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

Machine learning in computational fluid dynamics

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

Lectures

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+3	Finite-volume-based simulations in a nutshell	link	view
4+5	Introduction to machine learning	link	view
6	Surrogate modeling for discrete predictions	link	view
7+8	Surrogate modeling for continuous predictions	link	view
9	Approximating flow fields from limited data	link	view
10+11	Analyzing coherent structures	link	view
12	Reduced-order modeling of flow fields	link	view
13	Optimal open-loop control	link	view
14+15	Closed-loop control using DRL	link	view

Exercises

Prerequisites

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+3	End-to-end simulations in OpenFOAM and Basilisk	view
4+5	End-to-end machine learning project in PyTorch	view
6	Building a robust path regime classification model	view
7+8	Computing highly accurate mass transfer at rising bubbles	view
9	Learning the flow past a cylinder from limited data	view
10+11	Analyzing coherent structures with POD and DMD	view
12	Creating a reduced-order model using CNM	view
13	Optimal open-loop control of the flow past a cylinder	view
14+15	Closed-loop control of the flow past a cylinder	view

Datasets

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 might 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. It also helps greatly if you label your issue using one or more of the predefined labels (lecture, exercise, OpenFOAM, ...), and if you take some time to state your problem as clearly as possible. Note that everyone is welcome to participate in discussion and solving issues.

If you are a student at TU Braunschweig enrolled in the course Machine Learning in Computational Fluid Dynamics, you may also get in touch via the studIP platform or via mail. However, the issue-workflow described above is the preferred method.

Glossary

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

• YouTube channel of Steve Brunton
• YouTube channel of József Nagy
• YouTube channel Fluid Mechanics 101