Sequential Design and Analysis of High-Accuracy and Low-Accuracy Computer Codes

Abstract

A growing trend in engineering and science is to use multiple computer codes with different levels of accuracy to study the same complex system. We propose a framework for sequential design and analysis of a pair of high-accuracy and low-accuracy computer codes. It first runs the two codes with a pair of nested Latin hypercube designs (NLHDs). Data from the initial experiment are used to fit a prediction model. If the accuracy of the fitted model is less than a prespecified threshold, the two codes are evaluated again with input values chosen in an elaborate fashion so that their expanded scenario sets still form a pair of NLHDs. The nested relationship between the two scenario sets makes it easier to model and calibrate the difference between the two sources. If necessary, this augmentation process can be repeated a number of times until the prediction model based on all available data has reasonable accuracy. The effectiveness of the proposed method is illustrated with several examples. Matlab codes are provided in the online supplement to this article.

KEY WORDS:

• Gaussian process model
• Kriging
• Nested Latin hypercube design

ACKNOWLEDGMENTS

Xiong is supported by the National Natural Science Foundation of China (Grant No. 10801130). Qian is supported by NSF grant CMMI 0969616. Wu is supported by NSF grants DMS 0705261 and 1007574.