On kernel functions for bi-fidelity Gaussian process regressions

This paper investigates the impact of kernel functions on the accuracy of bi-fidelity Gaussian process regressions (GPR) for engineering applications. The potential of composite kernel learning (CKL) and model selection is also studied, aiming to ease the process of manual kernel selection. Using the autoregressive Gaussian process as the base model, this paper studies four kernel functions and their combinations: Gaussian, Matern-3/2, Matern 5/2, and Cubic. Experiments on four engineering test problems show that the best kernel is problem dependent and sometimes might be counter intuitive, even when a large amount of low-fidelity data already aids the model. In this regard, using CKL or automatic kernel selection via cross validation and maximum likelihood can reduce the tendency to select a poor-performing kernel. In addition, the CKL technique can create a slightly more accurate model than the best-performing individual kernel. The main drawback of CKL is its significantly expensive computational cost. The results also show that, given a sufficient amount of samples, tuning the regression term is important to improve the accuracy and robustness of bi-fidelity GPR, while decreasing the importance of the proper kernel selection.