MathAI 2026Accepted2026

Four-Term Finite-Sample OOD Transfer Bound for Fourier Neural Operators

Derives a finite-sample transfer bound for nonlinear Fourier Neural Operators that separates complexity, discretization, distribution shift, and mesh aliasing.

Four channels · Darcy, Helmholtz, and Burgers diagnostics · aliasing made explicit

Four-panel figure illustrating complexity, discretization, shift, and aliasing in Fourier Neural Operators.

Abstract

Derives a finite-sample transfer bound for nonlinear Fourier Neural Operators that separates complexity, discretization, distribution shift, and mesh aliasing.