@P.Fonseca, short answer not in the short or intermediate time frame. Longer answer: I am not convinced of the usefulness of NN for PDE solving. The methods we use today have well known and understood error estimators. Something that, to the best of my knowledge, NN do not have. The place where I see NN might be useful is for fining initial guesses for nonlinear PDEs. That seems to coincide with what people say in your cited reference:

"Models trained on one geometry may not directly generalize to another geometry. But we may use it as a pre-trained model or a preconditioner to help to get the solution on a different geometry." That said, SW did request some PDE solving to be implemented based on NN, but I declined that because I have a gazillion other fish to fry which are a much easier catch. So maybe the NN team will jump on this band wagon, but I am not aware of that.

Let me ask a counter question. Where do you see the usefulness of NN for PDE solving and would Suez, for example make use of that?

@user21 actually, I share of your point of view. It might be of added value for initialization, and eventually for intermediate warp speed jumps, in the sense that both the knowledge of a given convergence step and of the previous ones might allow to jump some steps ahead. But subsequent cleanups seem mandatory with well know classic methods. One interesting aspect of the fast initialization it can bring is related to non unique solution cases... how would/will one control it.