Custom losses (e.g. H^1-norm)

[pescap]

Hi,
I was trying to reproduce the method proposed in: Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems, for example using H^1 (Sobolev) norm instead of a L^2 norm.

Generally, the losses take (y_true, y_pred) as inputs.

Is there a simple way to incorporate x to the losses in order to evaluate gradient based losses/norms?

In parallel, it could be interesting to enable "custom losses" for model.compile(), i.e. something like
model.compile(loss_fn = custom_loss)
with a previously defined custom_loss(y_true, y_pred) or even custom_loss(y_true, y_pred, x)

Thank you for your help!
Paul

[lululxvi]

The code of gPINN will be public soon.

DeepXDE already supports it:

def custom_loss(y_true, y_pred):
    ...

model.compile(loss=custom_loss)

But not custom_loss(y_true, y_pred, x).