Neural PDE surrogates are trained on numerical solver outputs that contain both physical evolution and solver-specific discretization errors. Because surrogates are also evaluated against held-out trajectories from the same solver, standard benchmarks cannot distinguish fidelity to the exact evolution from imitation of …
Neural surrogates for vector-valued partial differential equations can fit training data yet change their predictions when the same physical state is expressed in a rotated coordinate frame. We study this failure on three-dimensional Navier--Stokes dynamics observed at irregularly placed points. We introduce the Invari …
Guided diffusion samplers are increasingly used to reconstruct physical fields from sparse observations, but standard diagnostics do not say how much of the reconstruction was actually determined by the data. We introduce effective data resolution for black-box generative posteriors: a comparison between the resolution …