Stochastic State-Space Inference and Prediction in Python (pySIP)

Ordinary differential equations, determined from first-principles, can be used for modeling physical systems. However, the exact dynamics of such systems are uncertain and only measured at discrete-time instants through non-ideal sensors. In this case, stochastic differential equations provide a modeling framework which is more robust to these uncertainties. The stochastic part of the state-space model can accommodate for unmodeled disturbances, which do not have a significant influence on the system dynamics. Otherwise, unmeasured disturbances can be modeled as temporal Gaussian Processes with certain parametrized covariance structure. The resulting Latent Force Model is a combination of parametric grey-box model and non-parametric Gaussian process model.

pySIP provides a framework for infering continuous time linear stochastic state-space models. For that purpose, it is possible to chose between a frequentist and a Bayesian workflow. Each workflow allows to estimate the parameters, assess the inference and model reliability, and perform model selection.

pySIP is being developed in the perspective to build a library which gather models from different engineering applications. Currently, applications involving dynamic thermal models (RC network) and temporal Gaussian Processes are being prioritized. Nevertheless, any model following the formalism of pySIP can benefit from the features.

pySIP is currently under development and in beta version. Please feel free to contact us if you want to be involved in the current development process.

You can find the documentation here : it contains a quick start guide, a cookbook, a tour of the library internals and a reference documentation.

IMPORTANT - Migration to v1.0.0

The version 1.0.0 of pySIP is a major update of the library. It focused on (slightly) reducing the scope of the library and delegating some tasks to other libraries (mainly scipy for the distribution, numba for the code acceleration and pymc for the bayesian inference).

Regression are expected to happen, but the library should be in road to a more stable state.

Main changes are:

• using pymc3 for the bayesian inference (all the mcmc module have been removed)
• removing all analytical jacobian computation (using numerical approximation of the jacobian instead)
• full Regressor class rework : there is no more separation between the FrequentistRegressor and the BayesianRegressor. The regressor has now the ability to perform both frequentist (with the regressor.fit method) and bayesian (with the regressor.sample method) inference.
• the KalmanQR class is now accelerated using numba
• the library use pandas.DataFrame or xarray.Dataset as output for the Regressor class, allowing easier manipulation of the results.

Do not hesitate to open an issue if you encounter any problem with the new version. If you encounter a regression, it should be possible to re-introduce the functionality. When the version will be in the main branch, a gitter channel will be created to help the migration.

A release tag is available for the previous version of the library (v0.9.0). It will also be updated on pip : if you are not ready to migrate to the new version, you can install the previous version using pip install git+https://github.com/locie/[email protected].

Contributors

• Loïc Raillon - Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, LOCIE, 73000 Chambéry, France,
• Maxime Janvier - Lancey Energy Storage
• Nicolas Cellier - IMT Mines Albi - CGI (current maintainer)

Funding

• Auvergne Rhône-Alpes, project HESTIA-Diag, habitat Econome avec Système Thermique Innovant Adapté pour le Diagnostic