, cutoffs, cutoff_func=numba.njit)
+

2+3+many-body single-element kernel between two force and energy components.

+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – First local environment.

    • +

  • env2 (AtomicEnvironment) – Second local environment.

    • +

  • d1 (int) – Force component of the first environment.

    • +

  • hyps (np.ndarray) – Hyperparameters of the kernel function (sig2, ls2, +sig3, ls3, sigm, lsm, sig_n).

    • +

  • cutoffs (np.ndarray) – Two-element array containing the 2- and 3-body +cutoffs.

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

Value of the 2+3+many-body kernel.

+
+
Return type
+

float

+
+
+
+ +
+
+flare.kernels.sc.two_plus_three_plus_many_body_grad(env1: AtomicEnvironment, env2: AtomicEnvironment, d1: int, d2: int, hyps, cutoffs, cutoff_func=numba.njit)
+

2+3+many-body single-element kernel between two force components.

+
+
Parameters
+
    +

  • env1 (AtomicEnvironment) – First local environment.

    • +

  • env2 (AtomicEnvironment) – Second local environment.

    • +

  • d1 (int) – Force component of the first environment.

    • +

  • d2 (int) – Force component of the second environment.

    • +

  • hyps (np.ndarray) – Hyperparameters of the kernel function (sig2, ls2, +sig3, ls3, sigm, lsm, sig_n).

    • +

  • cutoffs (np.ndarray) – Two-element array containing the 2- and 3-body +cutoffs.

    • +

  • cutoff_func (Callable) – Cutoff function of the kernel.

    • +
+
+
Returns
+

Value of the 2+3+many-body kernel.

+
+
Return type
+

float

+
+
+
+
diff --git a/flare/learners/gp_from_aimd.html b/flare/learners/gp_from_aimd.html index 4f4e80f56..12858e1af 100644 --- a/flare/learners/gp_from_aimd.html +++ b/flare/learners/gp_from_aimd.html @@ -53,7 +53,10 @@
  • Bayesian Active Learning
    • @@ -97,8 +100,72 @@
    -
    -

    GP From AIMD

    +
    +

    GP From AIMD

    +

    Tool to enable the development of a GP model based on an AIMD +trajectory with many customizable options for fine control of training. +Contains methods to transfer the model to an OTF run or MD engine run.

    +
    +

    Seed frames

    +

    The various parameters in the TrajectoryTrainer class related to +“Seed frames” are to help you train a model which does not yet have a +training set. Uncertainty- and force-error driven training will go better with +a somewhat populated training set, as force and uncertainty estimates +are better behaveed with more data.

    +

    You may pass in a set of seed frames or atomic environments. +All seed environments will be added to the GP model; seed frames will +be iterated through and atoms will be added at random. +There are a few reasons why you would want to pay special attention to an +individual species.

    +

    If you are studying a system where the dynamics of one species are +particularly important and so you want a good representation in the training +set, then you would want to include as many as possible in the training set +during the seed part of the training.

    +

    Inversely, if a system has high representation of a species well-described +by a simple 2+3 body kernel, you may want it to be less well represented +in the seeded training set.

    +

    By specifying the pre_train_atoms_per_element, you can limit the number of +atoms of a given species which are added in. You can also limit the number +of atoms which are added from a given seed frame.

    +
    +
    +flare.learners.gp_from_aimd.parse_trajectory_trainer_output(file: str, return_gp_data: bool = False, compute_errors: bool = True) → Union[List[dict], Tuple[List[dict], dict]]
    +

    Reads output of a TrajectoryTrainer run by frame. return_gp_data returns +data about GP model growth useful for visualizing progress of model +training.

    +
    +
    Parameters
    +
      +

    • file – filename of output

      • +

    • return_gp_data – flag for returning extra GP data

      • +

    • compute_errors – Compute deviation from GP and DFT forces.

      • +
    +
    +
    Returns
    +

    List of dictionaries with keys ‘species’, ‘positions’, +‘gp_forces’, ‘dft_forces’, ‘gp_stds’, ‘added_atoms’, and +‘maes_by_species’, optionally, gp_data dictionary

    +
    +
    +
    + +
    +
    +flare.learners.gp_from_aimd.structures_from_gpfa_output(frame_dictionaries: List[dict]) → List[FLARE_Atoms]
    +

    Takes as input the first output from the parse_trajectory_trainer_output +function and turns it into a series of FLARE structures, with DFT forces mapped +onto the structures.

    +
    +
    Parameters
    +

    frame_dictionaries – The list of dictionaries which describe each GPFA frame.

    +
    +
    Returns
    +

    +
    +
    +
    + +
    diff --git a/flare/learners/learners.html b/flare/learners/learners.html index f54cf24ec..87ed55478 100644 --- a/flare/learners/learners.html +++ b/flare/learners/learners.html @@ -102,7 +102,10 @@

    Bayesian Active LearningOn-the-Fly Training
  • On-the-Fly Training in LAMMPS
    • -
  • GP From AIMD
    • +
  • GP From AIMD +
  • Conditions to add training data

    • diff --git a/flare/learners/otf.html b/flare/learners/otf.html index f37d86376..25a2b90de 100644 --- a/flare/learners/otf.html +++ b/flare/learners/otf.html @@ -97,8 +97,170 @@
    -
    -

    On-the-Fly Training

    +
    +

    On-the-Fly Training

    +

    OTF is the on-the-fly training module for ASE, WITHOUT molecular dynamics engine. +It needs to be used adjointly with ASE MD engine.

    +
    +
    +class flare.learners.otf.OTF(atoms, dt, number_of_steps, dft_calc, md_engine, md_kwargs, flare_calc=None, trajectory=None, prev_pos_init: ndarray = None, rescale_steps: List[int] = [], rescale_temps: List[int] = [], write_model: int = 0, force_only: bool = True, std_tolerance_factor: float = 1, skip: int = 0, init_atoms: List[int] = None, output_name: str = 'otf_run', max_atoms_added: int = 1, train_hyps: tuple = (0, 1), min_steps_with_model: int = 0, update_style: str = 'add_n', update_threshold: float = None, dft_kwargs=None, store_dft_output: Tuple[Union[str, List[str]], str] = None, build_mode='bayesian', wandb_log=None, **kwargs)
    +
    +
    Trains a Gaussian process force field on the fly during

    molecular dynamics.

    +
    +
    +
    +
    Parameters
    +
      +

    • atoms (ASE Atoms) – the ASE Atoms object for the on-the-fly MD run.

      • +

    • flare_calc – ASE calculator. Must have “get_uncertainties” method +implemented.

      • +

    • dt – the timestep in MD, in the units of pico-second.

      • +

    • number_of_steps (int) – the total number of steps for MD.

      • +

    • dft_calc (ASE Calculator) – any ASE calculator is supported, +e.g. Espresso, VASP etc.

      • +

    • md_engine (str) – the name of MD thermostat, only VelocityVerlet, +NVTBerendsen, NPTBerendsen, NPT and Langevin, NoseHoover +are supported.

      • +

    • md_kwargs (dict) – Specify the args for MD as a dictionary, the args are +as required by the ASE MD modules consistent with the md_engine.

      • +

    • trajectory (ASE Trajectory) – default None, not recommended, +currently in experiment.

      • +
    +
    +
    +

    The following arguments are for on-the-fly training, the user can also +refer to flare.otf.OTF

    +
    +
    Parameters
    +
      +

    • prev_pos_init ([type], optional) – Previous positions. Defaults +to None.

      • +

    • rescale_steps (List[int], optional) – List of frames for which the +velocities of the atoms are rescaled. Defaults to [].

      • +

    • rescale_temps (List[int], optional) – List of rescaled temperatures. +Defaults to [].

      • +

    • write_model (int, optional) – If 0, write never. If 1, write at +end of run. If 2, write after each training and end of run. +If 3, write after each time atoms are added and end of run. +If 4, write after each training and end of run, and back up +after each write.

      • +

    • force_only (bool, optional) – If True, only use forces for training. +Default to False, use forces, energy and stress for training.

      • +

    • std_tolerance_factor (float, optional) – Threshold that determines +when DFT is called. Specifies a multiple of the current noise +hyperparameter. If the epistemic uncertainty on a force +component exceeds this value, DFT is called. Defaults to 1.

      • +

    • skip (int, optional) – Number of frames that are skipped when +dumping to the output file. Defaults to 0.

      • +

    • init_atoms (List[int], optional) – List of atoms from the input +structure whose local environments and force components are +used to train the initial GP model. If None is specified, all +atoms are used to train the initial GP. Defaults to None.

      • +

    • output_name (str, optional) – Name of the output file. Defaults to +‘otf_run’.

      • +

    • max_atoms_added (int, optional) – Number of atoms added each time +DFT is called. Defaults to 1.

      • +

    • train_hyps (tuple, optional) – Specifies the range of steps the +hyperparameters of the GP are optimized. If the number of DFT +calls is in this range, the hyperparameters are frozen. +Defaults to (None, None) which means always training.

      • +

    • min_steps_with_model (int, optional) – Minimum number of steps the +model takes in between calls to DFT. Defaults to 0.

      • +

    • dft_kwargs ([type], optional) – Additional arguments which are +passed when DFT is called; keyword arguments vary based on the +program (e.g. ESPRESSO vs. VASP). Defaults to None.

      • +

    • store_dft_output (Tuple[Union[str,List[str]],str], optional) – After DFT calculations are called, copy the file or files +specified in the first element of the tuple to a directory +specified as the second element of the tuple. +Useful when DFT calculations are expensive and want to be kept +for later use. The first element of the tuple can either be a +single file name, or a list of several. Copied files will be +prepended with the date and time with the format +‘Year.Month.Day:Hour:Minute:Second:’.

      • +

    • build_mode (str) – default “bayesian”, run on-the-fly training. +“direct” mode constructs GP model from a given list of frames, with +FakeMD and FakeDFT. Each frame needs to have a global +property called “target_atoms” specifying a list of atomic +environments added to the GP model.

      • +
    +
    +
    +
    +
    +compute_properties()
    +
    +
    Compute energies, forces, stresses, and their uncertainties with

    the FLARE ASE calcuator, and write the results to the +OTF structure object.

    +
    +
    +
    + +
    +
    +md_step()
    +

    Get new position in molecular dynamics based on the forces predicted by +FLARE_Calculator or DFT calculator

    +
    + +
    +
    +rescale_temperature(new_pos: ndarray)
    +

    Change the previous positions to update the temperature

    +
    +
    Parameters
    +

    new_pos (np.ndarray) – Positions of atoms in the next MD frame.

    +
    +
    +
    + +
    +
    +run()
    +

    Performs an on-the-fly training run.

    +

    If OTF has store_dft_output set, then the specified DFT files will +be copied with the current date and time prepended in the format +‘Year.Month.Day:Hour:Minute:Second:’.

    +
    + +
    +
    +run_dft()
    +

    Calculates DFT forces on atoms in the current structure.

    +

    If OTF has store_dft_output set, then the specified DFT files will +be copied with the current date and time prepended in the format +‘Year.Month.Day:Hour:Minute:Second:’.

    +

    Calculates DFT forces on atoms in the current structure.

    +
    + +
    +
    +train_gp()
    +

    Optimizes the hyperparameters of the current GP model.

    +
    + +
    +
    +update_gp(train_atoms: List[int], dft_frcs: ndarray, dft_energy: float = None, dft_stress: ndarray = None)
    +

    Updates the current GP model.

    +
    +
    Parameters
    +
      +

    • train_atoms (List[int]) – List of atoms whose local environments +will be added to the training set.

      • +

    • dft_frcs (np.ndarray) – DFT forces on all atoms in the structure.

      • +
    +
    +
    +
    + +
    +
    +update_temperature()
    +

    Updates the instantaneous temperatures of the system.

    +
    + +
    +
    diff --git a/flare/learners/utils.html b/flare/learners/utils.html index 2816190c0..0debc904c 100644 --- a/flare/learners/utils.html +++ b/flare/learners/utils.html @@ -97,8 +97,155 @@
    -
    -

    Conditions to add training data

    +
    +

    Conditions to add training data

    +

    Utility functions for various tasks.

    +
    +
    +flare.learners.utils.get_max_cutoff(cell: numpy.ndarray) → float
    +
    +
    Compute the maximum cutoff compatible with a 3x3x3 supercell of a

    structure. Called in the Structure constructor when +setting the max_cutoff attribute, which is used to create local +environments with arbitrarily large cutoff radii.

    +
    +
    +
    +
    Parameters
    +

    cell (np.ndarray) – Bravais lattice vectors of the structure stored as +rows of a 3x3 Numpy array.

    +
    +
    Returns
    +

    +
    Maximum cutoff compatible with a 3x3x3 supercell of the

    structure.

    +
    +
    +

    +
    +
    Return type
    +

    float

    +
    +
    +
    + +
    +
    +flare.learners.utils.is_force_in_bound_per_species(abs_force_tolerance: float, predicted_forces: ndarray, label_forces: ndarray, structure, max_atoms_added: int = inf, max_by_species: dict = {}, max_force_error: float = inf) -> (<class 'bool'>, typing.List[int])
    +

    Checks the forces of GP prediction assigned to the structure against a +DFT calculation, and return a list of atoms which meet an absolute +threshold abs_force_tolerance.

    +

    Can limit the total number of target atoms via max_atoms_added, and limit +per species by max_by_species.

    +

    The max_atoms_added argument will ‘overrule’ the +max by species; e.g. if max_atoms_added is 2 and max_by_species is {“H”:3}, +then at most two atoms total will be added.

    +

    Because adding atoms which are in configurations which are far outside +of the potential energy surface may not always be +desirable, a maximum force error can be passed in; atoms with

    +
    +
    Parameters
    +
      +

    • abs_force_tolerance – If error exceeds this value, then return +atom index

      • +

    • predicted_forces – Force predictions made by GP model

      • +

    • label_forces – “True” forces computed by DFT

      • +

    • structure – FLARE Structure

      • +

    • max_atoms_added – Maximum atoms to return

      • +

    • max_by_species – Limit to a maximum number of atoms by species

      • +

    • max_force_error – In order to avoid counting in highly unlikely +configurations, if the error exceeds this, do not add atom

      • +
    +
    +
    Returns
    +

    Bool indicating if any atoms exceeded the error +threshold, and a list of indices of atoms which did sorted by their +error.

    +
    +
    +
    + +
    +
    +flare.learners.utils.is_std_in_bound(std_tolerance: float, noise: float, structure: FLARE_Atoms, max_atoms_added: int = inf, update_style: str = 'add_n', update_threshold: float = None) -> (<class 'bool'>, typing.List[int])
    +

    Given an uncertainty tolerance and a structure decorated with atoms, +species, and associated uncertainties, return those which are above a +given threshold, agnostic to species.

    +

    If std_tolerance is negative, then the threshold used is the absolute +value of std_tolerance.

    +

    If std_tolerance is positive, then the threshold used is +std_tolerance * noise.

    +

    If std_tolerance is 0, then do not check.

    +
    +
    Parameters
    +
      +

    • std_tolerance – If positive, multiply by noise to get cutoff. If +negative, use absolute value of std_tolerance as cutoff.

      • +

    • noise – Noise variance parameter

      • +

    • structure (FLARE Structure) – Input structure

      • +

    • max_atoms_added – Maximum # of atoms to add

      • +

    • update_style – A string specifying the desired strategy for +adding atoms to the training set. Current options are ``add_n’’, which +adds the n = max_atoms_added highest-uncertainty atoms, and +``threshold’’, which adds all atoms with uncertainty greater than +update_threshold.

      • +

    • update_threshold – A float specifying the update threshold. Ignored +if update_style is not set to ``threshold’’.

      • +
    +
    +
    Returns
    +

    (True,[-1]) if no atoms are above cutoff, (False,[…]) if at +least one atom is above std_tolerance, with the list indicating +which atoms have been selected for the training set.

    +
    +
    +
    + +
    +
    +flare.learners.utils.is_std_in_bound_per_species(rel_std_tolerance: float, abs_std_tolerance: float, noise: float, structure: FLARE_Atoms, max_atoms_added: int = inf, max_by_species: dict = {}) -> (<class 'bool'>, typing.List[int])
    +

    Checks the stds of GP prediction assigned to the structure, returns a +list of atoms which either meet an absolute threshold or a relative +threshold defined by rel_std_tolerance * noise. Can limit the +total number of target atoms via max_atoms_added, and limit per species +by max_by_species.

    +

    The max_atoms_added argument will ‘overrule’ the +max by species; e.g. if max_atoms_added is 2 and max_by_species is {“H”:3}, +then at most two atoms will be added.

    +
    +
    Parameters
    +
      +

    • rel_std_tolerance – Multiplied by noise to get a lower +bound for the uncertainty threshold defined relative to the model.

      • +

    • abs_std_tolerance – Used as an absolute lower bound for the +uncertainty threshold.

      • +

    • noise – Noise hyperparameter for model, used to define relative +uncertainty cutoff.

      • +

    • structure – FLARE structure decorated with +uncertainties in structure.stds.

      • +

    • max_atoms_added – Maximum number of atoms to return from structure.

      • +

    • max_by_species – Dictionary describing maximum number of atoms to +return by species (e.g. {‘H’:1,’He’:2} will return at most 1 H and 2 He +atoms.)

      • +
    +
    +
    Returns
    +

    Bool indicating if any atoms exceeded the uncertainty +threshold, and a list of indices of atoms which did, sorted by their +uncertainty.

    +
    +
    +
    + +
    +
    +flare.learners.utils.subset_of_frame_by_element(frame: FLARE_Atoms, predict_atoms_per_element: dict) → List[int]
    +

    Given a structure and a dictionary formatted as {“Symbol”:int, +..} describing a number of atoms per element, return a sorted list of +indices corresponding to a random subset of atoms by species +:param frame: +:param predict_atoms_by_species: +:return:

    +
    +
    diff --git a/flare/md/fake.html b/flare/md/fake.html index 67956edae..409522871 100644 --- a/flare/md/fake.html +++ b/flare/md/fake.html @@ -105,6 +105,79 @@

    Fake MD
    +
    +class flare.md.fake.FakeDFT(**kwargs)
    +

    Fake DFT to read energy/forces/stress from a trajectory file.

    +
    +
    Parameters
    +
      +

    • filename (str) – The name of the trajectory file to read in.

      • +

    • format (str) – The format supported by ASE IO.

      • +

    • index (float or str) – The indices of frames to read from the +trajectory. Default is “:”, which reads the whole trajectory.

      • +
    +
    +
    +
    +
    +calculate(atoms=None, properties=None, system_changes=None)
    +

    Do the calculation.

    +
    +
    properties: list of str

    List of what needs to be calculated. Can be any combination +of ‘energy’, ‘forces’, ‘stress’, ‘dipole’, ‘charges’, ‘magmom’ +and ‘magmoms’.

    +
    +
    system_changes: list of str

    List of what has changed since last calculation. Can be +any combination of these six: ‘positions’, ‘numbers’, ‘cell’, +‘pbc’, ‘initial_charges’ and ‘initial_magmoms’.

    +
    +
    +

    Subclasses need to implement this, but can ignore properties +and system_changes if they want. Calculated properties should +be inserted into results dictionary like shown in this dummy +example:

    +
    self.results = {'energy': 0.0,
+                'forces': np.zeros((len(atoms), 3)),
+                'stress': np.zeros(6),
+                'dipole': np.zeros(3),
+                'charges': np.zeros(len(atoms)),
+                'magmom': 0.0,
+                'magmoms': np.zeros(len(atoms))}
+
    +
    +

    The subclass implementation should first call this +implementation to set the atoms attribute and create any missing +directories.

    +
    + +
    +
    +implemented_properties: List[str] = ['energy', 'forces', 'stress']
    +

    Properties calculator can handle (energy, forces, …)

    +
    + +
    + +
    +
    +class flare.md.fake.FakeMD(*args: Any, **kwargs: Any)
    +

    Fake MD for offline training with OTF module and AIMD trajectories

    +
    +
    Parameters
    +
      +

    • atoms (ASE Atoms) – The list of atoms.

      • +

    • timestep (float) – The time step.

      • +

    • filenames (list) – The name of the trajectory file to read in.

      • +

    • format (str) – The format supported by ASE IO.

      • +

    • index (float or str) – The indices of frames to read from the +trajectory. Default is “:”, which reads the whole trajectory.

      • +

    • io_kwargs (dict) – The arguments needed for reading specific format.

      • +
    +
    +
    +
    +

    diff --git a/flare/md/lammps.html b/flare/md/lammps.html index e8f84a1f6..7bb5a7b1b 100644 --- a/flare/md/lammps.html +++ b/flare/md/lammps.html @@ -96,8 +96,160 @@
    -
    -

    LAMMPS Calculator and MD

    +
    +

    LAMMPS Calculator and MD

    +
    +
    +class flare.md.lammps.LAMMPS_MD(*args: Any, **kwargs: Any)
    +

    Run MD with LAMMPS based on the ase.md.md.MolecularDynamics. +It includes using LAMMPS_MOD to run multiple steps, and supports +Bayesian active learning with flare.

    +
    +
    Parameters
    +

    parameters (dict) – LAMMPS input commands.

    +
    +
    +
    +
    +backup(curr_trj)
    +

    Back up the current trajectory into .xyz file. The atomic positions, +velocities, forces and uncertainties are read from lammps trajectory. +The step, potential energy and stress are read from thermo.txt

    +
    +
    Parameters
    +

    curr_trj (list[ase.Atoms]) – lammps trajectory of current run read +by ASE.

    +
    +
    +
    + +
    +
    +step(std_tolerance, N_steps)
    +

    Run lammps until the uncertainty interrupts. Notice this method neither runs +only a single MD step, nor finishes all the N_steps. The MD exits only when +1) the maximal atomic uncertainty goes beyond std_tolerance, or +2) all the N_steps are finished without uncertainty beyond std_tolerance.

    +
    +
    Parameters
    +
      +

    • std_tolerance (float) – the threshold for atomic uncertainty, above which the +MD will be interrupted and DFT will be called.

      • +

    • N_steps (int) – number of MD steps left to run.

      • +
    +
    +
    +
    + +
    + +
    +
    +class flare.md.lammps.LAMMPS_MOD(*args: Any, **kwargs: Any)
    +

    A modified ASE LAMMPS calculator based on ase.lammpsrun.LAMMPS, +to allow for more flexible input parameters, including compute, +region, dump, fix/nvt, fix/npt etc.

    +

    The input arguments are the same as +https://databases.fysik.dtu.dk/ase/ase/calculators/lammps.html#ase.calculators.lammpsrun.LAMMPS

    +

    Example:

    +
    from ase import Atom
+from ase.build import bulk
+from flare.md.lammps import LAMMPS_MOD
+
+Ni = bulk("Ni", cubic=True)
+H = Atom("H", position=Ni.cell.diagonal() / 2)
+NiH = Ni + H
+
+files = []
+param_dict = {
+    "pair_style": "lj/cut 2.5",
+    "pair_coeff": ["* * 1 1"],
+    "compute": ["1 all pair/local dist", "2 all reduce max c_1"],
+    "velocity": ["all create 300 12345 dist gaussian rot yes mom yes"],
+    "fix": ["1 all nvt temp 300 300 $(100.0*dt)"],
+    "dump_period": 1,
+    "timestep": 0.001,
+    "keep_alive": False,
+}
+
+lmp_calc = LAMMPS_MOD(
+    command=<lammps_executable>,
+    label="my_lammps",
+    files=files,
+    keep_tmp_files=True,
+    tmp_dir="tmp",
+)
+lmp_calc.set(**param_dict)
+NiH.calc = lmp_calc
+NiH.calc.calculate(NiH, set_atoms=False)
+forces = NiH.get_forces()
+
    +
    +

    Supported customized commands for LAMMPS input:

    +
    mass (set by arg `masses`)
+package
+atom_style, bond_style, angle_style, dihedral_style, improper_style, kspace_style
+units (default: metal)
+boundary
+neighbor
+newton
+kim_interactions
+pair_style (default: lj/cut 2.5)
+pair_coeff (default: * * 1 1)
+*compute
+*region
+*dump
+group
+fix
+timestep
+minimize
+run
+
    +
    +

    Note:

    +
      +

    • additional commands needed at the beginning can be specified in the arg model_init

      • +

    • additional commands needed after “pair_coeff” can be specified in the arg model_post

      • +
    +

    Non-customized input commands:

    +
    atom_modify sort 0 0.0
+read_data
+fix fix_nve all nve
+dump dump_all all custom trj_file (dump_period) id type x y z vx vy vz fx fy fz
+thermo_style custom (thermo_args)
+thermo_modify flush yes format float %23.16g
+thermo 1
+
    +
    +

    Customized parameters:

    +
    dump_period
+thermo_args
+specorder
+
    +
    +
    +
    +calculate(atoms=None, properties=None, system_changes=None, set_atoms=False)
    +

    Modify parameters

    +
    + +
    + +
    +
    +flare.md.lammps.check_sgp_match(atoms, sgp_calc, logger, specorder, command)
    +

    Check if the lammps trajectory or calculator matches the SGP predictions

    +
    + +
    +
    +flare.md.lammps.get_kinetic_stress(atoms)
    +

    LAMMPS stress tensor = virial + kinetic, +kinetic = sum(m_k * v_ki * v_kj) / V. +We subtract the kinetic term and keep only the virial term. +In the calculator, results[“stress”] += kinetic_atoms gives virial.

    +
    +
    diff --git a/flare/md/nosehoover.html b/flare/md/nosehoover.html index c2da891ed..7dc9bc8f9 100644 --- a/flare/md/nosehoover.html +++ b/flare/md/nosehoover.html @@ -96,8 +96,46 @@
    -
    -

    NoseHoover (NVT Ensemble)

    +
    +

    NoseHoover (NVT Ensemble)

    +

    Custom Nose-Hoover NVT thermostat based on ASE.

    +

    This code was originally written by Jonathan Mailoa based on these notes:

    +
    +
    +

    It was then adapted by Simon Batzner to be used within ASE. Parts of the overall outline of the class are also based on the Langevin class in ASE.

    +
    +
    +class flare.md.nosehoover.NoseHoover(*args: Any, **kwargs: Any)
    +

    Nose-Hoover (constant N, V, T) molecular dynamics.

    +

    Usage: NoseHoover(atoms, dt, temperature)

    +
    +
    Parameters
    +
      +

    • atoms (ASE Atoms) – The list of atoms.

      • +

    • timestep (float) – The time step.

      • +

    • temperature (float) – Target temperature of the MD run in [K * units.kB]

      • +

    • nvt_q (float) – Q in the Nose-Hoover equations.

      • +
    +
    +
    +

    Example Usage:

    +
    nvt_dyn = NoseHoover(
+    atoms=atoms,
+    timestep=0.5 * units.fs,
+    temperature=300. * units.kB,
+    nvt_q=334.
+)
+
    +
    +
    +
    +step()
    +

    Perform a MD step.

    +
    + +
    +
    diff --git a/flare/utils/env_getarray.html b/flare/utils/env_getarray.html index e63598a8a..9efa229e4 100644 --- a/flare/utils/env_getarray.html +++ b/flare/utils/env_getarray.html @@ -95,8 +95,164 @@
    -
    -

    Construct Atomic Environment

    +
    +

    Construct Atomic Environment

    +
    +
    +flare.utils.env_getarray.get_2_body_arrays(positions, atom: int, cell, r_cut, cutoff_2, species, sweep, nspecie, species_mask, twobody_mask)
    +

    Returns distances, coordinates, species of atoms, and indices of neighbors +in the 2-body local environment. This method is implemented outside +the AtomicEnvironment class to allow for njit acceleration with Numba.

    +
    +
    Parameters
    +
      +

    • positions (np.ndarray) – Positions of atoms in the structure.

      • +

    • atom (int) – Index of the central atom of the local environment.

      • +

    • cell (np.ndarray) – 3x3 array whose rows are the Bravais lattice vectors of the +cell.

      • +

    • cutoff_2 (np.ndarray) – 2-body cutoff radius.

      • +

    • species (np.ndarray) – Numpy array of species represented by their atomic numbers.

      • +

    • nspecie – number of atom types to define bonds

      • +

    • species_mask – mapping from atomic number to atom types

      • +

    • twobody_mask – mapping from the types of end atoms to bond types

      • +
    +
    +
    Type
    +

    int

    +
    +
    Type
    +

    np.ndarray

    +
    +
    Type
    +

    np.ndarray

    +
    +
    Returns
    +

    Tuple of arrays describing pairs of atoms in the 2-body local +environment.

    +

    bond_array_2: Array containing the distances and relative +coordinates of atoms in the 2-body local environment. First column +contains distances, remaining columns contain Cartesian coordinates +divided by the distance (with the origin defined as the position of the +central atom). The rows are sorted by distance from the central atom.

    +

    bond_positions_2: Coordinates of atoms in the 2-body local environment.

    +

    etypes: Species of atoms in the 2-body local environment represented by +their atomic number.

    +

    bond_indices: Structure indices of atoms in the local environment.

    +

    +
    +
    Return type
    +

    np.ndarray, np.ndarray, np.ndarray, np.ndarray

    +
    +
    +
    + +
    +
    +flare.utils.env_getarray.get_3_body_arrays(bond_array_2, bond_positions_2, ctype, etypes, r_cut, cutoff_3, nspecie, species_mask, cut3b_mask)
    +

    Returns distances and coordinates of triplets of atoms in the +3-body local environment.

    +
    +
    Parameters
    +
      +

    • bond_array_2 (np.ndarray) – 2-body bond array.

      • +

    • bond_positions_2 (np.ndarray) – Coordinates of atoms in the 2-body local +environment.

      • +

    • ctype – atomic number of the center atom

      • +

    • cutoff_3 (np.ndarray) – 3-body cutoff radius.

      • +

    • nspecie – number of atom types to define bonds

      • +

    • species_mask – mapping from atomic number to atom types

      • +

    • cut3b_mask – mapping from the types of end atoms to bond types

      • +
    +
    +
    Type
    +

    int

    +
    +
    Type
    +

    int

    +
    +
    Type
    +

    np.ndarray

    +
    +
    Type
    +

    np.ndarray

    +
    +
    Returns
    +

    Tuple of 4 arrays describing triplets of atoms in the 3-body local +environment.

    +

    bond_array_3: Array containing the distances and relative +coordinates of atoms in the 3-body local environment. First column +contains distances, remaining columns contain Cartesian coordinates +divided by the distance (with the origin defined as the position of the +central atom). The rows are sorted by distance from the central atom.

    +

    cross_bond_inds: Two dimensional array whose row m contains the indices +of atoms n > m that are within a distance cutoff_3 of both atom n and the +central atom.

    +

    cross_bond_dists: Two dimensional array whose row m contains the +distances from atom m of atoms n > m that are within a distance cutoff_3 +of both atom n and the central atom.

    +

    triplet_counts: One dimensional array of integers whose entry m is the +number of atoms that are within a distance cutoff_3 of atom m.

    +

    +
    +
    Return type
    +

    (np.ndarray, np.ndarray, np.ndarray, np.ndarray)

    +
    +
    +
    + +
    +
    +flare.utils.env_getarray.get_m2_body_arrays(positions, atom: int, cell, r_cut, manybody_cutoff_list, species, sweep: numpy.ndarray, nspec, spec_mask, manybody_mask, cutoff_func=numba.njit)
    +
    +
    Parameters
    +
      +

    • positions (np.ndarray) – Positions of atoms in the structure.

      • +

    • atom (int) – Index of the central atom of the local environment.

      • +

    • cell (np.ndarray) – 3x3 array whose rows are the Bravais lattice vectors of the +cell.

      • +

    • manybody_cutoff_list (float) – 2-body cutoff radius.

      • +

    • species (np.ndarray) – Numpy array of species represented by their atomic numbers.

      • +
    +
    +
    Returns
    +

    Tuple of arrays describing pairs of atoms in the 2-body local +environment.

    +
    +
    +
    + +
    +
    +flare.utils.env_getarray.get_m3_body_arrays(positions, atom: int, cell, cutoff: float, species, sweep, cutoff_func=numba.njit)
    +

    Note: here we assume the cutoff is not too large, +i.e., 2 * cutoff < cell_size

    +
    + +
    +
    +flare.utils.env_getarray.q3_value_mc(distances, cross_bond_inds, cross_bond_dists, triplets, r_cut, species_list, etypes, cutoff_func, q_func=numba.njit)
    +

    Compute value of many-body many components descriptor based +on distances of atoms in the local many-body environment.

    +
    +
    Parameters
    +
      +

    • distances (np.ndarray) – distances between atoms i and j

      • +

    • r_cut (float) – cutoff hyperparameter

      • +

    • ref_species (int) – species to consider to compute the contribution

      • +

    • etypes (np.ndarray) – atomic species of neighbours

      • +

    • cutoff_func (callable) – cutoff function

      • +

    • q_func (callable) – many-body pairwise descrptor function

      • +
    +
    +
    Returns
    +

    the value of the many-body descriptor

    +
    +
    Return type
    +

    float

    +
    +
    +
    +
    diff --git a/flare/utils/mask_helper.html b/flare/utils/mask_helper.html index 20de1fa8c..3d65f226c 100644 --- a/flare/utils/mask_helper.html +++ b/flare/utils/mask_helper.html @@ -95,9 +95,417 @@
    -
    -

    Advanced Hyperparameters Set Up

    -
    +
    +

    Advanced Hyperparameters Set Up

    +

    For multi-component systems, the configurational space can be highly complicated. +One may want to use different hyper-parameters and cutoffs for different interactions, +or do constraint optimisation for hyper-parameters.

    +

    To use more hyper-parameters, we need special kernel function that can differentiate different +pairs, triplets and other descriptors and determine which number to use for what interaction.

    +

    This kernel can be enabled by using the hyps_mask argument of the GaussianProcess class. +It contains multiple arrays to describe how to break down the array of hyper-parameters and +apply them when computing the kernel. Detail descriptions of this argument can be seen in +kernel/mc_sephyps.py.

    +

    The ParameterHelper class is to generate the hyps_mask with a more human readable interface.

    +

    Example:

    +
    >>> pm = ParameterHelper(species=['C', 'H', 'O'],
+...                      kernels={'twobody':[['*', '*'], ['O','O']],
+...                      'threebody':[['*', '*', '*'],
+...                          ['O','O', 'O']]},
+...                      parameters={'twobody0':[1, 0.5, 1], 'twobody1':[2, 0.2, 2],
+...                            'threebody0':[1, 0.5], 'threebody1':[2, 0.2],
+...                            'cutoff_threebody':1},
+...                      constraints={'twobody0':[False, True]})
+>>> hm = pm.as_dict()
+>>> kernels = hm['kernels']
+>>> gp_model = GaussianProcess(kernels=kernels,
+...                            hyps=hyps, hyps_mask=hm)
+
    +
    +

    In this example, four atomic species are involved. There are many kinds +of twobodys and threebodys. But we only want to use eight different signal variance +and length-scales.

    +

    In order to do so, we first define all the twobodys to be group “twobody0”, by +listing “-” as the first element in the twobody argument. The second +element O-O is then defined to be group “twobody1”. Note that the order +matters here. The later element overrides the ealier one. If +twobodys=[[‘O’, ‘O’], [‘*’, ‘*’]], then all twobodys belong to group “twobody1”.

    +

    Similarly, O-O-O is defined as threebody1, while all remaining ones +are left as threebody0.

    +

    The hyperpameters for each group is listed in the order of +[sig, ls, cutoff] in the parameters argument. So in this example, +O-O interaction will use [2, 0.2, 2] as its sigma, length scale, and +cutoff.

    +

    For threebody, the parameter arrays only come with two elements. So there +is no cutoff associated with threebody0 or threebody1; instead, a universal +cutoff is used, which is defined as ‘cutoff_threebody’.

    +

    The constraints argument define which hyper-parameters will be optimized. +True for optimized and false for being fixed.

    +

    Here are a couple more simple examples.

    +

    Define a 5-parameter 2+3 kernel (1, 0.5, 1, 0.5, 0.05)

    +
    >>> pm = ParameterHelper(kernels=['twobody', 'threebody'],
+...                     parameters={'sigma': 1,
+...                                 'lengthscale': 0.5,
+...                                 'cutoff_twobody': 2,
+...                                 'cutoff_threebody': 1,
+...                                 'noise': 0.05})
+
    +
    +

    Define a 5-parameter 2+3 kernel (1, 1, 1, 1, 0.05)

    +
    >>> pm = ParameterHelper(kernels=['twobody', 'threebody'],
+...                      parameters={'cutoff_twobody': 2,
+...                                  'cutoff_threebody': 1,
+...                                  'noise': 0.05},
+...                      ones=ones,
+...                      random=not ones)
+
    +
    +

    Define a 9-parameter 2+3 kernel

    +
    >>> pm = ParameterHelper()
+>>> pm.define_group('specie', 'O', ['O'])
+>>> pm.define_group('specie', 'rest', ['C', 'H'])
+>>> pm.define_group('twobody', '**', ['*', '*'])
+>>> pm.define_group('twobody', 'OO', ['O', 'O'])
+>>> pm.define_group('threebody', '***', ['*', '*', '*'])
+>>> pm.define_group('threebody', 'Oall', ['O', 'O', 'O'])
+>>> pm.set_parameters('**', [1, 0.5])
+>>> pm.set_parameters('OO', [1, 0.5])
+>>> pm.set_parameters('Oall', [1, 0.5])
+>>> pm.set_parameters('***', [1, 0.5])
+>>> pm.set_parameters('cutoff_twobody', 5)
+>>> pm.set_parameters('cutoff_threebody', 4)
+
    +
    +

    See more examples in functions ParameterHelper.define_group , ParameterHelper.set_parameters, +and in the tests tests/test_parameters.py

    +

    If you want to add in a new hyperparameter set to an already-existing GP, you can perform the +following steps:

    +

    >> hyps_mask = pm.as_dict() +>> hyps = hyps_mask[‘hyps’] +>> kernels = hyps_mask[‘kernels’] +>> gp_model.update_kernel(kernels, ‘mc’, hyps_mask) +>> gp_model.hyps = hyps

    +
    +
    +class flare.utils.parameter_helper.ParameterHelper(hyps_mask=None, species=None, kernels={}, cutoff_groups={}, parameters=None, constraints={}, allseparate=False, random=False, ones=False, verbose='WARNING')
    +

    A helper class to construct the hyps_mask dictionary for AtomicEnvironment +, GaussianProcess and MappedGaussianProcess

    +
    +
    Parameters
    +
      +

    • hyps_mask (dict) – Not implemented yet

      • +

    • species (dict, list) – Define specie groups

      • +

    • kernels (dict, list) – Define kernels and groups for the kernels

      • +

    • cutoff_groups (dict) – Define different cutoffs for different species

      • +

    • parameters (dict) – Define signal variance, length scales, and cutoffs

      • +

    • constraints (dict) – If listed as False, the cooresponding hyperparmeters +will not be trained

      • +

    • allseparate (bool) – If True, define each type pair/triplet into a +separate group.

      • +

    • random (bool) – If True, randomized all signal variances and lengthscales

      • +

    • one (bool) – If True, set all signal variances and lengthscales to one

      • +

    • verbose (str) – Level to print with “ERROR”, “WARNING”, “INFO”, “DEBUG”

      • +
    +
    +
    +
      +

    • the species is an optional input. It can be left as None if the user only wants +to set up one group of hyper-parameters for each kernel.

      • +

    • the kernels can be defined along with or without groups. But the later mode +is not compatible with the allseparate flag.

      +
      >>> kernels=['twobody', 'threebody'],
+
      +
      +

      or

      +
      >>> kernels={'twobody':[['*', '*'], ['O','O']],
+...          'threebody':[['*', '*', '*'],
+...                       ['O','O', 'O']]},
+
      +
      +

      Current options for the kernels are twobody, threebody and manybody (based on coordination number).

      +
      • +

    • See format of species, kernels (dict), and cutoff_groups in list_groups() function.

      • +

    • See format of parameters and constraints in list_parameters() function.

      • +
    +
    +
    +all_separate_groups(group_type)
    +

    Separate all possible types of twobodys, threebodys, manybody. +One type per group.

    +
    +
    Parameters
    +

    group_type (str) – “specie”, “twobody”, “threebody”, “cut3b”, “manybody”

    +
    +
    +
    + +
    +
    +as_dict()
    +

    Dictionary representation of the mask. The output can be used for AtomicEnvironment +or the GaussianProcess

    +
    + +
    +
    +define_group(group_type, name, element_list, parameters=None, atomic_str=False)
    +

    Define specie/twobody/threebody/3b cutoff/manybody group

    +
    +
    Parameters
    +
      +

    • group_type (str) – “specie”, “twobody”, “threebody”, “cut3b”, “manybody”

      • +

    • name (str) – the name use for indexing. can be anything but “*”

      • +

    • element_list (list) – list of elements

      • +

    • parameters (list) – corresponding parameters for this group

      • +

    • atomic_str (bool) – whether the elements in element_list are +specified by group names or periodic table element names.

      • +
    +
    +
    +

    The function is helped to define different groups for specie/twobody/threebody +/3b cutoff/manybody terms. This function can be used for many times. +The later one always overrides the former one.

    +

    The name of the group has to be unique string (but not “*”), that +define a group of species or twobodys, etc. If the same name is used, +in two function calls, the definitions of the group will be merged. +Both calls will be effective.

    +

    element_list has to be a list of atomic elements, or a list of +specie group names (which should be defined in previous calls), or “*”. +“*” will loop the function over all previously defined species. +It has to be two elements for twobody/3b cutoff/manybody term, or +three elements for threebody. For specie group definition, it can be +as many elements as you want.

    +

    If multiple define_group calls have conflict with element, the later one +has higher priority. For example, twobody 1-2 are defined as group1 in +the first call, and as group2 in the second call. In the end, the twobody +will be left as group2.

    +

    Example 1:

    +
    >>> define_group('specie', 'water', ['H', 'O'])
+>>> define_group('specie', 'salt', ['Cl', 'Na'])
+
    +
    +

    They define H and O to be group water, and Na and Cl to be group salt.

    +

    Example 2.1:

    +
    >>> define_group('twobody', 'in-water', ['H', 'H'], atomic_str=True)
+>>> define_group('twobody', 'in-water', ['H', 'O'], atomic_str=True)
+>>> define_group('twobody', 'in-water', ['O', 'O'], atomic_str=True)
+
    +
    +

    Example 2.2:

    +
    >>> define_group('twobody', 'in-water', ['water', 'water'])
+
    +
    +

    The 2.1 is equivalent to 2.2.

    +

    Example 3.1:

    +
    >>> define_group('specie', '1', ['H'])
+>>> define_group('specie', '2', ['O'])
+>>> define_group('twobody', 'Hgroup', ['H', 'H'], atomic_str=True)
+>>> define_group('twobody', 'Hgroup', ['H', 'O'], atomic_str=True)
+>>> define_group('twobody', 'OO', ['O', 'O'], atomic_str=True)
+
    +
    +

    Example 3.2:

    +
    >>> define_group('specie', '1', ['H'])
+>>> define_group('specie', '2', ['O'])
+>>> define_group('twobody', 'Hgroup', ['H', '*'], atomic_str=True)
+>>> define_group('twobody', 'OO', ['O', 'O'], atomic_str=True)
+
    +
    +

    Example 3.3:

    +
    >>> list_groups('specie', ['H', 'O'])
+>>> define_group('twobody', 'Hgroup', ['H', '*'])
+>>> define_group('twobody', 'OO', ['O', 'O'])
+
    +
    +

    Example 3.4:

    +
    >>> list_groups('specie', ['H', 'O'])
+>>> define_group('twobody', 'OO', ['*', '*'])
+>>> define_group('twobody', 'Hgroup', ['H', '*'])
+
    +
    +

    3.1 to 3.4 are all equivalent.

    +
    + +
    +
    +fill_in_parameters(group_type, random=False, ones=False, universal=False)
    +

    Separate all possible types of twobodys, threebodys, manybody. +One type per group. And fill in either universal ls and sigma from +pre-defined parameters from set_parameters(“sigma”, ..) and set_parameters(“ls”, ..) +or random parameters if random is True.

    +
    +
    Parameters
    +
      +

    • group_type (str) – “specie”, “twobody”, “threebody”, “cut3b”, “manybody”

      • +

    • definition_list (list, dict) – list of elements

      • +
    +
    +
    +
    + +
    +
    +find_group(group_type, element_list, atomic_str=False)
    +

    find the group that contains the input pair

    +
    +
    Parameters
    +
      +

    • group_type (str) – species, twobody, threebody, cut3b, manybody

      • +

    • element_list (list) – list of elements for a pair/triplet/coordination-pair

      • +

    • atomic_str (bool) – whether the elements in element_list are +specified by group names or periodic table element names.

      • +
    +
    +
    Return type
    +

    name (str)

    +
    +
    +
    + +
    +
    +static from_dict(hyps_mask, verbose=False, init_spec=[])
    +

    convert dictionary mask to HM instance +This function is not tested yet

    +
    + +
    +
    +list_groups(group_type, definition_list)
    +

    define groups in batches.

    +
    +
    Parameters
    +
      +

    • group_type (str) – “specie”, “twobody”, “threebody”, “cut3b”, “manybody”

      • +

    • definition_list (list, dict) – list of elements

      • +
    +
    +
    +

    This function runs define_group in batch. Please first read +the manual of define_group.

    +

    If the definition_list is a list, it is equivalent to +executing define_group through the definition_list.

    +
    >>> for all terms in the list:
+>>>     define_group(group_type, group_type+'n', the nth term in the list)
+
    +
    +

    So the first twobody defined will be group twobody0, second one will be +group twobody1. For specie, it will define all the listed elements as +groups with only one element with their original name.

    +

    If the definition_list is a dictionary, it is equivalent to

    +
    >>> for k, v in the dict:
+>>>     define_group(group_type, k, v)
+
    +
    +

    It is not recommended to use the dictionary mode, especially when +the group definitions are conflicting with each other. There is no +guarantee that the priority order is the same as you want.

    +

    Unlike ParameterHelper.define_group(), it can only be called once for each +group_type, and not after any ParameterHelper.define_group() calls.

    +
    + +
    +
    +list_parameters(parameter_dict: dict, constraints: dict = {})
    +

    Define many groups of parameters

    +
    +
    Parameters
    +
      +

    • parameter_dict (dict) – dictionary of all parameters

      • +

    • constraints (dict) – dictionary of all constraints

      • +
    +
    +
    +

    Example:

    +
    >>> parameter_dict={"group_name":[sig, ls, cutoffs], ...}
+>>> constraints={"group_name":[True, False, False], ...}
+
    +
    +

    The name of parameters can be the group name previously defined in +define_group or list_groups function. Aside from the group name, +noise, cutoff_twobody, cutoff_threebody, and +cutoff_manybody are reserved for noise parmater +and universal cutoffs, while sigma and lengthscale are +reserved for universal signal variances and length scales.

    +

    For non-reserved keys, the value should be a list of 2 to 3 elements, +corresponding to the sigma, lengthscale and cutoff (if the third one +is defined). For reserved keys, the value should be a float number.

    +

    The parameter_dict and constraints should use the same set of keys. +If a key in constraints is not used in parameter_dict, it will be ignored.

    +

    The value in the constraints can be either a single bool, which apply +to all parameters, or list of bools that apply to each parameter.

    +
    + +
    +
    +set_constraints(name, opt)
    +

    Set the parameters for certain group

    +
    +
    Parameters
    +
      +

    • name (str) – name of the patermeters

      • +

    • opt (bool, list) – whether to optimize the parameter or not

      • +
    +
    +
    +

    The name of parameters can be the group name previously defined in +define_group or list_groups function. Aside from the group name, +noise, cutoff_twobody, cutoff_threebody, and +cutoff_manybody are reserved for noise parmater +and universal cutoffs, while sigma and lengthscale are +reserved for universal signal variances and length scales.

    +

    The optimization flag can be a single bool, which apply to all +parameters under that name, or list of bools that apply to each +parameter.

    +
    + +
    +
    +set_parameters(name, parameters, opt=True)
    +

    Set the parameters for certain group

    +
    +
    Parameters
    +
      +

    • name (str) – name of the patermeters

      • +

    • parameters (list) – the sigma, lengthscale, and cutoff of each group.

      • +

    • opt (bool, list) – whether to optimize the parameter or not

      • +
    +
    +
    +

    The name of parameters can be the group name previously defined in +define_group or list_groups function. Aside from the group name, +noise, cutoff_twobody, cutoff_threebody, and +cutoff_manybody are reserved for noise parmater +and universal cutoffs, while sigma and lengthscale are +reserved for universal signal variances and length scales.

    +

    The parameter should be a list of 2-3 elements, for sigma, +lengthscale (and cutoff if the third one is defined).

    +

    The optimization flag can be a single bool, which apply to all +parameters, or list of bools that apply to each parameter.

    +
    + +
    +
    +summarize_group(group_type)
    +

    Sort and combine all the previous definition to internal varialbes

    +
    +
    Parameters
    +

    group_type (str) – species, twobody, threebody, cut3b, manybody

    +
    +
    +
    + +
    + +
    +
    +flare.utils.parameter_helper.nprandom()
    +

    random(size=None)

    +

    Return random floats in the half-open interval [0.0, 1.0). Alias for +random_sample to ease forward-porting to the new random API.

    +
    + +
    diff --git a/flare/utils/utils.html b/flare/utils/utils.html index bc523ef20..6e9b6f91e 100644 --- a/flare/utils/utils.html +++ b/flare/utils/utils.html @@ -102,6 +102,19 @@

    UtilityConstruct Atomic Environment

    +

    Utility functions for various tasks.

    +
    +
    +class flare.utils.NumpyEncoder(*, skipkeys=False, ensure_ascii=True, check_circular=True, allow_nan=True, sort_keys=False, indent=None, separators=None, default=None)
    +

    Special json encoder for numpy types for serialization +use as

    +

    json.loads(… cls = NumpyEncoder)

    +

    or:

    +

    json.dumps(… cls = NumpyEncoder)

    +

    Thanks to StackOverflow users karlB and fnunnari, who contributed this from: +https://stackoverflow.com/a/47626762

    +
    +
    diff --git a/genindex.html b/genindex.html index 630b45b61..36a0cd8fd 100644 --- a/genindex.html +++ b/genindex.html @@ -80,14 +80,64 @@

    Index

    - B + A + | B | C | D + | E + | F + | G + | H + | I | K + | L + | M | N + | O + | P + | Q + | R | S + | T + | U + | V + | W
    +

    A

    + + + +
    +

    B

    - +
    @@ -127,6 +183,22 @@

    B

    C

    - +
    @@ -163,6 +255,8 @@

    C

    D

    +

    E

    + + + +
    + +

    F

    + + + +
    + +

    G

    + + + +
    + +

    H

    + + +
    + +

    I

    + + + +
    +

    K

    +
    + +

    L

    + + + +
    + +

    M

    + + +
    @@ -289,12 +878,12 @@

    N

  • NormalizedDotProduct::envs_struc_grad (C++ function)
    • - - + + + +

    O

    + + + +
    + +

    P

    + + + +
    + +

    Q

    + + + +
    + +

    R

    + + +
    @@ -317,6 +1034,20 @@

    N

    S

    +
    + +

    T

    + + + +
    + +

    U

    + + + +
    + +

    V

    + + +
    + +

    W

    + + +
    diff --git a/index.html b/index.html index 064a77833..9bd8e47a8 100644 --- a/index.html +++ b/index.html @@ -156,7 +156,10 @@

    ContentsBayesian Active Learning diff --git a/objects.inv b/objects.inv index e336e2db9d359d0b52b7ba405de2b89c0d1885f1..02fc688ae32dd90f35b0a31326d42e2d13cb1ad4 100644 GIT binary patch literal 23111 zcmV)!K#;#9AX9K?X>NERX>N99Zgg*Qc_4OWa&u{KZXhxWBOp+6Z)#;@bUGkrY+-U` z3L_v^WpZ8b#rNMXCQiPX<{x4c-qx{S(DtjwdT8jMMlUmV}~at?u*{kQmO4wORX!ledjF$ z1i&gC8PLlA--BL1p#>=IRf~PAWTpOegi@krQVoE)K`bneG7if_3_2+wDQzeTqM`|DG== z%2V<3WqEzAn>P|FIsNW|9uj(zRpAdH?)u2rvQTn#82lG>Q;eH@&V$4D$qx`;!vbQ?)J9`ep?b4z!R-MGmEOvCk-D%!VtRC^IIKVS62E-8WVmZ} z%YHDx?K#{}8+NlJ8=0J2^O9xbm=qThIKjG4caQR#uc3Dm` ztnPWoTAeQ39amu|0L^K3|BygKt%A_y>YYFgK1)VF%pUU)N7+0IRZL9i>Cr?1bm1ly z>P7WqjpLwxtg_>i)8d4wA!{9n4=hWfFj41hF77M^t+5TKne&D=Q;H4f91d*8>hc}) z1Itx~4UkBSZb&}1X%LZ5Dbo$e$4Uk9I8V9J0vt!6e5s`K0|L>(w{$Ok}O`nyg%*^1sQblDw(zhDI>0K8L>xn zf@I5!ESvz;;9#P_j8igGTspLv7utnp)J}C!GMV#a|KYpSE^xtk2E)LAfpR z;A>LT4h?LtkFgT9rB&{m(sX`&nu{vpx-6%cR;OrLxAa0vysbY{j21?PYm-}6pevIb z7wM0~PT%wS1CW)tEv8??#-#dgOm^<}S8euH0_G__PSj!F3I!{i6%aVyXKzE9YmzI+{ 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000000000..d67202f88 --- /dev/null +++ b/py-modindex.html @@ -0,0 +1,269 @@ + + + + + + Python Module Index — flare 1.4.0 documentation + + + + + + + + + + + + + + + + + + + + + +
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    Python Module Index

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    + flare +
        + flare.bffs.gp.calculator +
        + flare.bffs.gp.gp +
        + flare.bffs.gp.gp_algebra +
        + flare.bffs.gp.predict +
        + flare.bffs.mgp.mgp +
        + flare.bffs.mgp.splines_methods +
        + flare.bffs.sgp.calculator +
        + flare.bffs.sgp.sparse_gp +
        + flare.descriptors.env +
        + flare.io.otf_parser +
        + flare.io.output +
        + flare.kernels.cutoffs +
        + flare.kernels.kernels +
        + flare.kernels.mc_3b_sepcut +
        + flare.kernels.mc_mb_sepcut +
        + flare.kernels.mc_sephyps +
        + flare.kernels.mc_simple +
        + flare.kernels.sc +
        + flare.learners.gp_from_aimd +
        + flare.learners.otf +
        + flare.learners.utils +
        + flare.md.fake +
        + flare.md.lammps +
        + flare.md.nosehoover +
        + flare.utils +
        + flare.utils.env_getarray +
        + flare.utils.parameter_helper +
        + flare.utils.parameters +
    + + +
    +
    +
    + +
    + +
    +

    © Copyright 2021, Jonathan Vandermause, Yu Xie, Anders Johansson, Cameron Owen.

    +
    + + Built with Sphinx using a + theme + provided by Read the Docs. + + +
    +
    +
    +
    +
    + + + + \ No newline at end of file diff --git a/searchindex.js b/searchindex.js index ed20454f0..7f212db3d 100644 --- a/searchindex.js +++ b/searchindex.js @@ -1 +1 @@ -Search.setIndex({"docnames": ["citing", "contribute/contribute", "contribute/standards", "contribute/workflow", "faqs", "flare/bffs/bffs", "flare/bffs/gp/calculator", "flare/bffs/gp/gp", "flare/bffs/gp/gp_algebra", "flare/bffs/gp/predict", "flare/bffs/mgp/formulas", "flare/bffs/mgp/mgp", "flare/bffs/mgp/splines_methods", "flare/bffs/sgp/calculator", "flare/bffs/sgp/sgp", "flare/descriptors/descriptors", "flare/descriptors/env", "flare/flare", "flare/io/io", "flare/io/otf_parser", "flare/io/output", "flare/kernels/cutoffs", "flare/kernels/helper", "flare/kernels/kernels", "flare/kernels/mc_sephyps", "flare/kernels/mc_simple", "flare/kernels/sc", "flare/learners/gp_from_aimd", "flare/learners/learners", "flare/learners/lmpotf", "flare/learners/otf", "flare/learners/utils", "flare/md/fake", "flare/md/lammps", 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