A novel sampling method for adaptive gradient-enhanced Kriging

Abstract

This paper presents a novel infill-sampling strategy for adaptive gradient-enhanced Kriging (AGEK) that delivers superior results on a limited budget. The primary innovation of this method is the adaptive use of gradient information, blurring the line between Kriging and gradient-enhanced Kriging. To construct a flexible AGEK model that automatically determines whether to incorporate gradients, our proposed method unfolds in three stages: (1) primary infill-sampling, (2) secondary infill-sampling, and (3) modeling time stages. In the first stage, the primary infill-sampling technique identifies potential sample point sites. In the second stage, the secondary infill-sampling process decides whether to obtain only the response or both the response and gradient at the selected sample point. During this stage, a newly defined pseudo expected improvement reduction, pseudo integrated uncertainty reduction, and weight functions are incorporated into the secondary infill-sampling criteria. In the third stage, we propose a strategy to manage instances where training time becomes overly demanding. Benchmark test results validate the excellent performance of the proposed method. Finally, in application to an engineering problem, our method outperforms conventional approaches by producing more accurate results within a limited computational budget.