The False Promise of Zero-Shot Super-Resolution in Machine-Learned Operators

An empirical critique of “zero-shot super-resolution” in machine-learned operators (MLOs) for PDEs, and a practical fix.

• Decomposes multi-resolution inference into two behaviors — frequency extrapolation and cross-resolution interpolation — and shows MLOs fail at both in a zero-shot setting.
• MLOs are brittle and susceptible to aliasing when evaluated at resolutions different from their training grid, both for super- and sub-resolution.
• Proposes a simple, computationally-efficient, data-driven multi-resolution training protocol that overcomes aliasing and restores robust multi-resolution generalization.