fOGA: Orthogonal Greedy Algorithm for Fractional Laplace Equations

TL;DR

This paper discretized the fractional Laplace operator using the Riemann-Liouville formula relevant to fractional equations, and constructed a shallow neural network to address the discrete fractional operator, coupled with the OGA algorithm.

Abstract

In this paper, we explore the finite difference approximation of the fractional Laplace operator in conjunction with a neural network method for solving it. We discretized the fractional Laplace operator using the Riemann-Liouville formula relevant to fractional equations. A shallow neural network was constructed to address the discrete fractional operator, coupled with the OGA algorithm. To validate the feasibility of our approach, we conducted numerical experiments, testing both the Laplace operator and the fractional Laplace operator, yielding favorable convergence results.