Sliced gradient-enhanced Kriging for high-dimensional function approximation
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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 large inherent correlation matrix and the associated high-dimensional hyper-parameter tuning problem. To address these issues, we propose a new method in this paper, called sliced GE-Kriging (SGE-Kriging) for reducing both the size of the correlation matrix and the number of hyper-parameters. Firstly, we perform a derivative-based global sensitivity analysis to detect the relative importance of each input variable with respect to model response. Then, we propose to 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. Additionally, 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 global sensitivity indices. Finally, we validate SGE-Kriging by means of numerical experiments with several benchmarks problems. 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 in high-dimensional problems.
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