Deterministic learning of a completely resonant nonlinear wave system with dirichlet boundary conditions

Abstract

In this paper, we investigate the identification of system dynamics of a completely resonant nonlinear wave system described by partial differential equation (PDE) via deterministic learning. Firstly, the wave system is firstly dis-cretized into a finite-dimensional dynamical system described by ordinary differential equation (ODE). Then, it is proved that the finite-dimensional dynamical system keeps the essential features of the wave system and contains almost all system dynamics of the wave system. Finally, dynamical radial basis function (RBF) neural networks (NN) is constructed by the deterministic learning theorem, and accurate NN approximation of the finite-dimensional nonlinear dynamical system is achieved in local region along system trajectory. Simulation studies are included to demonstrate the effectiveness of the proposed approach.