  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 (GP) 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.
