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This paper develops a frequentist solution to the functional calibrationproblem, where the value of a calibration parameter in a computer model isallowed to vary with the value of control variables in the physical system. Theneed of functional calibration is motivated by engineering applications whereusing a constant calibration parameter results in a significant mismatchbetween outputs from the computer model and the physical experiment.Reproducing kernel Hilbert spaces (RKHS) are used to model the optimalcalibration function, defined as the functional relationship between thecalibration parameter and control variables that gives the best prediction.This optimal calibration function is estimated through penalized least squareswith an RKHS-norm penalty and using physical data. An uncertaintyquantification procedure is also developed for such estimates. Theoreticalguarantees of the proposed method are provided in terms of predictionconsistency and consistency of estimating the optimal calibration function. Theproposed method is tested using both real and synthetic data and exhibits morerobust performance in prediction and uncertainty quantification than theexisting parametric functional calibration method and a state-of-art Bayesianmethod.

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