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Recent Advances on Machine Learning for Computational Fluid Dynamics: A Survey

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Awesome-AI4CFD

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


Existing Benchmarks

Title Venue Date Code Note
Star
PDEBench
NeurIPS 2022 2022-10-13 GitHub Local Demo
Star
DeepXDE: A Deep Learning Library for Solving Differential Equations
SIAM Review 2021-01 GitHub -
Star
DrivAerNet: A Parametric Car Dataset for Data-Driven Aerodynamic Design and Graph-Based Drag Prediction
Arxiv 2024-05 GitHub -

Data-driven Surrogates

Dependent on Discretization

On Structured Grids

Title Venue Date Code Demo
Star
[Towards Physics-informed Deep Learning for Turbulent Flow Prediction]
KDD 2020 2020-08-20 Github -
Star
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

On Unstructured Mesh

Title Venue Date Code Demo
Star
Learning to Simulate Complex Physics with Graph Networks
ICML 2020 2020-09-14 Github Video
Star
Learning Mesh-Based Simulation with Graph Networks
ICLR 2021
2021-06-18 Github Video
Star
Message Passing Neural PDE Solvers
ICLR 2022 2023-03-20 Github Local Demo
Star
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 - -

On Lagrangian Particle

Title Venue Date Code Demo
Star
LAGRANGIAN FLUID SIMULATION WITH CONTINUOUS CONVOLUTIONS
ICLR2020 2019-09-25 Github -
Star
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 - -

Independent on Discretization

Deep Operator Network

Title Venue Date Code Demo
Star
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 -
Star
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 -

In Physical Space

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 - -
Star
LNO: Laplace neural operator for solving differential equations.
Arxiv 2023 Github Video
Star
Koopman Neural Operator as a mesh-free solver of non-linear PDEs.
Arxiv 2023 Github -
Star
In-context operator learning for differential equation problems.
PNAS 2023 Github -

Fourier Neural Operator

Title Venue Date Code Demo
Star
Fourier neural operator for parametric partial differential equations.
ICLR 2021 Github Video
Star
Factorized fourier neural operators
ICLR 2023 Github -
Star
Clifford neural layers for pde modeling
ICLR 2023 Github -

Geometry-informed neural operator for large-scale 3d pdes.
NeurIPS 2023 - -

Physics-driven Surrogates

Physics-Informed Neural Network (PINN)

Title Venue Date Code Demo
Star
Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear PDEs
JCP(Journal of Computational Physics) 2019 Github -
Star
Physics-informed learning of governing equations from scarce data.
Nature Communications 2021 Github -
Star
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 - -

Discretized PDE-Informed Neural Network

Title Venue Date Code Demo
Star
Evolutional Deep Neural Network
Physical Review E 2021-10-04 Github -
Adlgm: An efficient adaptive sampling dl galerkin method
JCP - -
Star
Implicit Neural Spatial Representations for Time-dependent PDEs
ICML 2023 2022-09-29 Github -
Star
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 -

ML-assisted Numerical Solutions

Assist Simulation at Coarser Scales

Title Venue Date Code Demo
Star
Learning data-driven discretizations for partial differential equations.
PNAS 2019 Github -

Machine learning accelerated computational fluid dynamics.
PNAS 2021 - -
Star
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 - -
Star
A multi-scale sampling method for accurate and robust deep neural network to predict combustion chemical kinetics
2022 Github -
Star
A neural pde solver with temporal stencil modeling.
arXiv. 2023 Github -

Scalable projection-based RO models for large multiscale fluid systems.
AIAA 2023 - -

Preconditioning

Title Venue Date Code Demo
Star
Learning to simulate complex physics with graph networks
ICML 2020 Github video
Star
Learning to optimize multigrid pde solvers
ICML 2019 Github -
Star
Learning algebraic multigrid using graph neural networks.
ICML 2020 Github -

Miscellaneous

Title Venue Date Code Demo

Using ML to augment coarse-grid CFD simulations.
arXiv. 2020 - -
Star
Solver-in-the-loop:Learning from differentiable physics to interact with iterative pde-solvers
NeuraIPS 2020 Github -
Star
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 - -

Application Novelty

Aerodynamics

Title Venue Date Code Demo
Star
Neural-fly enables rapid learning for agile flight in strong winds
Science Robotics 2022 Github -
Star
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 - -

Combustion & Reacting Flow

Title Venue Date Code Demo
Star
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 -

Atmosphere & Ocean Science

Title Venue Date Code Demo

FourCastNet: A global data-driven HR weather model using AFNO
arXiv. 2022 - -
Star
Accurate medium-range global weather forecasting with 3d nns.
Nature 2023 Github -
Star
Learning skillful medium-range global weather forecasting
Science 2023 Github -

Evaluation of Deep Neural Operator models toward ocean forecasting
OCEANS 2023 - -
Star
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 - -

Biology Fluid

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 - -

Plasma

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 - -

Contributing

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