Incremental Spatial and Spectral Learning of Neural Operators for Solving Large-Scale PDEs

arXiv:2211.15188v4 Announce Type: replace
Abstract: Fourier Neural Operators (FNO) offer a principled approach to solving challenging partial differential equations (PDE) such as turbulent flows. At the core of FNO is a spectral layer that leverages a discretization-convergent representation in the Fourier domain, and learns weights over a fixed set of frequencies. However, training FNO presents two significant challenges, particularly in large-scale, high-resolution applications: (i) Computing Fourier transform on high-resolution inputs is computationally intensive but necessary since fine-scale details are needed …

abstract arxiv core cs.lg differential domain fourier incremental layer operators representation scale spatial type