Great paper!

Off the top of your head, are you aware of any similar general-multiphysics NN work that's been applied to electromagnetics problems? In particular, some colleagues in my lab are investigating imaging via acoustic waves which are induced by microwave absorptive heating (in liquids, biological tissues, etc.); this approach is most commonly known as RF-induced thermoacoustic imaging [1]. It's very tricky to model this phenomenon in simulation, doubly so to measure it experimentally.

Most in my lab (myself included) are leery of throwing NNs at problems and seeing what sticks, but sometimes I wonder whether a model like yours might help us skip past the boring details to get at the novel technical stuff, or else extend simulations to more complicated boundary conditions.

[1] https://ieeexplore.ieee.org/abstract/document/6248685

Some month ago i stumbled upon two arcticles discussing PINNs and their failiures in more complex settings. are there similar challenges?

I think you mean this: https://genesis-embodied-ai.github.io/ It seems that this is much more focused on robotics, but interesting nonetheless.

Author here: we do NOT do conservation of energy/momentum. We are currently trying to incorporate that in a follow up paper, but for now, the models that try that (e.g. PINNs (soft constraint) or hard constraint models, all perform badly when modeling multiple systems.

Perhaps, we will encounter the bitter lesson again and a well trained model will solve this. But as I said, we are also looking at hybrid models

I think very few of these "replace numerical solver with ML model" papers do anything to verify invariants are satisfied (they often are not well preserved). They basically all just check that the model approximately reproduces some dynamics on a test data of PDEs, that's often sampled from the same distribution as the training dataset...

I guess it can be implemented in the 'sampler' part. When solving an actual PDE, project the output of the AI onto a space that preserves the invariants.

Author here: we do NOT do conservation of energy/momentum. We are currently trying to incorporate that in a follow up paper, but for now, the models that try that (e.g. PINNs (soft constraint) or hard constraint models, all perform bad when modeling multiple systems.

Perhaps, we will encounter the bitter lesson again and a well trained model will solve this. But as I said, we are also looking at hybrid models

From a quick scan, I do not think they explicitly encode that. They want "the model to predict the evolution of diverse physical systems governed by partial differential equations". It looks like a more sophisticated sibling of time series forecasting models rather than a physics-informed nonparametric symbolic regression model.

Why? Is this important as a sanity check in the absence of any independent verifications?