Using Kriging models for approximating computer models and quantifying their uncertainty

Kriging models are statistical methods for approximating and estimating computer models. Kriging models have been used to replace time-consuming computer models with fast-running alternatives. Kriging models are constructed based on some assumptions. Thus, if these assumptions are not suitable and consistent with the computer model outputs, inferences and results of the Kriging models will not be accurate. Therefore, KMs need to be subjected to validation measures before using them in different areas of science. In this paper, we propose some measures that can be used for validating Kriging models. These measures are based on comparing KM predictions and computer model outputs. We investigate the performance of the proposed measures via some real examples of computer models, the Borehole model, and the Piston Simulation function.