Training RBF Neural Networks For the Solution of Elliptic Boundary Value Problems

Authors

Andreas Karageorghis, University of CyprusFollow
C.S. Chen, University of Southern MississippiFollow

Document Type

Article

Publication Date

11-15-2022

Department

Mathematics

School

Mathematics and Natural Sciences

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.

Comments

© 2022. This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0/.

Published version found at: https://doi.org/10.1016/j.camwa.2022.08.029

Publication Title

Computers & Mathematics With Applications

Volume

126

First Page

196

Last Page

211

Recommended Citation

Karageorghis, A., Chen, C. (2022). Training RBF Neural Networks For the Solution of Elliptic Boundary Value Problems. Computers & Mathematics With Applications, 126, 196-211.
Available at: https://aquila.usm.edu/fac_pubs/21286