Coupled DeepONet PDE with Hard Boundary Conditions

[schrodingersket]

Hi there,

This paper discusses an implementation of DeepONets which supports multiple function outputs and enforcing hard Dirichlet boundary conditions, but I couldn't find an example of that implementation in https://github.com/lu-group/deeponet-fno. Is there support for this in DeepXDE? Looks like there pull request open for this functionality.

One of my DeepONet boundary conditions involves the function which sampled from the input space. Is there a way to expose this function to apply_output_transform in a manner similar to the way that DirichletBC and IC do in order to enforce that as a hard constraint? The constraint is essentially just u(L) + v(L) = 1.0, where v is the function from the input space. Also, is it possible to differentiate these functions within a PDE function? I tried using dde.grad.jacobian to differentiate with respect to the inputs, but that didn't quite seem to work (and returned a None value).

Thanks in advance! I'm happy to share details of the particular problem I'm working on if that's helpful, but I didn't want to distract from the question right off the bat.

[lululxvi]

You can see examples here https://deepxde.readthedocs.io/en/latest/demos/operator.html#pi-deeponet

[schrodingersket]

I did look through those examples; however, they do not seem to indicate whether apply_output_transform provides auxiliary functions from the branch network function space as an argument. I dug into the source code a bit and it seems that is not provided as a function argument, but I wanted to verify that to be the case.

Thanks again!