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.

复杂系统的精准响应面建模，往往因需开展大量高成本评估而面临瓶颈。本研究提出一种面向高斯过程（Gaussian Processes）的半监督与主动学习全新配置方案，该框架以邻接向量的形式融入流形信息，以补充额外的数据驱动特征。同时，本研究针对基础参数提出解析表达式，以实现自适应特征提取。此外，本研究采用复合似然函数进行模型训练，为依赖高成本矩阵求逆的边际似然方法提供了高效替代路径。本研究通过大规模仿真实验与案例研究，评估所提方法的有效性，并将其性能与文献中若干主流方法进行对比分析。