Identification of Partial Differential Equation Models for Continuous Spatio-Temporal Dynamical Systems

The identification of a class of continuous spatio-temporal dynamical systems from observations is presented in this paper. The proposed approach is a combination of implicit Adams integration and an orthogonal least-squares algorithm, in which the operators are expanded using polynomials as basis functions, and the spatial derivatives are estimated by finite difference methods. The resulting identified models of the spatio-temporal evolution form a system of partial differential equations. Examples are provided to demonstrate the efficiency of the proposed method