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 methods.