alt Hacker NewsHow do they prove their model preserves conservation principles? I looked in the paper & didn't find any evidence of how they verify that whatever their "trained" model is doing is actually physically plausible & maintains the relevant invariants like mass, energy, momentum, etc.
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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...
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.
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