[esafak]

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.

[NeoInHacker]

Yeah, It’s true that PDEs are the "top-tier tool" 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 "fall short": 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 "top-tier auxiliary," but by no means a "one-size-fits-all key."

[codethief]

> in quantum gravity

GP was asking about conservation laws but in gravity you don't even have energy-momentum conservation.