  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.
