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overview.md

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+Overview
+============================
+
+The following "book" of targets _"Physics-Based Deep Learning"_ techniques
+(PBDL), i.e., the field of methods with combinations of physical modeling and
+deep learning (DL) techniques. Here, DL will typically refer to methods based
+on artificial neural networks. The general direction of PBDL represents a very
+active, quickly growing and exciting field of research. As such, this collection 
+of materials is a living document, and will grow and change over time. Feel free
+to contribute 😀
+
+[TUM Physics-based Simulation Group](https://ge.in.tum.de).
+
+[Link collection](https://github.com/thunil/Physics-Based-Deep-Learning)
+
+## Motivation
+
+....
+
+## Categorization
+
+Within the area of _physics-based deep learning_, 
+we can distinguish a variety of different 
+approaches, from targeting designs, constraints, combined methods, and
+optimizations to applications. More specifically, all approaches either target
+_forward_ simulations (predicting state or temporal evolution) or _inverse_
+problems (e.g., obtaining a parametrization for a physical system from
+observations).
+
+![An overview of categories of physics-based deep learning methods](resources/physics-based-deep-learning-overview.jpg)
+
+No matter whether we're considering forward or inverse problem, 
+the most crucial differentiation for the following topics lies in the 
+nature of the integration  between DL techniques
+and the domain knowledge, typically in the form of model euqations.
+Looking ahead, we will particularly aim for a very tight intgration
+of the two, that goes beyond soft-constraints in loss functions.
+Taking a global perspective, the following three categories can be
+identified to categorize _physics-based deep learning_ (PBDL)
+techniques:
+
+- _Data-driven_: the data is produced by a physical system (real or simulated),
+  but no further interaction exists.
+
+- _Loss-terms_: the physical dynamics (or parts thereof) are encoded in the
+  loss function, typically in the form of differentiable operations. The
+  learning process can repeatedly evaluate the loss, and usually receives
+  gradients from a PDE-based formulation.
+
+- _Interleaved_: the full physical simulation is interleaved and combined with
+  an output from a deep neural network; this requires a fully differentiable
+  simulator and represents the tightest coupling between the physical system and
+  the learning process. Interleaved approaches are especially important for
+  temporal evolutions, where they can yield an estimate of future behavior of the
+  dynamics.
+
+Thus, methods can be roughly categorized in terms of forward versus inverse
+solve, and how tightly the physical model is integrated into the
+optimization loop that trains the deep neural network. Here, especially approaches
+that leverage _differentiable physics_ allow for very tight integration
+of deep learning and numerical simulation methods.
+
+The goal of this document is to introduce the different PBDL techniques,
+ordered in terms of growing tightness of the integration, give practical 
+starting points with code examples, and illustrate pros and cons of the 
+different approaches. In particular, it's important to know in which scenarios 
+each of the different techniques is particularly useful.
+
+