Iterative method for tuning complex simulation code

Abstract

Tuning a complex simulation code refers to the process of improving the agreement of a code calculation with respect to a set of experimental data by adjusting parameters implemented in the code. This process belongs to the class of inverse problems or model calibration. For this problem, the approximated nonlinear least squares (ANLS) method based on a Gaussian process (GP) metamodel has been employed by some researchers. A potential drawback of the ANLS method is that the metamodel is built only once and not updated thereafter. To address this difficulty, we propose an iterative algorithm in this study. In the proposed algorithm, the parameters of the simulation code and GP metamodel are alternatively re-estimated and updated by maximum likelihood estimation and the ANLS method. This algorithm uses both computer and experimental data repeatedly until convergence. A study using toy-models including inexact computer code with bias terms reveals that the proposed algorithm performs better than the ANLS method and the conditional-likelihood-based approach. Finally, an application to a nuclear fusion simulation code is illustrated.

Keywords:

• Best linear unbiased prediction
• Calibration
• Computer experiments
• Inexact computer model
• Kriging
• Numerical optimization

Correction Statement

This article has been corrected with minor changes. These changes do not impact the academic content of the article.

Acknowledgments

The authors would like to thank the reviewers and the associate editor for their helpful suggestions, which have greatly improved the presentation of this paper. This report follows some parts of an invited presentation by the third author at the GdR Mascot-Num annual conference at Ecole de Mines St-Etienne, France, in 2015. We would like to thank the organizers of this conference for the invitation and for their hospitality. We are also grateful to Professor Clifford Singer (Department of Nuclear Engineering, University of Illinois at Urbana-Champaign) for providing the tokamak data.

Additional information

Funding

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIP) (No. 2016R1A2B4014518). Seo’s work was funded by the Korea Meteorological Administration Research and Development Program “Enhancement of Convergence Technology of Analysis and Forecast on Severe Weather” under Grant 1365003081.