Sliced gradient-enhanced Kriging for high-dimensional function approximation

• URL: http://arxiv.org/abs/2204.03562v3
• Date: Thu, 4 Jan 2024 18:42:31 GMT
• Title: Sliced gradient-enhanced Kriging for high-dimensional function approximation
• Authors: Kai Cheng, Ralf Zimmermann
• Abstract summary: Gradient-enhanced Kriging (GE-Kriging) is a well-established surrogate modelling technique for approximating expensive computational models. It tends to get impractical for high-dimensional problems due to the size of the inherent correlation matrix. A new method, called sliced GE-Kriging (SGE-Kriging), is developed in this paper for reducing the size of the correlation matrix. 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.
• Score: 2.8228516010000617
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Gradient-enhanced Kriging (GE-Kriging) is a well-established surrogate modelling 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 hyper-parameter 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 hyper-parameters. 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 hyper-parameter tuning problem with a low-dimensional counterpart by learning the relationship between the hyper-parameters 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.

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