Use of Kriging Models to Approximate Deterministic Computer Models

TLDR

Kriging models have become increasingly popular for approximating computer models, yet their adoption is limited by unclear guidance on model form, inefficient parameter‑estimation algorithms, and inadequate quality‑assessment methods. The study compares Maximum Likelihood Estimation and Cross‑Validation parameter‑estimation techniques, along with R² and corrected AIC metrics, to evaluate and contrast different kriging model forms and determine whether more complex forms improve accuracy and ease of fitting. The authors apply these evaluation methods to six test problems, demonstrating how the metrics can be used to compare and select appropriate kriging model forms.

Abstract

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 usage of kriging models appears to be hampered by (1) the lack of guidance in selecting the appropriate form of the kriging model, (2) computationally efficient algorithms for estimating the model’s parameters, and (3) an effective method to assess the resulting model’s quality. In this paper, we compare (1) Maximum Likelihood Estimation (MLE) and Cross-Validation (CV) parameter estimation methods for selecting a kriging model’s parameters given its form and (2) and an R 2 of prediction and the corrected Akaike Information Criterion for assessing the quality of the created kriging model, permitting the comparison of different forms of a 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.