A Theoretical Study of Deep Learning-Based Numerical Solution of High Dimensional Fredholm Integral Equations

Abstract

Fredholm integral equations constitute a vital category for mathematical problems, wherein theunknown function gets determined through an integral relationship over a specified domain. Thesetypically emerge in mathematical engineering, probability, physics, inverse problems, potential theory, heat transfer and many other fields of applied mathematics. Although classical numerical methods havebeen proven to be useful, there’s a stark drawback in this age of digitization.