Mathematical Modeling on a Physics-Informed Radial Basis Function Network

Abstract

The article is devoted to approximate methods for solving differential equations. An approach based on neural networks with radial basis functions is presented. Neural network training algorithms adapted to radial basis function networks are proposed, in particular adaptations of the Nesterov and Levenberg-Marquardt algorithms. The effectiveness of the proposed algorithms is demonstrated for solving model problems of function approximation, differential equations, direct and inverse boundary value problems, and modeling processes in piecewise homogeneous media.