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
-
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.
-
Application of machine learning algorithms to flow modeling and optimization, 1999. (Paper)
-
Turbulence modeling in the age of data, 2019. (arXiv)
-
A perspective on machine learning in turbulent flows, 2020. (Paper)
-
Machine learning for fluid mechanics, 2020. (Paper)
-
A Perspective on machine learning methods in turbulence modelling, 2020. (arXiv)
-
Machine learning accelerated computational fluid dynamics, 2021. (arXiv)
-
Deep learning to replace, improve, or aid CFD analysis in built environment applications: A review, 2021. (Paper)
-
Physics-informed machine learning, 2021. (Paper)
-
Enhancing Computational Fluid Dynamics with Machine Learning, 2022. (Paper | arXiv)
-
Applying machine learning to study fluid mechanics, 2022. (Paper)
-
Machine learning and quantum computing for reactive turbulence modeling and simulation, 2021. (Paper)
-
Quantum reservoir computing of thermal convection flow, 2022. (arXiv)
-
Extracting Interpretable Physical Parameters from Spatiotemporal Systems using Unsupervised Learning, 2020. (ArXiv | Blog)
-
An interpretable framework of data-driven turbulence modeling using deep neural networks, 2021. (Paper)
-
Interpreted machine learning in fluid dynamics: explaining relaminarisation events in wall-bounded shear flows, 2022, (Paper | Data)
-
Explaining wall-bounded turbulence through deep learning (arXiv)
-
Automating Turbulence Modeling by Multi-Agent Reinforcement Learning (arXiv | Code)
-
Deep reinforcement learning for turbulent drag reduction in channel flows (arXiv | Code)
-
Reynolds averaged turbulence modeling using deep neural networks with embedded invariance, 2016. (Paper)
-
From deep to physics-informed learning of turbulence: Diagnostics, 2018. (Paper)
-
Subgrid modelling for two-dimensional turbulence using neural networks, 2018. (Paper | Code)
-
Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations, 2019. (Paper)
-
Neural network models for the anisotropic Reynolds stress tensor in turbulent channel flow, 2019. (Paper)
-
Data-driven fractional subgrid-scale modeling for scalar turbulence: A nonlocal LES approach, 2020. (Paper)
-
A machine learning framework for LES closure terms, 2020. (Paper)
-
A neural network based shock detection and localization approach for discontinuous Galerkin methods, 2020. (Paper)
-
Stable a posteriori LES of 2D turbulence using convolutional neural networks: Backscattering analysis and generalization to higher Re via transfer learning, 2021. (Paper)
-
Data-driven algebraic models of the turbulent Prandtl number for buoyancy-affected flow near a vertical surface, 2021. (Paper)
-
Convolutional Neural Network Models and Interpretability for the Anisotropic Reynolds Stress Tensor in Turbulent One-dimensional Flows, 2021. (arXiv)
-
Physics-aware deep neural networks for surrogate modeling of turbulent natural convection,2021. (arXiv)
-
Learned Turbulence Modelling with Differentiable Fluid Solvers, 2021. (arXiv] )
-
Physics-informed data based neural networks for two-dimensional turbulence, 2022. (arXiv] | Paper)
-
Deep Physics Corrector: A physics enhanced deep learning architecture for solving stochastic differential equations, 2022. (arXiv])
-
A Physics-informed Diffusion Model for High-fidelity Flow Field Reconstruction, 2022. (arXiv)
-
A fast and accurate physics-informed neural network reduced order model with shallow masked autoencoder, 2022. (arXiv | Paper)
-
Reservoir computing model of two-dimensional turbulent convection, 2020. (Paper)
-
Predictions of turbulent shear flows using deep neural networks, 2019. (Paper | Code)
-
Reduced-order modeling of advection-dominated systems with recurrent neural networks and convolutional autoencoders, 2020. (Paper | Code)
-
Time-series learning of latent-space dynamics for reduced-order model closure, 2020. (Paper | Code)
-
A deep learning enabler for nonintrusive reduced order modeling of fluid flows, 2019. (arXiv)
-
Echo state network for two-dimensional turbulent moist Rayleigh-Bénard convection, 2020. (arXiv)
-
DeepCFD: Efficient steady-state laminar flow approximation with deep convolutional neural networks, 2020. (Paper | Code)
-
From coarse wall measurements to turbulent velocity fields with deep learning, 2021. (Paper)
-
Convolutional neural network and long short-term memory based reduced order surrogate for minimal turbulent channel flow, 2021. (Paper, | Data: Contact authors)
-
Direct data-driven forecast of local turbulent heat flux in Rayleigh–Bénard convection, 2022. (arXiv | Paper | Data: Contact authors)
-
Cost function for low‑dimensional manifold topology assessment (Paper | Data | Code)
-
Deep learning in turbulent convection networks, 2019. (Paper)
-
Time-resolved turbulent velocity field reconstruction using a long short-term memory (LSTM)-based artificial intelligence framework, 2019. (Paper)
-
Unsupervised deep learning for super-resolution reconstruction of turbulence, 2020. (arXiv)
-
Nonlinear mode decomposition with convolutional neural networks for fluid dynamics, 2020. (arXiv)
-
Forecasting of spatiotemporal chaotic dynamics with recurrent neural networks: a comparative study of reservoir computing and backpropagation algorithms, 2019. (arXiv)
-
Data-assisted reduced-order modeling of extreme events in complex dynamical systems, 2018. (Paper)
-
Nonlinear mode decomposition with convolutional neural networks for fluid dynamics, 2020. (arXiv)
-
Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations, 2020. (Paper)
-
Engine Combustion System Optimization Using Computational Fluid Dynamics and Machine Learning: A Methodological Approach, 2021. (Paper)
-
Physics guided machine learning using simplified theories, 2021. (Paper | Code)
-
Prospects of federated machine learning in fluid dynamics, 2022. (Paper)
-
Graph neural network-accelerated Lagrangian fluid simulation, 2022. (Paper))
-
International Workshop on Data-driven Modeling and Optimization in Fluid Mechanics, 2019, Karlsruhe, Germany.
-
Symposium on Model-Consistent Data-driven Turbulence Modeling, 2021, Virtual Event.
-
Turbulence Modeling: Roadblocks, and the Potential for Machine Learning, 2022, USA.
-
Mini symposia: Analysis of Real World and Industry Applications: emerging frontiers in CFD computing, machine learning and beyond, 2022, Yokohama, Japan.
-
IUTAM Symposium on Data-driven modeling and optimization in fluid mechanics, 2022, Denmark.
-
33rd Parallel Computational Fluid Dynamics International Conference, 2022, Italy.
-
Workshop: data-driven methods in fluid mechanics, 2022, Leeds, UK.
-
Lecture Series on Hands on Machine Learning for Fluid Dynamics 2023, 2023, von Karman Institute, Belgium.
-
KTH FLOW: A rich dataset of different turbulent flow generated by DNS, LES and experiments. (Simulation data | Experimental data | Paper-1)
-
Vreman Research: Turbulent channel flow dataset generated from simulation, could be useful in closure modeling. (Data | Paper-1 | Paper-2)
-
Johns Hopkins Turbulence Databases: High quality datasets for different flow problems. (Database | Paper)
-
CTR Stanford: Dataset for turbulent pipe flow and boundary layer generated with DNS. (Database | Paper)
-
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
-
Convolutional Neural Networks for Steady Flow Approximation, 2016. (Autodesk)
-
CFD + Machine learning for super fast simulations, 2017. (Reddit)
-
What is the role of Artificial Intelligence (AI) or Machine Learning in CFD?, 2017. (Quora)
-
Supercomputing simulations and machine learning help improve power plant, 2018.
-
When CAE Meets AI: Deep Learning For CFD Simulations, 2019. (Ubercloud)
-
Machine Learning in Computational Fluid Dynamics, 2020. (TowardsDataScience)
-
Studying the nature of turbulence with Neural Concept's deep learning platform, 2020. (Numeca)
-
A case for machine learning in CFD, 2020. (Medium)
-
Machine Learning for Accelerated Aero-Thermal Design in the Age of Electromobility, 2020. (Engys)
-
A general purpose list for transitioning to data science and ML, 2021.
-
A compiled list of projects from NVIDIA where AI and CFD were used, 2021.
-
AI for CFD, 2021. (Medium)
-
4 Myths about AI in CFD, 2021. (Siemens)
-
Accelerating Product Development with Physics-Informed Neural Networks and NVIDIA Modulus, 2021. (NVIDIA)
-
Center for Data-Driven Computational Physics, University of Michigan, USA.
-
VinuesaLab, KTH, Sweden.
-
DeepTurb: Deep Learning in and of Turbulence, TU Ilmenau, Germany.
-
Thuerey Group: Numerical methods for physics simulations with deep learning, TU Munich, Germany.
-
Focus Group Data-driven Dynamical Systems Analysis in Fluid Mechanics , TU Munich, Germany.
-
Mechanical and AI LAB (MAIL), Carnegie Mellon University, USA.
-
Karniadakis's CRUNCH group, Brown University, USA.
-
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.
-
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.