An Adjacency-Adaptive Gaussian Process Method for Sample Efficient Response Surface Modeling and Test-Point Acquisition

Accurate response surface modeling of complex systems is often hindered by the need for a considerable number of costly evaluations. In this work, we propose a novel configuration for semi-supervised and active learning in Gaussian processes, which incorporates manifold information in the form of adjacency vectors to enrich with additional data-driven features. We also introduce an analytical formulation for the base parameters to enable adaptive feature extraction. Additionally, we adopt the composite likelihood function for training, offering an efficient alternative to the marginal likelihood reliance on expensive matrix inversion. Through an extensive simulation study as well as a case study, we evaluate the effectiveness of the proposed method and compare its performance against some of the common methods in the literature.