Uncertainty quantification of multivariate Gaussian process regression for approximating multivariate computer codes

Abstract

Gaussian process regression (GPR) models have become popular as fast alternative models for complex computer codes. For complex computer code (CC) with multivariate outputs, a GPR model can be constructed separately for each CC output, ignoring the correlation between the different outputs. However, this may lead to poor performance of the GPR model. To tackle this problem, multivariate GPR models are used for complex multivariate deterministic computer codes. This paper proposes measures for quantifying uncertainty and checking the assumptions that are proposed in building multivariate GPR models. For comparison, we also constructed a univariate GPR model for each CC output to investigate the effect of ignoring the correlation between the different outputs. We found that the multivariate GPR model outperforms the univariate GPR model as it provides more accurate predictions and quantifies uncertainty about the CC outputs appropriately.