A Laplacian‐regularized dual‐phase Gaussian process technique for semi‐supervised response surface modeling of black‐box functions

Abstract

Numerous semi-supervised learning strategies are designed to reduce the number of experiments to model expensive black-box functions. However, most of the existing methods do not utilize the information of the estimated responses and the associated gradients in an effective manner. In this paper, we proposed a semi-supervised learning configuration for the Gaussian process which utilizes the estimated responses and their gradients in a dual-phase framework to improve the accuracy of estimation and reduce the number of expensive experiments required to represent a latent function. We also explore the incorporation of Laplacian regularization for information transfer using a combination of design vector and response surface elements between measured and unmeasured data points. Through several simulation studies and a case study on the evaluation of concrete strength prediction accuracy, we assess the effectiveness of the proposed framework and compare its performance against some of the existing Laplacian-regularized methods in the Literature.