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Welcome to the _Physics-based Deep Learning Book_ (v0.3, the _GenAI_ edition) 👋
**TL;DR**:
This document contains a practical and comprehensive introduction of everything
related to deep learning in the context of physical simulations.
As much as possible, all topics come with hands-on code examples in the
form of Jupyter notebooks to quickly get started.
Beyond standard _supervised_ learning from data,
we'll look at _physical loss_ constraints and _differentiable simulations_,
diffusion-based approaches for _probabilistic, generative models_,
as well as
reinforcement learning and neural network architectures.
We live in exciting times: these methods have a huge potential to fundamentally change what humans can achieve via computer simulations.
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_What's new in v0.3?_
Most importantly, this version has a large new chapter on generative modeling, offering a deep dive into topics such as denoising, flow-matching, autoregressive learning, the integration of physics-based constraints, and diffusion-based graph networks. Additionally, a new section explores neural architectures tailored for physics simulations, while all code examples have been updated to use the latest frameworks.Coming up
As a sneak preview, the next chapters will show:
How to train neural networks to predict the fluid flow around airfoils with diffusion modeling. This gives a probabilistic surrogate model that replaces and outperforms traditional simulators.
How to use model equations as residuals to train networks that represent solutions, and how to improve upon these residual constraints by using differentiable simulations.
How to more tightly interact with a full simulator for inverse problems. E.g., we’ll demonstrate how to circumvent the convergence problems of standard reinforcement learning techniques by leveraging simulators in the training loop.
We’ll also discuss the importance of choosing the right network architecture: whether to consider global or local interactions, continuous or discrete representations, and structured versus unstructured graph meshes.
Throughout this text, we will introduce different approaches for introducing physical models into deep learning, i.e., physics-based deep learning (PBDL) approaches. These algorithmic variants will be introduced in order of increasing tightness of the integration, and the pros and cons of the different approaches will be discussed. It’s important to know in which scenarios each of the different techniques is particularly useful.
```{admonition} Executable code, right here, right now :class: tip We focus on Jupyter notebooks, a key advantage of which is that all code examples can be executed on the spot, from your browser. You can modify things and immediately see what happens – give it a try by [running this teaser example in your browser].
Plus, Jupyter notebooks are great because they’re a form of literate programming.
## Comments and suggestions
This _book_, where "book" stands for a collection of digital texts and code examples,
is maintained by the
[Physics-based Simulation Group](https://ge.in.tum.de) at [TUM](https://www.tum.de).
Feel free to contact us if you have any comments, e.g., via [old fashioned email](mailto:i15ge@cs.tum.edu).
If you find mistakes, please also let us know! We're aware that this document is far from perfect,
and we're eager to improve it. Thanks in advance 😀!
Btw., we also maintain a [link collection](https://github.com/thunil/Physics-Based-Deep-Learning) with recent research papers.
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Some visual examples of numerically simulated time sequences. In this book, we explain how to realize algorithms that use neural networks alongside numerical solvers.Thanks!
This project would not have been possible without the help of many people who contributed. Thanks to everyone 🙏 Here’s an alphabetical list:
- Benjamin Holzschuh
- Philipp Holl
- Georg Kohl
- Mario Lino
- Qiang Liu
- Patrick Schnell
- Felix Trost
- Nils Thuerey
Additional thanks go to Li-Wei Chen, Xin Luo, Maximilian Mueller, Chloe Paillard, Kiwon Um, and all github contributors!
Citation
If you find this book useful, please cite it via:
@book{thuerey2021pbdl,
title={Physics-based Deep Learning},
author={N. Thuerey and B. Holzschuh and P. Holl and G. Kohl and M. Lino and Q. Liu and P. Schnell and F. Trost},
url={https://physicsbaseddeeplearning.org},
year={2021},
publisher={WWW}
}