Derivative Observations in Gaussian Process Models of Dynamic Systems

Abstract

Gaussian processes provide an approach to nonparametric modelling which allows a straightforward combination of function and derivative observations in an empirical model. This is of particular importance in identification of nonlinear dynamic systems from experimental data. 1) It allows us to combine derivative information, and associated uncertainty with normal function observations into the learning and inference pro- cess. This derivative information can be in the form of priors specified by an expert or identified from perturbation data close to equilibrium. 2) It allows a seamless fusion of multiple local linear models in a consis- tent manner, inferring consistent models and ensuring that integrability constraints are met. 3) It improves dramatically the computational ef- ficiency of Gaussian process models for dynamic system identification, by summarising large quantities of near-equilibrium data by a handful of linearisations, reducing the training set size – traditionally a problem for Gaussian process models.