On the accuracy of kriging model in active subspaces

Investigation on the accuracy of Kriging models in active subspaces was carried out. Our goal is to investigate how much a gain in the accuracy of Kriging model can be obtained by rotating and/or reducing the coordinate set through the active subspaces method procedure. The Kriging model in the transformed coordinate can then be used for various purposes such as uncertainty quantification and optimization. In this paper, we estimate the active subspaces structure with true and estimated gradient information directly from the Kriging model. Two test problems (i.e., borehole and inviscid FFAST airfoil problem) were employed as benchmark problems for our investigation. The results show that one can construct a more accurate Kriging model when a suitable new coordinate is discovered. We observe that using the estimated gradient is a far from optimal approach to find the proper coordinate rotation compared to that of, obviously, true gradient information. When compared to gradient-enhanced Kriging, the potential lowest accuracy that can be achieved by Kriging in the rotated space is almost comparable to that of the gradientenhanced one. This means that there is a potential for the Kriging model to achieve an accuracy that almost matches to that of the gradient-enhanced Kriging without utilizing gradient information.