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``` ```
Welcome to the _Physics-based Deep Learning Book_ (v0.2) 👋 Welcome to the _Physics-based Deep Learning Book_ (v0.3, the _GenAI_ edition) 👋
**TL;DR**: **TL;DR**:
This document contains a practical and comprehensive introduction of everything This document contains a practical and comprehensive introduction of everything
related to deep learning in the context of physical simulations. related to deep learning in the context of physical simulations.
As much as possible, all topics come with hands-on code examples in the As much as possible, all topics come with hands-on code examples in the
form of Jupyter notebooks to quickly get started. form of Jupyter notebooks to quickly get started.
Beyond standard _supervised_ learning from data, we'll look at _physical loss_ constraints, Beyond standard _supervised_ learning from data,
more tightly coupled learning algorithms with _differentiable simulations_, we'll look at _physical loss_ constraints and _differentiable simulations_,
training algorithms tailored to physics problems, diffusion-based approaches for _probabilistic, generative models_,
as well as as well as
reinforcement learning and uncertainty modeling. reinforcement learning and neural network architectures.
We live in exciting times: these methods have a huge potential to fundamentally We live in exciting times: these methods have a huge potential to fundamentally change what humans can achieve via computer simulations.
change what computer simulations can achieve.
```{note} ```{note}
_What's new in v0.2?_ _What's new in v0.3?_
For readers familiar with v0.1 of this text, the extended section {doc}`diffphys-examples` and the 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.
brand new chapter on improved learning methods for physics problems (starting with {doc}`physgrad`) are highly recommended starting points.
``` ```
--- ---
@@ -34,13 +32,13 @@ brand new chapter on improved learning methods for physics problems (starting wi
As a _sneak preview_, the next chapters will show: As a _sneak preview_, the next chapters will show:
- How to train networks to infer a fluid flow around shapes like airfoils, and estimate the uncertainty of the prediction. This gives a _surrogate model_ that replaces a traditional numerical simulation. - How to train neural networks to [predict the fluid flow around airfoils with diffusion modeling](probmodels-ddpm-fm). 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 use model equations as residuals to train networks that [represent solutions](diffphys-dpvspinn), and how to improve upon these residual constraints by using [differentiable simulations](diffphys-code-sol).
- 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. - How to more tightly interact with a full simulator for [inverse problems](diffphys-code-control). E.g., we'll demonstrate how to circumvent the convergence problems of standard reinforcement learning techniques by leveraging [simulators in the training loop](reinflearn-code).
- We'll also discuss the importance of _inversion_ for the update steps, and how higher-order information can be used to speed up convergence, and obtain more accurate neural networks. - We'll also discuss the importance of [choosing the right network architecture](supervised-arch): whether to consider global or local interactions, continuous or discrete representations, and structured versus unstructured graph meshes.
Throughout this text, Throughout this text,
we will introduce different approaches for introducing physical models we will introduce different approaches for introducing physical models
@@ -87,21 +85,22 @@ Some visual examples of numerically simulated time sequences. In this book, we e
This project would not have been possible without the help of many people who contributed. Thanks to everyone 🙏 Here's an alphabetical list: 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](https://ge.in.tum.de/about/)
- [Philipp Holl](https://ge.in.tum.de/about/philipp-holl/) - [Philipp Holl](https://ge.in.tum.de/about/philipp-holl/)
- [Maximilian Mueller](https://ge.in.tum.de/) - [Georg Kohl](https://ge.in.tum.de/about/georg-kohl/)
- [Mario Lino](https://ge.in.tum.de/about/mario-lino/)
- [Patrick Schnell](https://ge.in.tum.de/about/patrick-schnell/) - [Patrick Schnell](https://ge.in.tum.de/about/patrick-schnell/)
- [Felix Trost](https://ge.in.tum.de/) - [Felix Trost](https://ge.in.tum.de/about/)
- [Nils Thuerey](https://ge.in.tum.de/about/n-thuerey/) - [Nils Thuerey](https://ge.in.tum.de/about/n-thuerey/)
- [Kiwon Um](https://ge.in.tum.de/about/kiwon/)
Additional thanks go to Additional thanks go to
Georg Kohl for the nice divider images (cf. {cite}`kohl2020lsim`), Li-Wei Chen,
Li-Wei Chen for the airfoil data image, Maximilian Mueller,
and to Chloe Paillard,
Chloe Paillard for proofreading parts of the document. Kiwon Um,
and all github contributors!
% future:
% - [Georg Kohl](https://ge.in.tum.de/about/georg-kohl/)
## Citation ## Citation
@@ -109,10 +108,11 @@ If you find this book useful, please cite it via:
``` ```
@book{thuerey2021pbdl, @book{thuerey2021pbdl,
title={Physics-based Deep Learning}, title={Physics-based Deep Learning},
author={Nils Thuerey and Philipp Holl and Maximilian Mueller and Patrick Schnell and Felix Trost and Kiwon Um}, author={N. Thuerey and B. Holzschuh and P. Holl and G. Kohl and M. Lino andP. Schnell and F. Trost},
url={https://physicsbaseddeeplearning.org}, url={https://physicsbaseddeeplearning.org},
year={2021}, year={2021},
publisher={WWW} publisher={WWW}
} }
``` ```

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"source": [ "source": [
"try:\n", "try:\n",
" import google.colab # only to ensure that we are inside colab\n", " import google.colab # only to ensure that we are inside colab\n",
" %!pip install diffrax jax jaxlib scipy optax dm-haiku\n", " !pip install diffrax jax jaxlib scipy optax dm-haiku\n",
"except ImportError:\n", "except ImportError:\n",
" print(\"This notebook is running locally, please make sure the packages above are installed\")\n", " print(\"This notebook is running locally, please make sure the packages above are installed\")\n",
" pass" " pass"

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