Operator Learning: Algorithms and Analysis

arXiv:2402.15715v1 Announce Type: new
Abstract: Operator learning refers to the application of ideas from machine learning to approximate (typically nonlinear) operators mapping between Banach spaces of functions. Such operators often arise from physical models expressed in terms of partial differential equations (PDEs). In this context, such approximate operators hold great potential as efficient surrogate models to complement traditional numerical methods in many-query tasks. Being data-driven, they also enable model discovery when a mathematical description in terms of a PDE is …

abstract algorithms analysis and analysis application arxiv context cs.lg cs.na differential functions ideas machine machine learning mapping math.na operators spaces terms type