Training RBF neural networks for the solution of elliptic boundary value problems

Abstract

We propose a radial basis function (RBF) neural network method for solving two- and three–dimensional second and fourth order elliptic boundary value problems (BVPs). The neural network in question is trained by minimizing a nonlinear least squares functional, thus determining the optimal values of the various RBF parameters involved. The functional minimization is carried out using standard MATLAB® software efficiently. Several numerical experiments are presented to demonstrate the efficacy of the proposed method.