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Sliced gradient-enhanced Kriging for high-dimensional function approximation and aerodynamic modeling

Kai ChengRalf Zimmermann
Apr 2022
摘要
Gradient-enhanced Kriging (GE-Kriging) is a well-established surrogatemodelling technique for approximating expensive computational models. However,it tends to get impractical for high-dimensional problems due to the largeinherent correlation matrix and the associated high-dimensional hyper-parametertuning 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 thecorrelation matrix and the number of hyper-parameters. Firstly, we perform aderivative-based global sensitivity analysis to detect the relative importanceof each input variable with respect to model response. Then, we propose tosplit the training sample set into multiple slices, and invoke Bayes' theoremto approximate the full likelihood function via a sliced likelihood function,in which multiple small correlation matrices are utilized to describe thecorrelation of the sample set. Additionally, we replace the originalhigh-dimensional hyper-parameter tuning problem with a low-dimensionalcounterpart by learning the relationship between the hyper-parameters and theglobal sensitivity indices. Finally, we validate SGE-Kriging by means ofnumerical experiments with several benchmarks problems. The results show thatthe SGE-Kriging model features an accuracy and robustness that is comparable tothe standard one but comes at much less training costs. The benefits are mostevident in high-dimensional problems.
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