Sparse calibration based on adaptive lasso penalty for computer models

Abstract

Computer model calibration is a method to identify the unknown parameters of computer models, which is attaining more and more attention now. Most of the existing articles develop the calibration procedure under the assumption that the sample size of the physical experiments is larger than the dimension of the calibration parameters, which would not be satisfied in practice. In this article, we propose a sparse estimator of the calibration parameters and its robust version based on adaptive lasso penalty with adapting to the sample size of the physical experiments and the dimension of the calibration parameters, and the proposed robust estimator can deal with the heavy-tailed error and outliers efficiently. Subsequently, we investigate the nonasymptotic properties of the proposed estimators and obtain an upper bound of ${\mathcal{l}}_2$ error of the proposed estimators by the concentration inequalities. We conduct some numerical simulations and an application to composite fuselage simulation, which verify that the proposed estimators enjoy nice performance.

Keywords:

• Computer experiments
• Heavy-tailed error
• Outliers
• Robustness
• Sparse estimator

Acknowledgments

We thank the editor-in-chief and two anonymous reviewers for their valuable comments, which led to significant improvements of the original version of this article.

Additional information

Funding

This work was supported by Science Challenge Project, under Grant No. TZ2018001.