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.

翻译：梯度增强克里金（GE-Kriging）是一种成熟的代理建模技术，用于近似昂贵的高计算成本模型。然而，由于固有相关矩阵的规模以及相关的高维超参数调优问题，该方法在高维问题中往往难以实用。为解决这些问题，本文提出了一种名为切片梯度增强克里金（SGE-Kriging）的新方法，该方法旨在同时减小相关矩阵的规模和超参数的数量。我们首先将训练样本集划分为多个切片，并利用贝叶斯定理通过切片似然函数来近似完整似然函数——在此过程中使用多个小型相关矩阵而非单个大型矩阵来描述样本集的相关性。随后，通过学习超参数与基于导数的全局灵敏度指标之间的关系，将原始高维超参数调优问题转化为低维问题。最后，通过多个基准数值实验及一个高维气动建模问题验证了SGE-Kriging的性能。结果表明，SGE-Kriging模型在保持与标准方法相当的精度和鲁棒性的同时，训练成本显著降低。该优势在处理包含数十个变量的高维问题时尤为突出。