SLICED GRADIENT-ENHANCED KRIGING FOR HIGH-DIMENSIONAL FUNCTION APPROXIMATION

Kai Cheng

doi:10.1137/22M154315X

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SLICED GRADIENT-ENHANCED KRIGING FOR HIGH-DIMENSIONAL FUNCTION APPROXIMATION

2023-11-16

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Kai Cheng *

Ralf Zimmermann

DOI：10.1137/22M154315X

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Abstract

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Gradient-enhanced Kriging (GE-Kriging) is a well-established surrogate modeling technique for approximating expensive computational models. However, it tends to get impractical for high-dimensional problems due to the size of the inherent correlation matrix and the associated high-dimensional hyperparameter tuning problem. To address these issues, a new method, called sliced GE-Kriging (SGE-Kriging), is developed in this paper for reducing both the size of the correlation matrix and the number of hyperparameters. We first split the training sample set into multiple slices, and invoke Bayes' theorem to approximate the full likelihood function via a sliced likelihood function, in which multiple small correlation matrices are utilized to describe the correlation of the sample set rather than one large one. Then, we replace the original high-dimensional hyperparameter tuning problem with a low-dimensional counterpart by learning the relationship between the hyperparameters and the derivative-based global sensitivity indices. The performance of SGE-kriging is finally validated by means of numerical experiments with several benchmarks and a high-dimensional aerodynamic modeling problem. The results show that the SGE-Kriging model features an accuracy and robustness that is comparable to the standard one but comes at much less training costs. The benefits are most evident for high-dimensional problems with tens of variables.

Keywords:

gradient-enhanced Kriging

surrogate modeling

maximum likelihood estimation

global sensitivity analysis

hyperparameter tuning