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updated readme for v0.2

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# Welcome to the Physics-based Deep Learning book (PBDL)
# Welcome to the Physics-based Deep Learning book (PBDL) v0.2
This is the source code repository for the Jupyter book "Physics-based Deep Learning". You can find the full, readable version online at:
[https://physicsbaseddeeplearning.org/](https://physicsbaseddeeplearning.org/)
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* Field-based simulations (not much on Lagrangian methods)
* Combinations with deep learning (plenty of other interesting ML techniques exist, but won't be discussed here)
* Experiments as are left as an outlook (i.e., replacing synthetic data with real-world observations)
* Experiments as are left as an outlook (such as replacing synthetic data with real-world observations)
The name of this book, _Physics-based Deep Learning_, denotes combinations of physical modeling and numerical simulations with methods based on artificial neural networks. The general direction of Physics-Based Deep Learning represents a very active, quickly growing and exciting field of research.
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The resulting methods have a huge potential to improve what can be done with numerical methods: in scenarios where a solver targets cases from a certain well-defined problem domain repeatedly, it can for instance make a lot of sense to once invest significant resources to train a neural network that supports the repeated solves. Based on the domain-specific specialization of this network, such a hybrid could vastly outperform traditional, generic solvers.
# What's new?
* For readers familiar with v0.1 of this text, the brand new chapter on improved learning methods for physics problems is highly recommended: starting with https://www.physicsbaseddeeplearning.org/physgrad.html
# Teasers
To mention a few highlights: the book contains a notebook to train hybrid fluid flow (Navier-Stokes) solvers via differentiable physics to reduce numerical errors. Try it out:
https://colab.research.google.com/github/tum-pbs/pbdl-book/blob/main/diffphys-code-sol.ipynb
In v0.2 there's new notebook for an improved learning scheme which jointly computes update directions for neural networks and physics (via half-inverse gradients):
https://colab.research.google.com/github/tum-pbs/pbdl-book/blob/main/physgrad-hig-code.ipynb
It also has example code to train a Bayesian Neural Network for RANS flow predictions around airfoils that yield uncertainty estimates. You can run the code right away here:
https://colab.research.google.com/github/tum-pbs/pbdl-book/blob/main/bayesian-code.ipynb