Fast Analysis of Dynamic Systems Via Gaussian Emulator

Abstract

Dynamic systems are used in modeling diverse behaviors in a wide variety of scientific areas. Current methods for estimating parameters in dynamic systems from noisy data are computationally intensive (for example, relying heavily on the numerical solutions of the underlying differential equations). We propose a new inference method by creating a system driven by a Gaussian process to mirror the dynamic system. Auxiliary variables are introduced to connect this Gaussian system to the real dynamic system; and a sampling scheme is introduced to minimize the ‘distance’ between these two systems iteratively. The new inference method also covers the partially observed case in which only some components of the dynamic system are observed. The method offers a substantial saving of computational time and fast convergence while still retaining high estimation accuracy. We will illustrate the method by numerical examples.?