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This lecture was funded previously by the foundation for innovation in higher education.

Machine learning in computational fluid dynamics

This repository contains resources accompanying the lecture machine learning in fluid dynamics provided by the Institute of Fluid Mechanics at TU Dresden. Note that slides, notebooks, and other resources will be regularly updated throughout the term.


If equations in the lecture notebooks do not get rendered properly on Github, download the notebook and open it using jupyter-lab (refer to the first exercise session for an overview of dependencies and installation instructions).

# topic slides notebook
1 Course overview and motivation link view
2 Finite-volume-based simulations in a nutshell link view
3 Introduction to machine learning link view
4 Surrogate modeling for discrete predictions link view
5 Surrogate modeling for continuous predictions link view
6 Analyzing coherent structures link view
7 Reduced-order modeling of flow fields link view
8 Optimal open-loop control link view
9 Closed-loop control using DRL link view



The exercises are designed for native Linux operating systems like Ubuntu (recommended). They may also work on Windows Subsystem for Linux (WSL). To set up your system for the exercises, refer to the notebook accompanying exercise session 1.

Exercise sessions

# topic notebook
0 Course-specific Python refresher view
1 Setting up your system view
2 End-to-end simulations in OpenFOAM and Basilisk view
3 End-to-end machine learning project in PyTorch view
4 Building a robust path regime classification model view
5 Computing highly accurate mass transfer at rising bubbles view
6 Analyzing coherent structures with POD and DMD view
7 Creating a reduced-order model using CNM view
8 Optimal open-loop control of the flow past a cylinder view
9 Closed-loop control of the flow past a cylinder view


Both exercises and lectures sometimes require datasets. Usually, there are instructions how to create or extract the data yourself. For convenience, a downloadable snapshot of the latest data (20. Dec 2021) is provided, too.

Getting and providing help and feedback

If you

  • get stuck solving an exercise problem
  • have technical issues
  • have theoretical questions about math or programming
  • think that some instructions or explanations need improvement
  • want to report typos or logical errors
  • want to provide feedback and suggestions about the course

the easiest way to get in touch is to open a new issue in this repository. Before opening a new issue, please use the search function to see if a related issue was reported previously.

If you are a student at TU Dresden enrolled in the course Machine Learning in Fluid Dynamics, you may also get in touch via the OPAL platform or via mail.


The following list of acronyms may help you when exploring notebooks and slides:

  • CFD - computational fluid dynamics
  • CNM - cluster-based network modeling
  • DL - deep learning
  • DRL - deep reinforcement learning
  • GPU - graphics processing unit
  • IEEE - Institute of Electrical and Electronics Engineers
  • IEEE 754 - IEEE standard for floating-point arithmetics
  • JIT - just in time (compiler)
  • LES - large eddy simulation
  • LHS - latin hypercube sampling
  • MAE - mean absolute error
  • ML - machine learning
  • MPI - message passing interface
  • MSE - mean squared error
  • PINN - physics-informed neural network
  • RANS - Reynolds-averaged Navier Stokes
  • RL - reinforcement learning
  • TPU - tensor processing unit

References and other resources

Book recommendations

  • books for computational fluid dynamics
    • The OpenFOAM technology primer by T. Marić, J. Höpken, and K. G. Mooney
    • The finite volume method in computational fluid dynamics by F. Moukalled, L. Mangani, and M. Darwish
    • An introduction to computational fluid dynamics: the finite volume method by H. K. Versteeg and W. Malalasekera
  • books for linear algebra
    • Introduction to linear algebra by G. Strang
  • books for data-driven modelling and control
    • Data-driven science and engineering: machine learning, dynamical systems, and control by S. L. Brunton and J. N. Kutz
    • Dynamic mode decomposition: data-driven modeling of complex systems by J. N. Kutz, S. L. Brunton, B. W. Brunton, and J. L. Proctor
    • Grokking deep reinforcement learning by M. Morales
    • Deep learning with PyTorch by E. Stevens, L. Antiga, and T. Viehmann
  • books for programming
    • Python crash course by E. Matthes
    • C++ crash course: a fast-paced introduction by J. Lospinoso
    • The Linux command line by W. Shotts

Video content


Lecture material for machine learning applied to computational fluid mechanics







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