A Reproducing Kernel Hilbert Space Approach to Functional Calibration of Computer Models

TL;DR

This paper introduces a nonparametric RKHS-based method for functional calibration of computer models, allowing calibration parameters to vary with control variables, improving prediction accuracy and uncertainty quantification.

Contribution

It develops a frequentist RKHS approach for functional calibration, providing theoretical guarantees and demonstrating superior performance over existing methods.

Findings

Outperforms existing parametric and Bayesian calibration methods in predictions.

Provides theoretical guarantees for prediction and calibration function estimation.

Shows robustness in real and synthetic data applications.

Abstract

This paper develops a frequentist solution to the functional calibration problem, where the value of a calibration parameter in a computer model is allowed to vary with the value of control variables in the physical system. The need of functional calibration is motivated by engineering applications where using a constant calibration parameter results in a significant mismatch between outputs from the computer model and the physical experiment. Reproducing kernel Hilbert spaces (RKHS) are used to model the optimal calibration function, defined as the functional relationship between the calibration parameter and control variables that gives the best prediction. This optimal calibration function is estimated through penalized least squares with an RKHS-norm penalty and using physical data. An uncertainty quantification procedure is also developed for such estimates. Theoretical guarantees of the proposed method are provided in terms of prediction consistency and consistency of estimating the optimal calibration function. The proposed method is tested using both real and synthetic data and exhibits more robust performance in prediction and uncertainty quantification than the existing parametric functional calibration method and a state-of-art Bayesian method.