UNCERTAINTY QUANTIFICATION OF MULTIVARIATE GAUSSIAN PROCESS REGRESSION FOR APPROXIMATING MULTIVARIATE COMPUTER CODES

UNCERTAINTY QUANTIFICATION OF MULTIVARIATE GAUSSIAN PROCESS REGRESSION FOR APPROXIMATING MULTIVARIATE COMPUTER CODES

Y. Al-Taweel

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Abstract

Gaussian process regression (GPR) models have become popular as fast al- ternative 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 di erent 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 mea- sures 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 e ect of ignoring the correlation be- tween the di erent outputs. We found that the multivariate GPR model outperforms the univariate GPR model as it provides more accurate predictions and quanti es un- certainty about the CC outputs appropriately.

Keywords

multivariate Gaussian process, measures, multivariate deterministic computer codes.