Use of kriging models to approximate deterministic computer models

The use of kriging models for approximation and metamodel-based design and optimization has been steadily on the rise in the past decade. The widespread use of kriging models appears to be hampered by 1) computationally efficient algorithms for accurately estimating the model's parameters, 2) an effective method to assess the resulting model's quality, and 3) the lack of guidance in selecting the appropriate form of the kriging model. We attempt to address these issues by comparing 1) maximum likelihood estimation and cross validation parameter estimation methods for selecting a kriging model's parameters given its form and 2) an R² of prediction and the corrected Akaike information criterion assessment methods for quantifying the quality of the created kriging model. These methods are demonstrated with six test problems. Finally, different forms of kriging models are examined to determine if more complex forms are more accurate and easier to fit than simple forms of kriging models for approximating computer models.