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Awesome-AI4CFD

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

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# Awesome-AI4CFD

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[![Survey](https://img.shields.io/badge/Survey-AI4CFD-blue)](https://github.com/WillDreamer/Awesome-AI4CFD) 
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## [Recent Advances on Machine Learning for Computational Fluid Dynamics: A Survey](https://arxiv.org/abs/2408.12171)
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.

<center> Awesome-AI4CFD </center>

- [Awesome-AI4CFD](#awesome-ai4cfd)
  - [Existing Benchmarks](#existing-benchmarks)
  - [Data-driven Surrogates](#data-driven-surrogates)
    - [Dependent on Discretization](#dependent-on-discretization)
      - [On Structured Grids](#on-structured-grids)
      - [On Unstructured Mesh](#on-unstructured-mesh)
      - [On Lagrangian Particle](#on-lagrangian-particle)
    - [Independent on Discretization](#independent-on-discretization)
      - [Deep Operator Network](#deep-operator-network)
      - [In Physical Space](#in-physical-space)
      - [Fourier Neural Operator](#fourier-neural-operator)
  - [Physics-driven Surrogates](#physics-driven-surrogates)
    - [Physics-Informed Neural Network (PINN)](#physics-informed-neural-network-pinn)
    - [Discretized PDE-Informed Neural Network](#discretized-pde-informed-neural-network)
  - [ML-assisted Numerical Solutions](#ml-assisted-numerical-solutions)
    - [Assist Simulation at Coarser Scales](#assist-simulation-at-coarser-scales)
    - [Preconditioning](#preconditioning)
    - [Miscellaneous](#miscellaneous)
  - [Application Novelty](#application-novelty)
    - [Aerodynamics](#aerodynamics)
    - [Combustion \& Reacting Flow](#combustion--reacting-flow)
    - [Atmosphere \& Ocean Science](#atmosphere--ocean-science)
    - [Biology Fluid](#biology-fluid)
    - [Plasma](#plasma)
  - [Frontier Models](#frontier-models)
    - [Foundation Models](#foundation-models)
    - [Generative Models](#generative-models)   
  - [Contributing](#contributing)

---

## Existing Benchmarks

| Title | Venue | Date | Code | Note |
|:--------|:--------:|:--------:|:--------:|:--------:|
|![Star](https://img.shields.io/github/stars/pdebench/PDEBench) [**PDEBench**](https://arxiv.org/abs/2210.07182) | NeurIPS 2022 | 2022-10-13 | [GitHub](https://github.com/pdebench/PDEBench) | Local Demo |
|![Star](https://img.shields.io/github/stars/lululxvi/deepxde.svg?style=social&label=Star) [**DeepXDE: A Deep Learning Library for Solving Differential Equations**](https://epubs.siam.org/doi/pdf/10.1137/19M1274067) | SIAM Review | 2021-01 | [GitHub](https://github.com/lululxvi/deepxde) | - |
|![Star](https://img.shields.io/github/stars/Mohamedelrefaie/DrivAerNet.svg?style=social&label=Star) [**DrivAerNet: A Parametric Car Dataset for Data-Driven Aerodynamic Design and Graph-Based Drag Prediction**](https://arxiv.org/abs/2403.08055) | arXiv | 2024-05 | [GitHub](https://github.com/Mohamedelrefaie/DrivAerNet) | - |
|![Star](https://img.shields.io/github/stars/PolymathicAI/the_well.svg?style=social&label=Star) [**The Well: a Large-Scale Collection of Diverse Physics Simulations for Machine Learning**](https://arxiv.org/abs/2412.00568) | NeurIPS 2024 DB Track | 2024-12 | [GitHub](https://github.com/PolymathicAI/the_well) | - |

---

## Data-driven Surrogates

### Dependent on Discretization

#### On Structured Grids

| Title | Venue | Date | Code | Demo |
|:--------|:--------:|:--------:|:--------:|:--------:|
|![Star](https://img.shields.io/github/stars/Rose-STL-Lab/Turbulent-Flow-Net.svg?style=social&label=Star) [**Towards Physics-informed Deep Learning for Turbulent Flow Prediction**](https://arxiv.org/abs/1911.08655) | KDD 2020 | 2020-08-20 | [Github](https://github.com/Rose-STL-Lab/Turbulent-Flow-Net) | - |
|![Star](https://img.shields.io/github/stars/Rose-STL-Lab/Equivariant-Net.svg?style=social&label=Star) [**Incorporating Symmetry into Deep Dynamics Models for Improved Generalization**](https://arxiv.org/pdf/2002.03061.pdf) | ICLR 2021 | 2021-03-15 | [Github](https://github.com/Rose-STL-Lab/Equivariant-Net) |
| [**Approximately Equivariant Networks for Imperfectly Symmetric Dynamics**](https://proceedings.mlr.press/v162/wang22aa/wang22aa.pdf) | ICML 2022 | 2022-06-28 | [Github](https://github.com/Rose-STL-Lab/Approximately-Equivariant-Nets) |

#### On Unstructured Mesh

| Title | Venue | Date | Code | Demo |
|:--------|:--------:|:--------:|:--------:|:--------:|
| ![Star](https://img.shields.io/github/stars/google-deepmind/deepmind-research.svg?style=social&label=Star) [**Learning to Simulate Complex Physics with Graph Networks**](https://arxiv.org/abs/2002.09405) | ICML 2020 | 2020-09-14 | [Github](https://github.com/google-deepmind/deepmind-research/tree/master/learning_to_simulate) | [Video](https://sites.google.com/view/learning-to-simulate) |
| ![Star](https://img.shields.io/github/stars/google-deepmind/deepmind-research.svg?style=social&label=Star) [**Learning Mesh-Based Simulation with Graph Networks**](https://arxiv.org/abs/2010.03409) | ICLR 2021 | 2021-06-18 | [Github](https://github.com/google-deepmind/deepmind-research/tree/master/meshgraphnets) | [Video](https://sites.google.com/view/meshgraphnets) |
| ![Star](https://img.shields.io/github/stars/brandstetter-johannes/MP-Neural-PDE-Solvers.svg?style=social&label=Star) [**Message Passing Neural PDE Solvers**](https://arxiv.org/abs/2202.03376) | ICLR 2022 | 2023-03-20 | [Github](https://github.com/brandstetter-johannes/MP-Neural-PDE-Solvers) | Local Demo|
|![Star](https://img.shields.io/github/stars/jaggbow/magnet.svg?style=social&label=Star) [**MAgNet:Mesh Agnostic Neural PDE Solver**](https://arxiv.org/pdf/2210.05495.pdf) | NeurIPS 2022 | 2023-03-20 | [Github](https://github.com/jaggbow/magnet) | Local Demo|
| [**CARE:Modeling Interacting Dynamics Under Temporal Environmental Variation**](https://openreview.net/attachment?id=lwg3ohkFRv&name=pdf) | NeurIPS 2023 | 2023-12-15 | - | - |
|![Star](https://img.shields.io/github/stars/yuyudeep/hcmt.svg?style=social&label=Star) [**Learning Flexible Body Collision Dynamics with Hierarchical Contact Mesh Transformer**](https://openreview.net/forum?id=90yw2uM6J5) | ICLR 2024 | 2024-03-26 | [Github](https://github.com/yuyudeep/hcmt) | - |
|![Star](https://img.shields.io/github/stars/anthonyzhou-1/ldm_pdes.svg?style=social&label=Star) [**Text2PDE: Latent Diffusion Models for Accessible Physics Simulation**](https://openreview.net/forum?id=Nb3a8aUGfj) | ICLR 2025 | 2024-10-02 | [Github](https://github.com/anthonyzhou-1/ldm_pdes) | - |

#### On Lagrangian Particle

| Title | Venue | Date | Code | Demo |
|:--------|:--------:|:--------:|:--------:|:--------:|
|![Star](https://img.shields.io/github/stars/isl-org/DeepLagrangianFluids.svg?style=social&label=Star) [**LAGRANGIAN FLUID SIMULATION WITH CONTINUOUS CONVOLUTIONS**](https://openreview.net/pdf?id=B1lDoJSYDH) | ICLR2020 | 2019-09-25 | [Github](https://github.com/isl-org/DeepLagrangianFluids) | - |
|![Star](https://img.shields.io/github/stars/BaratiLab/FGN.svg?style=social&label=Star) [**Graph neural network accelerated lagrangian fluid simulation**](https://dl.acm.org/doi/abs/10.1016/j.cag.2022.02.004) | Comput Graph | 2022-04-01 | [Github](https://github.com/BaratiLab/FGN) | - |
| [**Fast Fluid Simulation via Dynamic Multi-Scale Gridding**](https://ojs.aaai.org/index.php/AAAI/article/view/25255/25027) | AAAI 2023 | 2023-06-26 | - | - |

---

### Independent on Discretization

#### Deep Operator Network

| Title | Venue | Date | Code | Demo |
|:--------|:--------:|:--------:|:--------:|:--------:|
| ![Star](https://img.shields.io/github/stars/lululxvi/deeponet.svg?style=social&label=Star) [**Learning nonlinear operators via deeponet based on the universal approximation theorem of operators**](https://www.nature.com/articles/s42256-021-00302-5.pdf) | Nature Machine Intelligence | 2021 | [Github](https://github.com/lululxvi/deeponet) | |
| [**Nomad: Nonlinear manifold decoders for operator learning**](https://arxiv.org/pdf/2206.03551) | NeurIPS | 2022 | - | |
| ![Star](https://img.shields.io/github/stars/lululxvi/deepxde.svg?style=social&label=Star) [**Fourier-mionet: Fourier enhanced multiple-input neural operators for multiphase modeling of geological carbon sequestration**](https://arxiv.org/pdf/2303.04778v1.pdf) | J. Comput. Phy. | Date Not Provided | [Github](https://github.com/lululxvi/deepxde) | - |
| [**Hyperdeeponet: learning operator with complex target function space using the limited resources via hypernetwork**](https://arxiv.org/pdf/2312.15949v1.pdf) | ICLR | 2023 | - | |

---

#### In Physical Space

| Title | Venue | Date | Code | Demo |
|:------|:-----:|:----:|:----:|:----:|
| [**Multipole graph neural operator for parametric PDEs**](https://arxiv.org/abs/2006.09535) | NeurIPS | 2020 | - | - |
| [**Geometry-informed neural operator for large-scale 3d pdes**](https://arxiv.org/pdf/2309.00583) | NeurIPS | 2023 | - | - |
| ![Star](https://img.shields.io/github/stars/samholt/NeuralLaplace.svg?style=social&label=Star) [**LNO: Laplace neural operator for solving differential equations**](https://arxiv.org/pdf/2303.10528) | arXiv | 2023 | [Github](https://github.com/samholt/NeuralLaplace) | [Video](https://www.youtube.com/watch?v=o799FwH85cw) |
| ![Star](https://img.shields.io/github/stars/Koopman-Laboratory/KoopmanLab.svg?style=social&label=Star) [**Koopman Neural Operator as a mesh-free solver of non-linear PDEs**](https://arxiv.org/abs/2301.10022) | arXiv | 2023 | [Github](https://github.com/Koopman-Laboratory/KoopmanLab) | - |
| ![Star](https://img.shields.io/github/stars/liuyangmage/in-context-operator-networks.svg?style=social&label=Star) [**In-context operator learning for differential equation problems**](https://placeholder-for-link-to-KNO-paper) | PNAS | 2023 | [Github](https://github.com/liuyangmage/in-context-operator-networks)| - |

---

#### Fourier Neural Operator

| Title | Venue | Date | Code | Demo |
|:------|:-----:|:----:|:----:|:----:|
| ![Star](https://img.shields.io/github/stars/khassibi/fourier-neural-operator.svg?style=social&label=Star) [**Fourier neural operator for parametric partial differential equations**](https://arxiv.org/pdf/2010.08895) | ICLR | 2021 | [Github](https://github.com/khassibi/fourier-neural-operator) | [Video](https://zongyi-li.github.io/blog/2020/fourier-pde/) |
| ![Star](https://img.shields.io/github/stars/alasdairtran/fourierflow.svg?style=social&label=Star) [**Factorized fourier neural operators**](https://arxiv.org/abs/2111.13802) | ICLR | 2023 | [Github](https://github.com/alasdairtran/fourierflow) | - |
| ![Star](https://img.shields.io/github/stars/microsoft/cliffordlayers) [**Clifford neural layers for pde modeling**](https://arxiv.org/pdf/2209.04934) | ICLR | 2023 | [Github](https://github.com/microsoft/cliffordlayers/tree/main) | - |
| [**Geometry-informed neural operator for large-scale 3d pdes.**](https://arxiv.org/abs/2309.00583) | NeurIPS | 2023 | -| - |
| [**Physics-informed neural operator for learning partial differential equations**](https://dl.acm.org/doi/full/10.1145/3648506) | ACM/IMS Journal of Data Science | 2025 | - | - | 
---

## Physics-driven Surrogates

### Physics-Informed Neural Network (PINN)

| Title | Venue | Date | Code | Demo |
|:------|:-----:|:----:|:----:|:----:|
| ![Star](https://img.shields.io/github/stars/maziarraissi/PINNs.svg?style=social&label=Star) [**Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear PDEs**](https://placeholder-for-link-to-PINN-paper) | JCP(Journal of Computational Physics) | 2019 | [Github](https://github.com/maziarraissi/PINNs) | - |
| ![Star](https://img.shields.io/github/stars/ZhaoChenCivilSciML/EQDiscovery-1.svg?style=social&label=Star) [**Physics-informed learning of governing equations from scarce data**](https://arxiv.org/abs/2005.03448) | Nature Communications | 2021 | [Github](https://github.com/ZhaoChenCivilSciML/EQDiscovery-1) | - |
| ![Star](https://img.shields.io/github/stars/Scien42/NSFnet.svg?style=social&label=Star) [**NSFnets (Navier-Stokes flow nets): Physics-informed neural networks for the incompressible Navier-Stokes equations**](https://arxiv.org/abs/2003.06496) | JCP(Journal of Computational Physics) | 2021 | [Github](https://github.com/Scien42/NSFnet) | - |
| [**Meta-auto-decoder for solving parametric partial differential equations**](https://arxiv.org/pdf/2111.08823) | NeurIPS | 2022 |- | - |
| [**Nas-pinn: neural architecture search-guided physics-informed neural network for solving pdes**](https://arxiv.org/pdf/2305.10127) | JCP(Journal of Computational Physics) | 2024 | - | - |

---

### Discretized PDE-Informed Neural Network

| Title | Venue | Date | Code | Demo |
|:--------|:--------:|:--------:|:--------:|:--------:|
| ![Star](https://img.shields.io/github/stars/YDuME/EDNN.svg?style=social&label=Star) [**Evolutional Deep Neural Network**](https://arxiv.org/pdf/2103.09959.pdf) | Physical Review E | 2021-10-04 | [Github](https://github.com/YDuME/EDNN) | - |
[**Adlgm: An efficient adaptive sampling dl galerkin method**](https://pdf.sciencedirectassets.com/272570/1-s2.0-S0021999123X00035/1-s2.0-S0021999123000396/main.pdf) | JCP | | - | - |
| ![Star](https://img.shields.io/github/stars/honglin-c/INSR-PDE) [**Implicit Neural Spatial Representations for Time-dependent PDEs**](https://arxiv.org/pdf/2210.00124.pdf) | ICML 2023 | 2022-09-29 | [Github](https://github.com/honglin-c/INSR-PDE) | - |
| ![Star](https://img.shields.io/github/stars/pehersto/ng.svg?style=social&label=Star) [**Neural galerkin schemes with active learning for high dimensional evolution equations**](https://arxiv.org/pdf/2203.01360.pdf) | JCP | 2024-01 | [Github](https://github.com/pehersto/ng) | - |
[**Multi-resolution partial differential equations preserved learning framework for spatiotemporal dynamics**](https://arxiv.org/abs/2205.03990) | Communications Physics | 2024-01-13 | [Github](https://github.com/bitzhangcy/Neural-PDE-Solver) | - |

---

## ML-assisted Numerical Solutions

### Assist Simulation at Coarser Scales

| Title | Venue | Date | Code | Demo |
|:--------|:--------:|:--------:|:--------:|:--------:|
| ![Star](https://img.shields.io/github/stars/google/data-driven-discretization-1d) [**Learning data-driven discretizations for partial differential equations**](https://arxiv.org/abs/1808.04930) | PNAS | 2019 | [Github](https://github.com/google/data-driven-discretization-1d) | - |
| [**Machine learning accelerated computational fluid dynamics**](https://arxiv.org/abs/2102.01010) | PNAS | 2021 | - | - |
| ![Star](https://img.shields.io/github/stars/tum-pbs/differentiable-piso.svg?style=social&label=Star) [**Learned turbulence modelling with differentiable fluid solvers: physics-based loss functions and optimisation horizons**](https://arxiv.org/abs/2202.06988) | JFM(Journal of Fluid Mechanics) | 2022 | [Github](https://github.com/tum-pbs/differentiable-piso) | - |
| [**Machine learning design of volume of fluid schemes for compressible flows**](https://www.sciencedirect.com/science/article/abs/pii/S0021999120300498) | JCP(Journal of Computational Physics) | 2020 | - | - |
| ![Star](https://img.shields.io/github/stars/tianhanz/DNN-Models-for-Chemical-Kinetics.svg?style=social&label=Star) [**A multi-scale sampling method for accurate and robust deep neural network to predict combustion chemical kinetics**](https://arxiv.org/abs/2201.03549) | arXiv | 2022 | [Github](https://github.com/tianhanz/DNN-Models-for-Chemical-Kinetics) | - |
| ![Star](https://img.shields.io/github/stars/Edward-Sun/TSM-PDE.svg?style=social&label=Star) [**A neural pde solver with temporal stencil modeling**](https://arxiv.org/abs/2302.08105) | arXiv | 2023 | [Github](https://github.com/Edward-Sun/TSM-PDE) | - |
| [**Scalable projection-based RO models for large multiscale fluid systems**](https://ui.adsabs.harvard.edu/link_gateway/2023AIAAJ..61.4499W/PUB_HTML) | AIAA | 2023 | - | - |

---

### Preconditioning

| Title | Venue | Date | Code | Demo |
|:--------|:--------:|:--------:|:--------:|:--------:|
| ![Star](https://img.shields.io/github/stars/danielgreenfeld3/Learning-to-optimize-multigrid-solvers) [**Learning to simulate complex physics with graph networks**](https://arxiv.org/pdf/2002.09405) | ICML | 2020 | [Github](https://github.com/google-deepmind/deepmind-research/tree/master/learning_to_simulate) | [video](https://raw.githubusercontent.com/WillDreamer/Awesome-AI4CFD/main/sites.google.com/view/learning-to-simulate) |
| ![Star](https://img.shields.io/github/stars/danielgreenfeld3/Learning-to-optimize-multigrid-solvers) [**Learning to optimize multigrid pde solvers**](https://arxiv.org/pdf/1902.10248) | ICML | 2019 | [Github](https://github.com/danielgreenfeld3/Learning-to-optimize-multigrid-solvers) | - |
| ![Star](https://img.shields.io/github/stars/ilayluz/learning-amg.svg?style=social&label=Star) [**Learning algebraic multigrid using graph neural networks**](https://arxiv.org/pdf/2003.05744) | ICML | 2020 | [Github](https://github.com/ilayluz/learning-amg) | - |

---

### Miscellaneous

| Title | Venue | Date | Code | Demo |
|:--------|:--------:|:--------:|:--------:|:--------:|
| [**Using ML to augment coarse-grid CFD simulations**](https://arxiv.org/pdf/2010.00072) | arXiv | 2020 |-| - |
| ![Star](https://img.shields.io/github/stars/tum-pbs/Solver-in-the-Loop.svg?style=social&label=Star) [**Solver-in-the-loop:Learning from differentiable physics to interact with iterative pde-solvers**](https://arxiv.org/abs/2007.00016) |NeuraIPS | 2020 | [Github](https://github.com/tum-pbs/Solver-in-the-Loop) | - |
| ![Star](https://img.shields.io/github/stars/locuslab/cfd-gcn.svg?style=social&label=Star) [**Combining differentiable pde solvers and graph neural networks for fluid flow prediction**](https://arxiv.org/pdf/2007.04439) | ICML | 2020 | [Github](https://github.com/locuslab/cfd-gcn) | - |
| [**A deep learning based accelerator for fluid simulations**](https://arxiv.org/pdf/2005.04485) | ICS | 2020 | - | - |

---

## Application Novelty

### Aerodynamics

| Title | Venue | Date | Code | Demo |
|:--------|:--------:|:--------:|:--------:|:--------:|
|![Star](https://img.shields.io/github/stars/aerorobotics/neural-fly.svg?style=social&label=Star) [**Neural-fly enables rapid learning for agile flight in strong winds**](https://arxiv.org/pdf/2205.06908) | Science Robotics | 2022 | [Github](https://github.com/aerorobotics/neural-fly) | - |
|![Star](https://img.shields.io/github/stars/areenraj/transonic-flow-supercritical-airfoil.svg?style=social&label=Star) [**Prediction of transonic flow over supercritical airfoils using geometric encoding and deep-learning strategies**](https://arxiv.org/pdf/2303.03695) | Physics of Fluids |2023 | [Github](https://github.com/areenraj/transonic-flow-supercritical-airfoil) | - |
| [**Shock wave prediction in transonic flow fields using domain-informed probabilistic deep learning**](https://www.researchgate.net/profile/Bilal-Mufti-3/publication/377320644_Shock_wave_prediction_in_transonic_flow_fields_using_domain-informed_probabilistic_deep_learning/links/65a477e0af617b0d8744e8ea/Shock-wave-prediction-in-transonic-flow-fields-using-domain-informed-probabilistic-deep-learning.pdf?_tp=eyJjb250ZXh0Ijp7ImZpcnN0UGFnZSI6InB1YmxpY2F0aW9uIiwicGFnZSI6InB1YmxpY2F0aW9uIn19) | Physics of Fluids | 2024 | - | - |

---

### Combustion & Reacting Flow

| Title | Venue | Date | Code | Demo |
|:--------|:--------:|:--------:|:--------:|:--------:|
|![Star](https://img.shields.io/github/stars/DENG-MIT/Stiff-PINN) [**Stiff-pinn: Physics-informed neural network for stiff chemical kinetics**](https://arxiv.org/pdf/2011.04520)) | The Journal of Physical Chemistry A | 2021 | [Github](https://github.com/DENG-MIT/Stiff-PINN) | - |
| [**A multi-scale sampling method for accurate and robust deep neural network to predict combustion chemical kinetics**](https://arxiv.org/pdf/2201.03549) | Combustion and Flame | 2022 | [Github](https://github.com/tianhanz/DNN-Models-for-Chemical-Kinetics) | - |

---

### Atmosphere & Ocean Science

| Title | Venue | Date | Code | Demo |
|:--------|:--------:|:--------:|:--------:|:--------:|
| [**FourCastNet: A global data-driven HR weather model using AFNO**](https://arxiv.org/pdf/2202.11214) | arXiv | 2022 | - | - |
|![Star](https://img.shields.io/github/stars/198808xc/Pangu-Weather) [**Accurate medium-range global weather forecasting with 3d nns**](https://www.nature.com/articles/s41586-023-06185-3.pdf) | Nature | 2023 | [Github](https://github.com/198808xc/Pangu-Weather) | - |
|![Star](https://img.shields.io/github/stars/google-deepmind/graphcast) [**Learning skillful medium-range global weather forecasting**](https://arxiv.org/pdf/2212.12794) | Science | 2023 | [Github](https://github.com/google-deepmind/graphcast) | - |
| [**Evaluation of Deep Neural Operator models toward ocean forecasting**](https://arxiv.org/pdf/2308.11814) | OCEANS | 2023 | - | - |
|![Star](https://img.shields.io/github/stars/gegewen/ufno) [**U-fno an enhanced FNO-based DL model for multiphase flow**](https://arxiv.org/pdf/2109.03697) | AWR | 2022 | [Github](https://github.com/gegewen/ufno) | - |
| [**Fourier-mionet: Fourier-enhanced multiple-input neural operators for multiphase modeling of geological carbon sequestration**](https://arxiv.org/pdf/2303.04778) | arXiv | 2023 | - | - |

---

### Biology Fluid

| Title | Venue | Date | Code | Demo |
|:--------|:--------:|:--------:|:--------:|:--------:|
| [**Simulating progressive intramural damage leading to aortic dissection using DeepONet: an operator–regression neural network**](https://royalsocietypublishing.org/doi/pdf/10.1098/rsif.2021.0670) | Journal of The Royal Society Interface | 2022 | - | - |
| [**Improving microstructural integrity, interstitial fluid, and blood microcirculation images**](https://onlinelibrary.wiley.com/doi/epdf/10.1002/mrm.29753) | JSMRM | 2023 | - | - |
| [**Multiple case PINN for biomedical tube flows**](https://arxiv.org/pdf/2309.15294.pdf) | arXiv | 2023 | - | - |

---

### Plasma

| Title | Venue | Date | Code | Demo |
|:--------|:--------:|:--------:|:--------:|:--------:|
| [**Low-temperature plasma simulation based on physics-informed neural networks**](https://arxiv.org/pdf/2206.15294) | Phys. Fluids | 2022 | - | - |
| [**Fourier neural operator for plasma modelling**](https://arxiv.org/pdf/2302.06542.pdf) | arXiv | 2023 | - | - |

---
## Frontier Models

### Foundation Models

| Title | Venue | Date | Code | Demo |
|:--------|:--------:|:--------:|:--------:|:--------:|
|![Star](https://img.shields.io/github/stars/camlab-ethz/poseidon.svg?style=social&label=Star) [**Poseidon: Efficient Foundation Models for PDEs**](https://arxiv.org/abs/2405.19101) | NeurIPS 2024 | 2024 | [Github](https://github.com/camlab-ethz/poseidon) | - |
| [**Self-supervised Pretraining for Partial Differential Equations**](https://arxiv.org/abs/2407.06209) | arXiv | 2024 | - | - |

---
### Generative Models

| Title | Venue | Date | Code | Demo |
|:--------|:--------:|:--------:|:--------:|:--------:|
|![Star](https://img.shields.io/github/stars/jhhuangchloe/DiffusionPDE.svg?style=social&label=Star) [**DiffusionPDE: Generative PDE-Solving under Partial Observation**](https://neurips.cc/virtual/2024/poster/92980) | NeurIPS 2024 | 2024 | [Github](https://github.com/jhhuangchloe/DiffusionPDE) | - |
|![Star](https://img.shields.io/github/stars/tum-pbs/dgn4cfd.svg?style=social&label=Star) [**Learning Distributions of Complex Fluid Simulations with Diffusion Graph Networks**](https://openreview.net/pdf?id=uKZdlihDDn) | ICLR 2025 | 2025 | [Github](https://github.com/tum-pbs/dgn4cfd) | - |
---

## Citation

This project has been led by researchers from Peking University, University of California, Los Angeles, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, University of Maryland, College Park, Stanford University, Westlake University, Microsoft AI4Science.

If you find this project useful for your research, please consider citing

```
@article{wang2024recent,
  title={Recent advances on machine learning for computational fluid dynamics: A survey},
  author={Wang, Haixin and Cao, Yadi and Huang, Zijie and Liu, Yuxuan and Hu, Peiyan and Luo, Xiao and Song, Zezheng and Zhao, Wanjia and Liu, Jilin and Sun, Jinan and others},
  journal={arXiv preprint arXiv:2408.12171},
  year={2024}
}
```

---

## 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 **<whx@cs.ucla.edu>**. We will response to your request as soon as possible!

Awesome-AI4CFD

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