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're the author of any relevant content then please feel free to add it here.

Table of Contents

• Awesome Machine Learning for Fluid Mechanics
  • Frameworks
  • Research articles
    • Editorials
    • Review papers
    • Quantum Machine Learning
    • Interpreted (/Explainable) Machine Learning
    • Physics-informed ML
    • Reduced-order modeling aided ML
    • Pattern identification and experimental applications
    • Reinforcement learning
    • Geometry optimization/ generation
    • Others
  • ML-focused events
  • Available datasets
  • Online resources
  • Blogs, discussions and news articles
  • Ongoing researchs, projects and labs
  • Opensource codes, tutorials and examples
  • Companies focusing on ML
  • Opensource CFD codes

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

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

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

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

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

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

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

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

• 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.

• 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.

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

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

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

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

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

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

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

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

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

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 (arXiv)

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

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

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

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

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

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

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

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

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

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

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

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

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

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)

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)

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

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

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

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

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

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)

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.

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)

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

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

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

• 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)

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

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

• Interviews with researchers, podcast revolving around fluid mechanics, machine learning and simulation on this YouTube channel

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

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)

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: Machine Learning for Fluid Dynamics, Europe.

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

• 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.

• Image Based CFD Using Deep Learning

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

• TensorFlowFoam with few tutorials on TensorFlow and OpenFoam.

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

• 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.

• Neural Concepts is harnessing deep learning for the accelerated simulation and design.
• Flowfusic is a cloud based provider for CFD simulation based upon OpenFOAM. They are exploring some use cases for AI and CFD.
• byteLAKE offers a CFD Suite, which is a collection of AI models to significantly accelerate the execution of CFD simulations.
• NVIDIA is leading with many product and libraries.

Following opensource CFD codes can be adapated 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