I have a problem similar to a Stefan problem and I wanted to ask if there is any tooling to make this kind of problem simpler/more efficient to solve.
Especially the moving boundary seems difficult to achieve.
Using NeuralPDE.jl might be possible here? Though I have to agree that @StefanKarpinski can be quite a problem.
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How would the NeuralPDE be able to handle the free boundary inside the system? Is there a nice way to define the changing domains?
Otherwise a quite manual approach of cell splitting/merging in a finite volume discretization combined with a level set method could be used, I think… but it seems like a lot of work.
You can treat the boundary as larger and use a characteristic function that changes over time. The PINN would be fine with the discontinuity that makes in the untrained version.