Optimal Sequential Design For Global Fit In Computer Experiment

In this paper, we study the global fit optimization problem in computer experimen-t. We first introduce the ordinary kriging model and two existing sequential designs for optimal global fit, namely CVPE criterion and EIGF criterion. By utilizing the gradi-ent information, we propose a new sequential design criterion, called EIGFG criterion. And using the framework of the sequential minimal energy design (SMED), we further propose modified EIGF criterion and EIGFG criterion, called ME-EIGF criterion and ME-EIGFG criterion. Finally, we examine these sequential design criteria through sim-ulation. It is found that (ⅰ) EIGFG criterion is better than EIGF criterion in terms of prediction error;(ⅱ) the methods via SMED improve the prediction performance of EIGF and EIGFG criterion;(ⅲ) although CVPE criterion has better prediction, the cost in terms of computing time consumption is much higher than the others, especially when n increases. Therefore, we would recommend the sequential design through CVPE criterion when the number of design points is small and the ME-EIGFG criterion (or ME-EIGF criterion) when the number of design points becomes large.