Integrating Differential Physics into NN Training

About

This article is almost copy and paste of below link.

https://physicsbaseddeeplearning.org/diffphys-examples.html

Comparing with straight forward Differential Physics, It seemes that a bit complitated for me. So, I am going to summarize what thes method is going to do beriefly here.

Switching the Order (PDE forward pass -> )

What is interesting is, they claims that we could imagine a swap of the NN and DP components, giving the following structure:

Since this process is going to deal with outputs from solver, It looks a bit wierld. But, actually, it might be useful for some reason. In this case, the NN is going to correct state output from PDE forward pass. It means that physics solver is not always perfect. The NN is auxually used in some cases. The authors mentioned about recurrent process or evaluation of this

Examples: 2 Scenerios

This is picked up from textbook. it says
First, we’ll show a scenario that employs deep learning to represent the errors of numerical simulations, following Um et al. [UBH+20]. 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 how to let NNs solve tough inverse problems, namely the long-term control of a Navier-Stokes simulation, following Holl et al. [HKT19]. 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. (Later on, in Controlling Burgers’ Equation with Reinforcement Learning we will compare this approach to another DL variant using reinforcement learning.)

I am going to read thoes scenerio examples.