This review explores the recent advancements in enhancing Computational Fluid Dynamics (CFD) through Machine Learning (ML). The literature is systematically classified into three primary categories: Data-driven Surrogates, Physics-Informed Surrogates, and ML-assisted Numerical Solutions. Subsequently, we highlight applications of ML for CFD in critical scientific and engineering disciplines, including aerodynamics, atmospheric science, and biofluid dynamics, among others.
Awesome-AI4CFD- Awesome-AI4CFD
| Title | Venue | Date | Code | Note |
|---|---|---|---|---|
 PDEBench |
NeurIPS 2022 | 2022-10-13 | GitHub | Local Demo |
 DeepXDE: A Deep Learning Library for Solving Differential Equations |
SIAM Review | 2021-01 | GitHub | - |
 DrivAerNet: A Parametric Car Dataset for Data-Driven Aerodynamic Design and Graph-Based Drag Prediction |
Arxiv | 2024-05 | GitHub | - |
| Title | Venue | Date | Code | Demo |
|---|---|---|---|---|
 [Towards Physics-informed Deep Learning for Turbulent Flow Prediction] |
KDD 2020 | 2020-08-20 | Github | - |
 Incorporating Symmetry into Deep Dynamics Models for Improved Generalization |
ICLR 2021 | 2021-03-15 | Github | |
Approximately Equivariant Networks for Imperfectly Symmetric Dynamics |
ICML 2022 | 2022-06-28 | Github |
| Title | Venue | Date | Code | Demo |
|---|---|---|---|---|
 Learning to Simulate Complex Physics with Graph Networks |
ICML 2020 | 2020-09-14 | Github | Video |
| Learning Mesh-Based Simulation with Graph Networks |
ICLR 2021 |
2021-06-18 | Github | Video |
 Message Passing Neural PDE Solvers |
ICLR 2022 | 2023-03-20 | Github | Local Demo |
 MAgNet:Mesh Agnostic Neural PDE Solver |
NeurIPS 2022 | 2023-03-20 | Github | Local Demo |
CARE:Modeling Interacting Dynamics Under Temporal Environmental Variation |
NeurIPS 2023 | 2023-12-15 | - | - |
| Title | Venue | Date | Code | Demo |
|---|---|---|---|---|
 LAGRANGIAN FLUID SIMULATION WITH CONTINUOUS CONVOLUTIONS |
ICLR2020 | 2019-09-25 | Github | - |
 Graph neural network accelerated lagrangian fluid simulation |
Comput Graph | 2022-04-01 | Github | - |
Fast Fluid Simulation via Dynamic Multi-Scale Gridding |
AAAI 2023 | 2023-06-26 | - | - |
| Title | Venue | Date | Code | Demo |
|---|---|---|---|---|
 Learning nonlinear operators via deeponet based on the universal approximation theorem of operators. |
Nature Machine Intelligence | 2021 | Github | |
Nomad: Nonlinear manifold decoders for operator learning. |
NeurIPS | 2022 | - | |
| Fourier-mionet: Fourier enhanced multiple-input neural operators for multiphase modeling of geological carbon sequestration. |
J. Comput. Phy. | Date Not Provided | Github | - |
Hyperdeeponet: learning operator with complex target function space using the limited resources via hypernetwork. |
ICLR | 2023 | - |
| Title | Venue | Date | Code | Demo |
|---|---|---|---|---|
Multipole graph neural operator for parametric PDEs |
NeurIPS | 2020 | - | - |
Geometry-informed neural operator for large-scale 3d pdes |
NeurIPS | 2023 | - | - |
 LNO: Laplace neural operator for solving differential equations. |
Arxiv | 2023 | Github | Video |
 Koopman Neural Operator as a mesh-free solver of non-linear PDEs. |
Arxiv | 2023 | Github | - |
 In-context operator learning for differential equation problems. |
PNAS | 2023 | Github | - |
| Title | Venue | Date | Code | Demo |
|---|---|---|---|---|
 Fourier neural operator for parametric partial differential equations. |
ICLR | 2021 | Github | Video |
 Factorized fourier neural operators |
ICLR | 2023 | Github | - |
 Clifford neural layers for pde modeling |
ICLR | 2023 | Github | - |
Geometry-informed neural operator for large-scale 3d pdes. |
NeurIPS | 2023 | - | - |
| Title | Venue | Date | Code | Demo |
|---|---|---|---|---|
 Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear PDEs |
JCP(Journal of Computational Physics) | 2019 | Github | - |
 Physics-informed learning of governing equations from scarce data. |
Nature Communications | 2021 | Github | - |
 NSFnets (Navier-Stokes flow nets): Physics-informed neural networks for the incompressible Navier-Stokes equations |
JCP(Journal of Computational Physics) | 2021 | Github | - |
Meta-auto-decoder for solving parametric partial differential equations. |
NeurIPS | 2022 | - | - |
Nas-pinn: neural architecture search-guided physics-informed neural network for solving pdes. |
JCP(Journal of Computational Physics) | 2024 | - | - |
| Title | Venue | Date | Code | Demo |
|---|---|---|---|---|
 Evolutional Deep Neural Network |
Physical Review E | 2021-10-04 | Github | - |
| Adlgm: An efficient adaptive sampling dl galerkin method |
JCP | - | - | |
 Implicit Neural Spatial Representations for Time-dependent PDEs |
ICML 2023 | 2022-09-29 | Github | - |
 Neural galerkin schemes with active learning for high dimensional evolution equations |
JCP | 2024-01 | Github | - |
| Multi-resolution partial differential equations preserved learning framework for spatiotemporal dynamics |
Communications Physics | 2024-01-13 | Github | - |
| Title | Venue | Date | Code | Demo |
|---|---|---|---|---|
 Learning data-driven discretizations for partial differential equations. |
PNAS | 2019 | Github | - |
Machine learning accelerated computational fluid dynamics. |
PNAS | 2021 | - | - |
 Learned turbulence modelling with differentiable fluid solvers: physics-based loss functions and optimisation horizons. |
JFM(Journal of Fluid Mechanics) | 2022 | Github | - |
Machine learning design of volume of fluid schemes for compressible flows. |
JCP(Journal of Computational Physics) | 2020 | - | - |
 A multi-scale sampling method for accurate and robust deep neural network to predict combustion chemical kinetics |
2022 | Github | - | |
 A neural pde solver with temporal stencil modeling. |
arXiv. | 2023 | Github | - |
Scalable projection-based RO models for large multiscale fluid systems. |
AIAA | 2023 | - | - |
| Title | Venue | Date | Code | Demo |
|---|---|---|---|---|
 Learning to simulate complex physics with graph networks |
ICML | 2020 | Github | video |
| Learning to optimize multigrid pde solvers |
ICML | 2019 | Github | - |
 Learning algebraic multigrid using graph neural networks. |
ICML | 2020 | Github | - |
| Title | Venue | Date | Code | Demo |
|---|---|---|---|---|
Using ML to augment coarse-grid CFD simulations. |
arXiv. | 2020 | - | - |
 Solver-in-the-loop:Learning from differentiable physics to interact with iterative pde-solvers |
NeuraIPS | 2020 | Github | - |
 Combining differentiable pde solvers and graph neural networks for fluid flow prediction |
ICML | 2020 | Github | - |
A deep learning based accelerator for fluid simulations |
ICS | 2020 | - | - |
| Title | Venue | Date | Code | Demo |
|---|---|---|---|---|
 Neural-fly enables rapid learning for agile flight in strong winds |
Science Robotics | 2022 | Github | - |
 Prediction of transonic flow over supercritical airfoils using geometric encoding and deep-learning strategies |
Physics of Fluids | 2023 | Github | - |
Shock wave prediction in transonic flow fields using domain-informed probabilistic deep learning. |
Physics of Fluids | 2024 | - | - |
| Title | Venue | Date | Code | Demo |
|---|---|---|---|---|
 Stiff-pinn: Physics-informed neural network for stiff chemical kinetics |
The Journal of Physical Chemistry A | 2021 | Github | - |
A multi-scale sampling method for accurate and robust deep neural network to predict combustion chemical kinetics |
Combustion and Flame | 2022 | Github | - |
| Title | Venue | Date | Code | Demo |
|---|---|---|---|---|
FourCastNet: A global data-driven HR weather model using AFNO |
arXiv. | 2022 | - | - |
 Accurate medium-range global weather forecasting with 3d nns. |
Nature | 2023 | Github | - |
 Learning skillful medium-range global weather forecasting |
Science | 2023 | Github | - |
Evaluation of Deep Neural Operator models toward ocean forecasting |
OCEANS | 2023 | - | - |
 U-fno an enhanced FNO-based DL model for multiphase flow |
AWR | 2022 | Github | - |
Fourier-mionet: Fourier-enhanced multiple-input neural operators for multiphase modeling of geological carbon sequestration. |
arXiv. | 2023 | - | - |
| Title | Venue | Date | Code | Demo |
|---|---|---|---|---|
Simulating progressive intramural damage leading to aortic dissection using DeepONet: an operator–regression neural network |
Journal of The Royal Society Interface | 2022 | - | - |
Improving microstructural integrity, interstitial fluid, and blood microcirculation images. |
JSMRM | 2023 | - | - |
Multiple case PINN for biomedical tube flows |
arXiv. | 2023 | - | - |
| Title | Venue | Date | Code | Demo |
|---|---|---|---|---|
Low-temperature plasma simulation based on physics-informed neural networks. |
Phys. Fluids | 2022 | - | - |
Fourier neural operator for plasma modelling |
arXiv. | 2023 | - | - |
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