Optimization of Multi-Fidelity Computer Experiments via the EQIE Criterion

Abstract

Computer experiments based on mathematical models are powerful tools for understanding physical processes. This article addresses the problem of kriging-based optimization for deterministic computer experiments with tunable accuracy. Our approach is to use multi-fidelity computer experiments with increasing accuracy levels and a nonstationary Gaussian process model. We propose an optimization scheme that sequentially adds new computer runs by following two criteria. The first criterion, called EQI, scores candidate inputs with given level of accuracy, and the second criterion, called EQIE, scores candidate combinations of inputs and accuracy. From simulation results and a real example using finite element analysis, our method outperforms the expected improvement (EI) criterion that works for single-accuracy experiments. Supplementary materials for this article are available online.

• Design of experiment
• Expected improvement criterion
• Gaussian process model
• Kriging
• Multi-fidelity experiment

ACKNOWLEDGMENTS

The authors are grateful to the referees, associate editor, Yuanzhen He, Shifeng Xiong, V. Roshan Joseph, and Simon Mak for their valuable comments. Wu’s work is supported by NSF DMS-1308424 and DOE DE-SC0010548. Tuo’s work is also supported by the National Center for Mathematics and Interdisciplinary Sciences, CAS and NSFC 11271355. He’s work is also supported by NSFC 11501550.