Sample-Efficient Response Surface Modeling and Test-Point Acquisition

Many real-world problems involve estimating expensive black-box functions that require significant resources to evaluate each set of input parameters. Additionally, the number of points required to explore the input-output relationship of these complex systems often increases with the number of input variables.Two semi-supervised learning frameworks are introduced that utilize a Gaussian process (GP) as its foundation. In one, GPs are leveraged in a dual-phase framework that incorporates spatial, response, and gradient feature extraction to enrich parameter regularization with experiment-specific properties. It then extends the GP model to enlist all prescribed points in its infrastructure for latent function estimation (and can be used for test point selection). In the second approach, semi-supervised learning is executed by utilizing the adjacency information between all points within an engineering procedure employed by a GP. This information is consumed as a measure of covariance rather than yielding levels of penalization as is typically done in established geometry-preserving methods. In further distinction, modeling and acquisition of subsequent points can then be conducted without the need for matrix inversions the size of the entire prescribed population.These works endeavor to contribute to the advancement of response surface modeling, and to the broader landscape of semi-supervised learning for optimizing resource-intensive evaluations. Through extensive simulation studies, the efficacy of the proposed frameworks is investigated and comparative evaluations against established strategies are performed to illustrate their utility in prediction and test-point acquisition.