An improved high-dimensional Kriging modeling method utilizing maximal information coefficient

PurposeKriging surrogate model has demonstrated a powerful ability to be applied to a variety of engineering challenges by emulating time-consuming simulations. However, when it comes to problems with high-dimensional input variables, it may be difficult to obtain a model with high accuracy and efficiency due to the curse of dimensionality. To meet this challenge, an improved high-dimensional Kriging modeling method based on maximal information coefficient (MIC) is developed in this work.Design/methodology/approachThe hyperparameter domain is first derived and the dataset of hyperparameter and likelihood function is collected by Latin Hypercube Sampling. MIC values are innovatively calculated from the dataset and used as prior knowledge for optimizing hyperparameters. Then, an auxiliary parameter is introduced to establish the relationship between MIC values and hyperparameters. Next, the hyperparameters are obtained by transforming the optimized auxiliary parameter. Finally, to further improve the modeling accuracy, a novel local optimization step is performed to discover more suitable hyperparameters.FindingsThe proposed method is then applied to five representative mathematical functions with dimensions ranging from 20 to 100 and an engineering case with 30 design variables.Originality/valueThe results show that the proposed high-dimensional Kriging modeling method can obtain more accurate results than the other three methods, and it has an acceptable modeling efficiency. Moreover, the proposed method is also suitable for high-dimensional problems with limited sample points.

Automated summary

In this work, an improved high-dimensional Kriging modeling method based on maximal information coefficient (MIC) is developed to address problems with high-dimensional input variables. The method optimizes hyperparameters using MIC values as prior knowledge and introduces an auxiliary parameter to establish the relationship between MIC values and hyperparameters. Experimental results show that the proposed method can achieve more accurate results than other three methods in problems with high-dimensional input variables, and it has acceptable modeling efficiency.