A comprehensive multi-fidelity surrogate framework based on Gaussian process for datasets with heterogeneous responses

Abstract

In recent decades, the multi-fidelity (MF) surrogate framework has seen widespread application across various scenarios. This framework significantly enhances the efficiency of surrogate modeling by integrating data of varying fidelity levels. However, research on the MF surrogate has predominantly focused on regression settings, aiming at approximating continuous responses, with limited attention to classification problems involving discrete responses. Moreover, no existing studies have addressed a heterogeneous MF dataset, where the data types (continuous or discrete) vary between different fidelities. This paper introduces a comprehensive MF surrogate framework based on Gaussian process, designed to handle a wide range of MF dataset types. Our framework employs a hierarchical Kriging scheme and Bayesian inference, adaptable to any MF dataset type. Given the challenges posed by discrete data in analytical inference, we incorporate the Laplace approximation for the latent function associated with discrete data in our framework. Additionally, we introduce a local scaling factor specifically for low-correlation classification problems in MF settings. The superiority of our method over conventional ones is demonstrated through both synthetic and engineering examples. Notably, in an engineering example featuring a heterogeneous MF dataset, our proposed MF surrogate model achieves an error reduction exceeding 50%.