Improved basis-screening Kriging model using sensitivity-based penalized maximum likelihood estimation

Abstract

Abstract In this study, we propose an improved basis-screening Kriging surrogate model that incorporates sensitivity-based penalized maximum likelihood estimation (SB-PMLE), in which the basis-screening procedure determines an appropriate upper limit for the order of the basis functions and sequentially selects the optimal basis function by evaluating its importance through the cross-validation error. Although hyperparameter estimation via maximum likelihood estimation is often unreliable due to strong nonlinearity near the origin and the presence of extensive plateau regions, even when advanced optimization methods such as the generalized pattern search are employed, these challenges often remain. The proposed SB-PMLE overcomes this issue by adaptively updating the penalty parameter using sensitivity information, thereby enhancing both robustness and computational efficiency in hyperparameter estimation. Consequently, hyperparameters can be obtained quickly and accurately, regardless of their initial values, and the precision and efficiency of the methodology are validated through several numerical examples.