Active data based Gaussian process models for nonlinear spatiotemporal systems

A new data-driven system identification method, called KL-GP, is proposed for spatiotemporal system. It combines Karhunen-Loève (KL) decomposition and Gaussian process (GP) models. As the nonlinear spatial-temporal spatiotemporal system has strong spatiotemporal characteristics, KL decomposition with good characteristics is employed for time/space separation and dimension reduction. Then the spatiotemporal output is expanded onto a low-dimensional KL space with temporal coefficients. GP models are employed to build up the temporal relation using these coefficients. In addition, a healthy spatial-temporal model that has accuracy predictions is always unknown in practice. GP provides an estimate of the variance of its predicted output. Using this characteristic, active data in the spatiotemporal system region can be found out for the model improvement. This enables the spatiotemporal system model to be updated without high computational demand. Simulation results of spatiotemporal system are presented to demonstrate the effectiveness of this KLGP modeling method.