Hierarchical Gaussian Process Surrogate Modeling Framework for Heterogeneous Multi-Fidelity Dataset

Abstract

Abstract Multi-fidelity (MF) surrogate modeling has been used to a variety of situations in the last few decades. The MF surrogate model integrates data from different levels of fidelity to enhance the efficiency of surrogate modeling. However, the majority of MF surrogate modeling research has been conducted in regression settings, which tries to approximate continuous responses, and few studies have focused on classification problems with discrete target responses. Furthermore, none of them have considered the MF dataset, which contains different types of responses together. In this paper, a hierarchical Gaussian process (HGP) surrogate modeling framework is proposed for various types of MF datasets. To manage diverse MF datasets in the same framework, the core strategy postulates low-fidelity (LF) models as a trend of high-fidelity (HF) models. The proposed framework adopts Bayesian inference and adapts Laplace approximation to MF classification-based surrogate models. Additionally, a local scaling factor is proposed to improve the accuracy of MF classification-based surrogate models when the correlation between HF and LF models is low. The proposed framework is then applied to synthetic and engineering examples, and its efficiency is compared to that of single-fidelity surrogate models. In the engineering example, the proposed MF surrogate model is used to predict the state of electrolyte, and it has a decreased error than the SF surrogate model by more than 50%.