An Efficient Hierarchical Kriging Modeling Method for High-dimension Multi-fidelity Problems

TL;DR

This paper introduces a hierarchical Kriging modeling approach that significantly reduces computational cost and improves accuracy for high-dimensional multi-fidelity problems by transforming hyperparameter optimization into a one-dimensional problem.

Contribution

The paper proposes an efficient hierarchical Kriging method utilizing maximal information coefficient and local search to optimize hyperparameters, reducing modeling time and cost in high-dimensional settings.

Findings

Modeling time reduced significantly

Cost savings of about 90% in engineering problem

Higher accuracy achieved compared to conventional methods

Abstract

Multi-fidelity Kriging model is a promising technique in surrogate-based design as it can balance the model accuracy and cost of sample preparation by fusing low- and high-fidelity data. However, the cost for building a multi-fidelity Kriging model increases significantly with the increase of the problem dimension. To attack this issue, an efficient Hierarchical Kriging modeling method is proposed. In building the low-fidelity model, the maximal information coefficient is utilized to calculate the relative value of the hyperparameter. With this, the maximum likelihood estimation problem for determining the hyperparameters is transformed as a one-dimension optimization problem, which can be solved in an efficient manner and thus improve the modeling efficiency significantly. A local search is involved further to exploit the search space of hyperparameters to improve the model accuracy. The high-fidelity model is built in a similar manner with the hyperparameter of the low-fidelity model served as the relative value of the hyperparameter for high-fidelity model. The performance of the proposed method is compared with the conventional tuning strategy, by testing them over ten analytic problems and an engineering problem of modeling the isentropic efficiency of a compressor rotor. The empirical results demonstrate that the modeling time of the proposed method is reduced significantly without sacrificing the model accuracy. For the modeling of the isentropic efficiency of the compressor rotor, the cost saving associated with the proposed method is about 90% compared with the conventional strategy. Meanwhile, the proposed method achieves higher accuracy.