Gaussian Processes-based Parametric Identification for Dynamical Systems

In this paper we present some results on parametric identification for dynamical systems. More specifically, we consider the general case of dynamics described by partial differential equations (PDEs), which includes the special case of ordinary differential equations (ODEs). We follow a stochastic approach and formulate the identification problem as a Gaussian process optimization with respect to the unknown parameters of the PDE. We use proper orthogonal decomposition (POD) model reduction theory together with a data-driven Gaussian Process Upper Confidence Bound (GP-UCB), to solve the identification problem. The proposed approach is validated on the coupled Burgers' equation benchmark.