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

• Awesome-AI4CFD
  • Existing Benchmarks
  • Data-driven Surrogates
    • Dependent on Discretization
      • On Structured Grids
      • On Unstructured Mesh
      • On Lagrangian Particle
    • Independent on Discretization
      • Deep Operator Network
      • In Physical Space
      • Fourier Neural Operator
  • Physics-driven Surrogates
    • Physics-Informed Neural Network (PINN)
    • Discretized PDE-Informed Neural Network
  • ML-assisted Numerical Solutions
    • Assist Simulation at Coarser Scales
    • Preconditioning
    • Miscellaneous
  • Application Novelty
    • Aerodynamics
    • Combustion & Reacting Flow
    • Atmosphere & Ocean Science
    • Biology Fluid
    • Plasma
  • Contributing

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Existing Benchmarks

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	-

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Data-driven Surrogates

Dependent on Discretization

On Structured Grids

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

On Unstructured Mesh

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	-	-

On Lagrangian Particle

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	-	-

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Independent on Discretization

Deep Operator Network

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	-

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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	-	-
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	-

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Fourier Neural Operator

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	-	-

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Physics-driven Surrogates

Physics-Informed Neural Network (PINN)

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	-	-

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Discretized PDE-Informed Neural Network

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	-

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ML-assisted Numerical Solutions

Assist Simulation at Coarser Scales

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	-	-

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Preconditioning

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	-

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Miscellaneous

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	-	-

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Application Novelty

Aerodynamics

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	-	-

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Combustion & Reacting Flow

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	-

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Atmosphere & Ocean Science

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	-	-

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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	-	-

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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	-	-

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Contributing

📮📮📮 If you want to add your model in our leaderboards, please feel free to fork and update your work in the table. You can also email wang.hx@stu.pku.edu.cn. We will response to your request as soon as possible!