Modeling and nonlinear parameter estimation with Kronecker product representation for coupled oscillators and spatiotemporal systems

We focus here on the question of global modeling, that is, building an ordinary differential equation (ODE) of minimal dimensions which models a given multivariate time dependent data-set. We give proof of convergence of the given method. We will furthermore introduce a new method which adapts the least-squares best approximation by a Kronecker product representation [C.F. Van Loan, N. Pitsianis, Approximation with Kronecker products. www.math.tkk.fi/ mhuhtane/kronecker.ps], to analyze underlying structure when it exists as a system of coupled oscillators. Several examples are presented including diffusively coupled chaotic systems. Some interesting prospective problems will be briefly discussed in the conclusions.