rename train_x_all to train_x_pde

[g-w1]

This resolves a TODO

Was split off from #1108

[lululxvi]

have you double-checked if all classes using train_x_all has been revised?

[g-w1]

Grepping for train_x_all returns nothing on this branch. However, I just realized that in #1108 I use train_x_pde, so it would make sense to merge this pull request before that one since it depends on this one.

[lululxvi]

As commented here, it is better to add train_x_pde, not replace train_x_all with train_x_pde. In some cases, we may actually use the meaning of train_x_all, but I am not sure which case. Need to look at all the code carefully.

[g-w1]

I have looked over the code, and I can't find a place where train_x_all does not contain PDE residual points.

If I added train_x_pde in addition to train_x_all, what would be different about them? The only thing that I can think of is that train_x_pde would only contain points in the domain as opposed to train_x_all also containing points on the boundary (or on the initial conditions in TimePDE).

What do you recommend for how to add it?

[lululxvi]

train_x_all contains all points (unordered, and does not have duplication). train_x_bc is the points for BC losses (may have have duplication). There are cases where there are only BC losses and no PDE losses. So, it is better to add train_x_pde. That is why we need the following if

deepxde/deepxde/data/pde.py

Line 164 in b87c1c6

if self.pde is not None:

So inside this if, we should add

self.train_x_pde = train_x_all  # Do deep copy

Otherwise, self.train_x_pde is an empty array. We may also need to modify other places.

This makes the code clean and easier to understand. But it uses more memory.