Experimental Design for Non-Parametric Correction of Misspecified Dynamical Models

Abstract: We consider a class of misspecified dynamical models where the governing term is only approximately known. Under the assumption that observations of the system's evolution are accessible for various initial conditions, our goal is to infer a non-parametric correction to the misspecified driving term such as to faithfully represent the system dynamics and devise system evolution predictions for unobserved initial conditions. We model the unknown correction term as a Gaussian Process and analyze the problem of efficient experimental design to find an optimal correction term under constraints such as a limited experimental budget. We suggest a novel formulation for experimental design for this Gaussian Process and show that approximately optimal (up to a constant factor) designs may be efficiently derived by utilizing results from the literature on submodular optimization. Our numerical experiments exemplify the effectiveness of these techniques.