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updated teaser, added dividers

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@@ -3,6 +3,8 @@ Summary and Discussion
The previous sections have explained the differentiable physics approach for deep learning, and have given a range of examples: from a very basic gradient calculation, all the way to complex learning setups powered by complex simulations. This is a good time to pause and take a step back, to take a look at what we have: in the end, the _differentiable physics_ component of these approaches is not too complicated. It's largely based on existing numerical methods, with a focus on efficiently using those methods to not only do a forward simulation, but also to compute gradient information. What is primarily exciting in this context are the implications that arise from the combination of these numerical methods with deep learning.
![Divider](resources/divider6.jpg)
## Integration
Most importantly, training via differentiable physics allows us to seamlessly bring the two fields together:
@@ -16,7 +18,7 @@ One key aspect that is important for these hybrids to work well is to let the NN
The hybrid approach also bears particular promise for simulators: it improves generalizing capabilities of the trained models by letting the PDE-solver handle large-scale _changes to the data distribution_ such that the learned model can focus on localized structures not captured by the discretization. While physical models generalize very well, learned models often specialize in data distributions seen at training time. This was, e.g., shown for the models reducing numerical errors of the previous chapter: the trained models can deal with solution manifolds with significant amounts of varying physical behavior, while simpler training variants quickly deteriorate over the course of recurrent time steps.
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![Divider](resources/divider7.jpg)
Training NNs via differentiable physics solvers, i.e., what we've described as "DP" in the previous
sections, is a very generic approach that is applicable to a wide range of combinations of PDE-based models