Awesome Machine Learning for Fluid Mechanics

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A curated list of machine learning papers, codes, libraries, and databases applied to fluid mechanics. This list in no way a comprehensive, therefore, if you observe something is missing then please feel free to add it here while adhering to contributing guidelines.

Table of Contents

• Awesome Machine Learning for Fluid Mechanics
  • Frameworks
  • Research articles
    • Editorials
    • Review papers
    • Applied Large Language Models
    • Quantum Machine Learning
    • Interpreted and Explainable Machine Learning
    • Physics-informed ML
    • Reduced-order modeling aided ML
    • Transfer Learning
    • Generative AI
    • Patten identification and generation
    • Reinforcement learning
    • Geometry optimization or generation
    • Others
  • ML-focused events
  • Available datasets
  • Online resources
  • Blogs and news articles
  • Ongoing research, projects and labs
  • Opensource codes, tutorials and examples
  • Companies focusing on ML
  • Opensource CFD codes
  • Support Forums

Table of contents generated with markdown-toc

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Frameworks

1. TensorFlow is a well-known machine learning library developed by Google.

2. PyTorch is another framework for machine learning developed at Facebook.

3. Scikit-learn is all-purpose machine learning library. It also provides the implementation of several other data analysis algorithm.

4. easyesn is a very good implementation of echo state network (ESN aka. reservoir computing). ESN often finds its application in dynamical systems.

5. EchoTorch is another good implementation for ESN based upon PyTorch.

6. flowTorch is a Python library for analysis and reduced order modeling of fluid flows.

7. neurodiffeq is a Python package for solving differential equations with neural networks.

8. SciANN is a Keras wrapper for scientific computations and physics-informed deep learning.

9. PySINDy is a package with several implementations for the Sparse Identification of Nonlinear Dynamical systems (SINDy). It is also well suited for a dynamical system.

10. smarties is a Reinforcement Learning (RL) software designed high-performance C++ implementations of deep RL learning algorithms including V-RACER, CMA, PPO, DQN, DPG, ACER, and NAF.

11. DRLinFluidsis a flexible Python package that enables the application of Deep Reinforcement Learning (DRL) techniques to Computational Fluid Dynamics (CFD). [Paper-1, Paper-2]

12. PyDMD is a python package for dynamic mode decomposition which is often used for reduced order modelling now.

13. PYPARSVD is an implementation for singular value decomposition (SVD) which is distributed and parallelized which makes it efficient for large data.

14. turbESN is a python-based package which relies on PyTorch for ESN as a backend which supports fully autonomous and teacher forced ESN predictions.

15. PyKoopman is a Python package for computing data-driven approximations to the Koopman operator. (Paper)

16. MODULO is a modal decomposition package developed at the von Karman Institute for Fluid Dynamics (VKI). It offers a wide range of decomposition techniques, allowing users to choose the most appropriate method for their specific problem.

17. DeepXDE is a library for scientific machine learning and physics-informed learning. DeepXDE includes PINN, DeepONet. It supports five tensor libraries as backends: TensorFlow 1.x (tensorflow.compat.v1 in TensorFlow 2.x), TensorFlow 2.x, PyTorch, JAX, and PaddlePaddle.

Research articles

Editorials

1. Editorial: Machine Learning and Physical Review Fluids: An Editorial Perspective, 2021.

2. An Old-Fashioned Framework for Machine Learning in Turbulence Modeling, 2023. (Presented at NASA)

Review papers

1. Application of machine learning algorithms to flow modeling and optimization, 1999. (Paper)

2. Turbulence modeling in the age of data, 2019. (arXiv)

3. A perspective on machine learning in turbulent flows, 2020. (Paper)

4. Machine learning for fluid mechanics, 2020. (Paper)

5. A Perspective on machine learning methods in turbulence modelling, 2020. (arXiv)

6. Machine learning accelerated computational fluid dynamics, 2021. (arXiv)

7. Deep learning to replace, improve, or aid CFD analysis in built environment applications: A review, 2021. (Paper)

8. Physics-informed machine learning, 2021. (Paper)

9. A review on deep reinforcement learning for fluid mechanics, 2021. (arXiv | Paper)

10. Enhancing Computational Fluid Dynamics with Machine Learning, 2022. (arXiv | Paper)

11. Applying machine learning to study fluid mechanics, 2022. (Paper)

12. Improving aircraft performance using machine learning: A review, 2022. (arXiv | Paper)

13. The transformative potential of machine learning for experiments in fluid mechanics, 2023. (Paper)

14. Super-resolution analysis via machine learning: a survey for fluid flows, 2023. (Open Access Paper)

15. From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learning, 2024. (arXiv)

16. Mixing Artificial and Natural Intelligence: From Statistical Mechanics to AI and Back to Turbulence, 2024. (arXiv | Paper)

17. Data-driven methods for flow and transport in porous media: A review, 2024. (arXiv | Paper)

Applied Large Language Models

1. MetaOpenFOAM: an LLM-based multi-agent framework for CFD, 2024. (arXiv | Code | YouTube Presentation)

Quantum Machine Learning

1. Machine learning and quantum computing for reactive turbulence modeling and simulation, 2021. (Paper)

2. Quantum reservoir computing of thermal convection flow, 2022. (arXiv)

3. Reduced-order modeling of two-dimensional turbulent Rayleigh-Bénard flow by hybrid quantum-classical reservoir computing, 2023. (arXiv)

Interpreted and Explainable Machine Learning

1. Extracting Interpretable Physical Parameters from Spatiotemporal Systems using Unsupervised Learning, 2020. (arXiv | Blog)

2. An interpretable framework of data-driven turbulence modeling using deep neural networks, 2021. (Paper)

3. Interpreted machine learning in fluid dynamics: explaining relaminarisation events in wall-bounded shear flows, 2022, (Paper | Data)

4. Explaining wall-bounded turbulence through deep learning. 2023. (arXiv)

5. Multiscale Graph Neural Network Autoencoders for Interpretable Scientific Machine Learning, 2023 (arXiv | Paper)

6. Feature importance in neural networks as a means of interpretation for data-driven turbulence models, 2023. (Open Access Paper)

7. Interpretable A-posteriori Error Indication for Graph Neural Network Surrogate Models, 2023. (arXiv | Paper)

8. Classically studied coherent structures only paint a partial picture of wall-bounded turbulence, 2024. (arXiv)

Physics-informed ML

1. Reynolds averaged turbulence modeling using deep neural networks with embedded invariance, 2016. (Paper)

2. From deep to physics-informed learning of turbulence: Diagnostics, 2018. (arXiv)

3. Subgrid modelling for two-dimensional turbulence using neural networks, 2018. (arXiv | Code)

4. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations, 2019. (Paper)

5. Neural network models for the anisotropic Reynolds stress tensor in turbulent channel flow, 2019. (arXiv)

6. Data-driven fractional subgrid-scale modeling for scalar turbulence: A nonlocal LES approach, 2020. (arXiv)

7. A machine learning framework for LES closure terms, 2020. (arXiv)

8. A neural network based shock detection and localization approach for discontinuous Galerkin methods, 2020. (arXiv)

9. Data-driven algebraic models of the turbulent Prandtl number for buoyancy-affected flow near a vertical surface, 2021. (arXiv)

10. Convolutional Neural Network Models and Interpretability for the Anisotropic Reynolds Stress Tensor in Turbulent One-dimensional Flows, 2021. (arXiv)

11. Physics-aware deep neural networks for surrogate modeling of turbulent natural convection,2021. (arXiv)

12. Learned Turbulence Modelling with Differentiable Fluid Solvers, 2021. (arXiv)

13. Physics-informed data based neural networks for two-dimensional turbulence, 2022. (arXiv | Paper)

14. Deep Physics Corrector: A physics enhanced deep learning architecture for solving stochastic differential equations, 2022. (arXiv)

15. A Physics-informed Diffusion Model for High-fidelity Flow Field Reconstruction, 2022. (arXiv)

16. A fast and accurate physics-informed neural network reduced order model with shallow masked autoencoder, 2022. (arXiv | Paper)

17. FluxNet: a physics-informed learning-based Riemann solver for transcritical flows with non-ideal thermodynamics, 2022. (Paper | Code)

18. An Improved Structured Mesh Generation Method Based on Physics-informed Neural Networks, 2022. (arXiv)

19. Physics-Informed Neural Networks for Inverse Problems in Supersonic Flows, 2022. (arXiv | Paper)

20. Extending a Physics-Informed Machine Learning Network for Superresolution Studies of Rayleigh-Bénard Convection, 2023. (arXiv)

21. Machine learning for RANS turbulence modeling of variable property flows, 2023. (arXiv | Paper)

22. A probabilistic, data-driven closure model for RANS simulations with aleatoric, model uncertainty, 2023. (arXiv)

23. Turbulence closure with small, local neural networks: Forced two-dimensional and $\beta$-plane flows, 2024. (Paper | arXiv)

24. Data-driven discovery of turbulent flow equations using physics-informed neural networks, 2024. (Paper)

25. Turbulence model augmented physics-informed neural networks for mean-flow reconstruction, 2024. (Paper | arXiv | Code)

26. Data-Driven Turbulence Modeling Approach for Cold-Wall Hypersonic Boundary Layers, 2024. (arXiv)

27. Generalized field inversion strategies for data-driven turbulence closure modeling, 2024. (Open access paper)

Reduced-order modeling aided ML

1. Reservoir computing model of two-dimensional turbulent convection, 2020. (arXiv)

2. Predictions of turbulent shear flows using deep neural networks, 2019. (arXiv | Code)

3. A deep learning enabler for nonintrusive reduced order modeling of fluid flows, 2019. (arXiv)

4. Reduced-order modeling of advection-dominated systems with recurrent neural networks and convolutional autoencoders, 2020. (arXiv | Code)

5. Time-series learning of latent-space dynamics for reduced-order model closure, 2020. (Paper | Code)

6. Echo state network for two-dimensional turbulent moist Rayleigh-Bénard convection, 2020. (arXiv)

7. DeepCFD: Efficient steady-state laminar flow approximation with deep convolutional neural networks, 2020. (arXiv | Code)

8. From coarse wall measurements to turbulent velocity fields with deep learning, 2021. (arXiv)

9. Convolutional neural network and long short-term memory based reduced order surrogate for minimal turbulent channel flow, 2021. (arXiv, | Data: Contact authors)

10. Direct data-driven forecast of local turbulent heat flux in Rayleigh–Bénard convection, 2022. (arXiv | arXiv | Data: Contact authors)

11. Cost function for low‑dimensional manifold topology assessment (Paper | Data | Code)

12. Data-Driven Modeling for Transonic Aeroelastic Analysis, 2023. (arXiv | Code, will be available)

13. Predicting the wall-shear stress and wall pressure through convolutional neural networks, 2023. (arXiv | Paper)

14. Deep learning-based reduced order model for three-dimensional unsteady flow using mesh transformation and stitching, 2023. (arXiv| Data : Contact authors)

15. Reduced-order modeling of fluid flows with transformers, 2023. (Paper)

16. Multi-fidelity reduced-order surrogate modeling, 2024. (arXiv | Paper)

17. β-Variational autoencoders and transformers for reduced-order modelling of fluid flows, 2024. (arXiv | Paper | Code | Data)

18. Shock wave prediction in transonic flow fields using domain-informed probabilistic deep learning, 2024. (Paper)

Transfer Learning

1. Stable a posteriori LES of 2D turbulence using convolutional neural networks: Backscattering analysis and generalization to higher Re via transfer learning, 2021. (arXiv)

2. Non-intrusive, transferable model for coupled turbulent channel-porous media flow based upon neural networks, 2024. (Paper | Data : Contact authors)

Generative AI

1. Inpainting Computational Fluid Dynamics with Deep Learning, 2024. (arXiv)

2. Generative Adversarial Reduced Order Modelling, 2024. (arXiv | Paper | Code)

3. Three-dimensional generative adversarial networks for turbulent flow estimation from wall measurements, 2024. (arXiv | Paper)

Patten identification and generation

1. Deep learning in turbulent convection networks, 2019. (Paper)

2. Time-resolved turbulent velocity field reconstruction using a long short-term memory (LSTM)-based artificial intelligence framework, 2019. (Paper)

3. Unsupervised deep learning for super-resolution reconstruction of turbulence, 2020. (arXiv)

4. Nonlinear mode decomposition with convolutional neural networks for fluid dynamics, 2020. (arXiv)

5. A deep neural network architecture for reliable 3D position and size determination for Lagrangian particle tracking using a single camera, 2023. (Open Access Paper | Data)

6. Sparse sensor reconstruction of vortex-impinged airfoil wake with machine learning, 2023. (arXiv | Open Access Paper)

7. Identifying regions of importance in wall-bounded turbulence through explainable deep learning, 2023. (arXiv | Code)

8. Data-driven estimation of scalar quantities from planar velocity measurements by deep learning applied to temperature in thermal convection, 2023. (Paper | Data : Contact authors)

9. Reconstruction of three-dimensional turbulent flow structures using surface measurements for free-surface flows based on a convolutional neural network, 2023. (Paper | [arXiv](https:/ /arxiv.org/abs/2301.11710))

10. Machine learning-based vorticity evolution and super-resolution of homogeneous isotropic turbulence using wavelet projection, 2024. (ResearchGate | Paper)

11. Data-driven nonlinear turbulent flow scaling with Buckingham Pi variables, 2024. (Paper | arXiv)

Reinforcement learning

1. Automating Turbulence Modeling by Multi-Agent Reinforcement Learning, 2020. (arXiv | Code)

2. Deep reinforcement learning for turbulent drag reduction in channel flows, 2023. (arXiv | Code)

3. DRLinFluids -- An open-source python platform of coupling Deep Reinforcement Learning and OpenFOAM, 2023. (arXiv | Paper | Code)

4. Deep Reinforcement Learning for the Management of the Wall Regeneration Cycle in Wall-Bounded Turbulent Flows, 2024. (arXiv | Paper | Code)

Geometry optimization or generation

1. Deep reinforcement learning for heat exchanger shape optimization, 2022. (Paper | Article)

2. Data-driven prediction of the performance of enhanced surfaces from an extensive CFD-generated parametric search space, 2023. (Paper | Data: Contact authors)

3. Robust optimization of heat-transfer-enhancing microtextured surfaces based on machine learning surrogate models, (Paper | Data: Contact authors)

4. Deep reinforcement learning and mesh deformation integration for shape optimization of a single pin fin within a micro channel, 2025. (Paper)

Others

1. Data-assisted reduced-order modeling of extreme events in complex dynamical systems, 2018. (Paper)

2. Forecasting of spatiotemporal chaotic dynamics with recurrent neural networks: a comparative study of reservoir computing and backpropagation algorithms, 2019. (arXiv)

3. Nonlinear mode decomposition with convolutional neural networks for fluid dynamics, 2020. (arXiv)

4. Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations, 2020. (Paper)

5. Engine Combustion System Optimization Using Computational Fluid Dynamics and Machine Learning: A Methodological Approach, 2021. (Paper)

6. Physics guided machine learning using simplified theories, 2021. (Paper | Code)

7. Prospects of federated machine learning in fluid dynamics, 2022. (Paper)

8. Graph neural network-accelerated Lagrangian fluid simulation, 2022. (Paper)

9. Learning Lagrangian Fluid Mechanics with E(3)-Equivariant Graph Neural Networks, 2023. (arXiv | Code)

10. An unsupervised machine-learning-based shock sensor for high-order supersonic flow solvers, 2023. (arXiv | Code)

11. Single-snapshot machine learning for turbulence super resolution, 2024. (arXiv)

ML-focused events

1. International Workshop on Data-driven Modeling and Optimization in Fluid Mechanics, 2019, Karlsruhe, Germany.

2. Symposium on Model-Consistent Data-driven Turbulence Modeling, 2021, Virtual Event.

3. Turbulence Modeling: Roadblocks, and the Potential for Machine Learning, 2022, USA.

4. Mini symposia: Analysis of Real World and Industry Applications: emerging frontiers in CFD computing, machine learning and beyond, 2022, Yokohama, Japan.

5. IUTAM Symposium on Data-driven modeling and optimization in fluid mechanics, 2022, Denmark.

6. 33rd Parallel Computational Fluid Dynamics International Conference, 2022, Italy.

7. Workshop: data-driven methods in fluid mechanics, 2022, Leeds, UK.

8. Lecture Series on Hands on Machine Learning for Fluid Dynamics 2023, 2023, von Karman Institute, Belgium.

9. 629 – Data-driven fluid mechanics, 2024, Italy.

10. Machine Learning for Fluid Mechanics: Analysis, Modeling, Control and Closures, February 2024, Belgium.

11. Workshop on Machine Learning for Fluid Dynamics, March 2024, France.

12. AI and Data-driven Simulation Forum, July 2024, Stuttgart, Germany.

13. D3S3: Data-driven and Differentiable Simulations, Surrogates, and Solvers -- Workshop @ NeurIPS ‘24, tentative 2024, Vancouver, Canada.

14. 4th Automotive CFD Prediction Workshop, November 2024, Belfast, Ireland.

15. Euromech Colloquium on Data-Driven Fluid Dynamics/2nd ERCOFTAC Workshop on Machine Learning for Fluid Dynamics, April 2025, London UK.

Available datasets

1. KTH FLOW: A rich dataset of different turbulent flow generated by DNS, LES and experiments. (Simulation data | Experimental data | Paper-1)

2. Vreman Research: Turbulent channel flow dataset generated from simulation, could be useful in closure modeling. (Data | Paper-1 | Paper-2)

3. Johns Hopkins Turbulence Databases: High quality datasets for different flow problems. (Database | Paper)

4. CTR Stanford: Dataset for turbulent pipe flow and boundary layer generated with DNS. (Database | Paper)

5. sCO2: Spatial data along the tube for heated and cooled pipe under supercritical pressure. It includes around 50 cases, which is a good start for regression based model to replace correlations. (Data | Paper-1 | Paper-2)

Online resources

1. A first course on machine learning from Nando di Freitas: Little old, recorded in 2013 but very concise and clear. (YouTube | Slides)

2. Steve Brunton has a wonderful channel for a variety of topics ranging from data analysis to machine learning applied to fluid mechanics. (YouTube)

3. Nathan Kutz has a super nice channel devoted to applied mathematics for fluid mechanics. (YouTube)

4. For beginners, a good resource to learn OpenFOAM from József Nagy. OpenFOAM can be adapted for applying ML model coupled with N-S equations (e.g. RANS/LES closure). (YouTube)

5. A course on Machine learning in computational fluid dynamics from TU Braunschweig.

6. Looking for coursed for TensorFlow, PyTorch, GAN etc. then have a look to this wonderful YouTube channel

7. Interviews with researchers, podcast revolving around fluid mechanics, machine learning and simulation on this YouTube channel from Jousef Murad

8. Lecture series videos from Data-Driven Fluid Mechanics: Combining First Principles and Machine Learning

Blogs and news articles

1. Convolutional Neural Networks for Steady Flow Approximation, 2016. (Autodesk)

2. CFD + Machine learning for super fast simulations, 2017. (Reddit)

3. What is the role of Artificial Intelligence (AI) or Machine Learning in CFD?, 2017. (Quora)

4. Supercomputing simulations and machine learning help improve power plant, 2018.

5. When CAE Meets AI: Deep Learning For CFD Simulations, 2019. (Ubercloud)

6. Machine Learning in Computational Fluid Dynamics, 2020. (TowardsDataScience)

7. Studying the nature of turbulence with Neural Concept's deep learning platform, 2020. (Numeca)

8. A case for machine learning in CFD, 2020. (Medium)

9. Machine Learning for Accelerated Aero-Thermal Design in the Age of Electromobility, 2020. (Engys)

10. A general purpose list for transitioning to data science and ML, 2021.

11. A compiled list of projects from NVIDIA where AI and CFD were used, 2021.

12. AI for CFD, 2021. (Medium)

13. 4 Myths about AI in CFD, 2021. (Siemens)

14. Accelerating Product Development with Physics-Informed Neural Networks and NVIDIA Modulus, 2021. (NVIDIA)

15. Optimize F1 aerodynamic geometries via Design of Experiments and machine learning, 2022. (AWS)

16. NVIDIA, Rolls-Royce and Classiq Announce Quantum Computing Breakthrough for Computational Fluid Dynamics in Jet Engines, 2023. (NVIDIA)

17. Develop Physics-Informed Machine Learning Models with Graph Neural Networks, 2023. (NVIDIA)

18. The AI algorithm reduces design cycles/costs and time-to-market for advanced products, 2023. (ANL)

19. Closing the gap between High-Performance Computing (HPC) and artificial intelligence (AI), 2023. (HPE)

20. AI for Science, Energy and Security (Special Remarks by DOE Secretary Granholm), 2024. (Panel discussion, NVIDIA)

Ongoing research, projects and labs

1. Center for Data-Driven Computational Physics, University of Michigan, USA.

2. VinuesaLab, KTH, Sweden.

3. DeepTurb: Deep Learning in and of Turbulence, TU Ilmenau, Germany.

4. Thuerey Group: Numerical methods for physics simulations with deep learning, TU Munich, Germany.

5. Focus Group Data-driven Dynamical Systems Analysis in Fluid Mechanics , TU Munich, Germany.

6. Mechanical and AI LAB (MAIL), Carnegie Mellon University, USA.

7. Karniadakis's CRUNCH group, Brown University, USA.

8. MS 6: Machine Learning and Simulation Science, University of Stuttgart, Germany.

9. Special Interest Groups 54: Machine Learning for Fluid Dynamics, Europe.

10. Fukagata Lab, Keio University, Japan.

Opensource codes, tutorials and examples

1. Repository OpenFOAM Machine Learning Hackathon have various projects originated from Data Driven Modelling Special Interest Group

2. Repositiory machine-learning-applied-to-cfd has some excellent examples to begin with CFD and ML.

3. Repository Computational-Fluid-Dynamics-Machine-Learning-Examples has an example implementation for predicting drag from the boundary conditions alongside predicting the velocity and pressure field from the boundary conditions.

4. Image Based CFD Using Deep Learning

5. Deep-Flow-Prediction has the code for data generation, neural network training, and evaluation.

6. TensorFlowFoam with few tutorials on TensorFlow and OpenFoam.

7. Reduced-order modeling of reacting flows using data-driven approaches have a Jupyter-Notebook example for the data driven modeling.

8. Tutorial on the Proper Orthogonal Decomposition (POD) by Julien Weiss: A step by step tutorial including the data and a Matlab implementation. POD is often used for dimensionality reduction.

9. Repository from KTH-FLOW for ML in Fluid Dynamics has several implementations from various published papers.

Companies focusing on ML

1. Neural Concepts is harnessing deep learning for the accelerated simulation and design.

2. Flowfusic is a cloud based provider for CFD simulation based upon OpenFOAM. They are exploring some use cases for AI and CFD.

3. byteLAKE offers a CFD Suite, which is a collection of AI models to significantly accelerate the execution of CFD simulations.

4. NVIDIA is leading with many product and libraries.

5. NAVASTO has few products where they are combining AI with CFD.

6. DeepSim is a startup backed by YCombinator

Opensource CFD codes

Following opensource CFD codes can be adapted for synthetic data generation. Some of them can also be used for RANS/LES closure modeling based upon ML.

1. Nek5000
2. OpenFOAM
3. PyFr
4. Nektar++
5. Flexi
6. SU2
7. code_saturne
8. Dolfyn
9. Neko
10. Snek5000

Support Forums

1. CFDOnline
2. StackExchange