If you have 2 or more functions as Neural nets, say f and g.
And they are coupled by a differential equation.
And we already idea how f should look like say we have a mock function f_m for f
How would I?

Train f to f_m.

Solve/optimize the PDE for g, without updating f.

Then solve/optimize the PDE for f, without updating g.

For step 1 ? If I want to train f to f_m over a Domain D, Is there any function that let me do that easy ?
Naturally, it can be done by calculating f_m on a discretization of D and the train on that data. I was just wondering if there was an easier way, as discretization suffer from the curse of dimensionality,

I would try splitting your system in to 2 with a registered interpolation providing the value of f to the first, which solves for g, then wrap the solution in a registered function and use it as the definition of g in the second.

Finding a good initialisation for f will be important here, perhaps you can run this scheme recursively starting from a random initialisation, but a different low order approximation would be better