Training RBF neural networks for solving nonlinear and inverse boundary value problems

Radial basis function neural networks (RBFNN) have been increasingly employed to solve boundary value problems (BVPs). In the current study, we propose such a technique for nonlinear (apparently for the first time) elliptic BVPs of orders two and four in 2-D and 3-D. The method is also extended, in a natural way, to solving 2-D and 3-D inverse BVPs. The RBFNN is trained via the least squares minimization of a nonlinear functional using the MATLAB (R) routine lsqnonlin . In this way, as well as the solution, appropriate values of the RBF approximation parameters are automatically delivered. The efficacy of the proposed RBFNN is demonstrated through several numerical experiments.