An efficient gradient-enhanced kriging modeling method assisted by fast kriging for high-dimension problems

Abstract

Purpose

The modeling cost of the gradient-enhanced kriging (GEK) method is prohibitive for high-dimensional problems. This study aims to develop an efficient modeling strategy for the GEK method.

Design/methodology/approach

A two-step tuning strategy is proposed for the construction of the GEK model. First, an auxiliary kriging is built efficiently. Then, the hyperparameter of the kriging model is served as a good initial guess to that of the GEK model, and a local optimal search is further used to explore the search space of hyperparameter to guarantee the accuracy of the GEK model. In the construction of the auxiliary kriging, the maximal information coefficient is adopted to estimate the relative magnitude of the hyperparameter, which is used to transform the high-dimension maximum likelihood estimation problem into a one-dimensional optimization. The tuning problem of the auxiliary kriging becomes independent of the dimension. Therefore, the modeling efficiency can be improved significantly.

Findings

The performance of the proposed method is studied with analytic problems ranging from 10D to 50D and an 18D aerodynamic airfoil example. It is further compared with two efficient GEK modeling methods. The empirical experiments show that the proposed model can significantly improve the modeling efficiency without sacrificing accuracy compared with other efficient modeling methods.

Originality/value

This paper developed an efficient modeling strategy for GEK and demonstrated the effectiveness of the proposed method in modeling high-dimension problems.

Citation

He, Y., Tan, K., Fu, C. and Luo, J. (2023), "An efficient gradient-enhanced kriging modeling method assisted by fast kriging for high-dimension problems", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 33 No. 12, pp. 3967-3993. https://doi.org/10.1108/HFF-02-2023-0080