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We study statistical calibration, i.e., adjusting features of a computational model that are not observable or controllable in its associated physical system. We focus on functional calibration, which arises in many manufacturing processes where the unobservable features, called calibration variables, are a function of the input variables. A major challenge in many applications is that computational models are expensive and can only be evaluated a limited number of times. Furthermore, without making strong assumptions, the calibration variables are not identifiable. We propose Bayesian Non-isometric Matching Calibration (BNMC) that allows calibration of expensive computational models with only a limited number of samples taken from a computational model and its associated physical system. BNMC replaces the computational model with a dynamic Gaussian process whose parameters are trained in the calibration procedure. To resolve the identifiability issue, we present the calibration problem from a geometric perspective of non-isometric curve to surface matching, which enables us to take advantage of combinatorial optimization techniques to extract necessary information for constructing prior distributions. Our numerical experiments demonstrate that in terms of prediction accuracy BNMC outperforms, or is comparable to, other existing calibration frameworks. [ABSTRACT FROM AUTHOR]

A method for constructing test functions for global optimization which utilizes continuous formulations of combinatorial optimization problems is suggested. In particular, global optimization formulations for the maximum independent set, maximum clique, and MAX CUT problems on arbitrary graphs are considered, and proofs for some of them are given. A number of sample test functions based on these formulations are proposed. [ABSTRACT FROM AUTHOR]