[anon389r58r58]

The general rule of thumb to go by is that whatever Karniadakis proposes, doesn't actually work outside of his benchmarks. PINNs don't really work, and _his flavor_ of neural operators also don't really work.

PINNs have serious problems with the way the "PDE-component" of the loss function needs to be posed, and outside of throwing tons of, often Chinese, PhD students, and postdocs at it, they usually don't work for actual problems. Mostly owed to the instabilities of higher order automatic derivatives, at which point PINN-people begin to go through a cascade of alternative approaches to obtain these higher-order derivatives. But these are all just hacks.