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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**:
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,
more tightly coupled learning algorithms with _differentiable simulations_,
training algorithms tailored to physics problems,
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 uncertainty modeling.
We live in exciting times: these methods have a huge potential to fundamentally
change what computer simulations can achieve.
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.
```{note}
_What's new in v0.2?_
For readers familiar with v0.1 of this text, the extended section {doc}`diffphys-examples` and the
brand new chapter on improved learning methods for physics problems (starting with {doc}`physgrad`) are highly recommended starting points.
_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.
```
---
@ -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:
- 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,
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:
- [Benjamin Holzschuh](https://ge.in.tum.de/about/)
- [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/)
- [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/)
- [Kiwon Um](https://ge.in.tum.de/about/kiwon/)
Additional thanks go to
Georg Kohl for the nice divider images (cf. {cite}`kohl2020lsim`),
Li-Wei Chen for the airfoil data image,
and to
Chloe Paillard for proofreading parts of the document.
Li-Wei Chen,
Maximilian Mueller,
Chloe Paillard,
Kiwon Um,
and all github contributors!
% future:
% - [Georg Kohl](https://ge.in.tum.de/about/georg-kohl/)
## Citation
@ -109,10 +108,11 @@ If you find this book useful, please cite it via:
```
@book{thuerey2021pbdl,
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},
year={2021},
publisher={WWW}
}
```

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"source": [
"try:\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",
" print(\"This notebook is running locally, please make sure the packages above are installed\")\n",
" pass"

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