Complex Examples with DP
=======================

The following two sections with show code examples of two more complex cases that 
will show what can be achieved via differentiable physics training.

First, we'll show a scenario that employs deep learning to learn the erros
of a numerical simulation, following Um et al. {cite}`um2020sol`.
This is a very fundamental task, and requires the learned model to closely
interact with a numerical solver. Hence, it's a prime example of 
situations where it's crucial to bring the numerical solver into the 
deep learning loop.

Next, we'll show a tough inverse problem, namely the long-term control
of a fluid simulation, following Holl et al.  {cite}`holl2019pdecontrol`. 
This task requires long term planning,
and hence needs two networks, one to _predict_ the evolution, 
and another one to _act_ to reach the desired goal. 

Both cases require quite a bit more resources than the previous examples, so you 
can expect these notebooks to run longer (and it's a good idea to use the checkpointing
mechanisms when working with these examples).