Discretization Error of Fourier Neural Operators

arXiv:2405.02221v1 Announce Type: cross
Abstract: Operator learning is a variant of machine learning that is designed to approximate maps between function spaces from data. The Fourier Neural Operator (FNO) is a common model architecture used for operator learning. The FNO combines pointwise linear and nonlinear operations in physical space with pointwise linear operations in Fourier space, leading to a parameterized map acting between function spaces. Although FNOs formally involve convolutions of functions on a continuum, in practice the computations are …

abstract architecture arxiv cs.lg cs.na data error fourier function linear machine machine learning maps math.na operations operators space spaces type