Dynamic Gaussian process regression for spatio-temporal data based on local clustering

Abstract

This paper introduces techniques in Gaussian process regression model for spatio-temporal data collected from complex systems. This study focuses on extracting local structures and then constructing surrogate models based on Gaussian process assumptions. The proposed Dynamic Gaussian Process Regression (DGPR) consists of a sequence of local surrogate models related to each other. In DGPR, the time-based spatial clustering is carried out to divide the systems into sub-spatio-temporal parts whose interior has similar variation patterns, where the temporal information is used as the prior information for training the spatial-surrogate model. The DGPR is robust and especially suitable for the loosely coupled model structure, also allowing for parallel computation. The numerical results of the test function show the effectiveness of DGPR. Furthermore, the shock tube problem is successfully approximated under different phenomenon complexity.