Author here,Wow, I didn&#x27;t think this would HN. I actually planned to do the advertisement rounds only after the final ICLR submission.This is our attempt at creating a model which understands multiple physics, which is in contrast to PINNs and Neural Operators, which focus on much more narrow systems.Obviously, the biggest issue is still data (3D and real-world problems), but I think we and a few other groups make significant progress here.

Not the &quot;foundational model&quot; of physics I was expecting, but this is still great to see!

Author here: we do NOT do conservation of energy&#x2F;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 &quot;replace numerical solver with ML model&quot; 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&#x27;s often sampled from the same distribution as the training dataset...

Author here: we do NOT do conservation of energy&#x2F;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

Yeah, It’s true that PDEs are the &quot;top-tier tool&quot; for describing physical phenomena—from the laws of motion in classical mechanics and electromagnetic waves in electromagnetism to the evolution of wave functions in quantum mechanics, they accurately model most macroscopic, classical scenarios. However, when it comes to covering all physical phenomena, they really &quot;fall short&quot;: in quantum gravity, spacetime may be discontinuous, making the concept of differentiation meaningless; for complex systems like turbulence, PDEs cannot be solved nor can they capture macroscopic laws; even for the randomness of quantum measurements, PDEs can only predict probability distributions and fail to explain the underlying nature. In short, they are a &quot;top-tier auxiliary,&quot; but by no means a &quot;one-size-fits-all key.&quot;

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

How do they prove their model preserves conservation principles? I looked in the paper &amp; didn&#x27;t find any evidence of how they verify that whatever their &quot;trained&quot; model is doing is actually physically plausible &amp; maintains the relevant invariants like mass, energy, momentum, etc.

ITAR will be quite a surprise to some when it suddenly makes an appearance.

Towards a Physics Foundation Model