  Calibration or parameter identification is used with computational mechanics
models related to observed data of the modeled process to find model parameters
such that good similarity between model prediction and observation is achieved.
We present a Bayesian calibration approach for surface coupled problems in
computational mechanics based on measured deformation of an interface when no
displacement data of material points is available. The interpretation of such a
calibration problem as a statistical inference problem, in contrast to
deterministic model calibration, is computationally more robust and allows the
analyst to find a posterior distribution over possible solutions rather than a
single point estimate. The proposed framework also enables the consideration of
unavoidable uncertainties that are present in every experiment and are expected
to play an important role in the model calibration process. To mitigate the
computational costs of expensive forward model evaluations, we propose to learn
the log-likelihood function from a controllable amount of parallel simulation
runs using Gaussian process regression. We introduce and specifically study the
effect of three different discrepancy measures for deformed interfaces between
reference data and simulation. We show that a statistically based discrepancy
measure results in the most expressive posterior distribution. We further apply
the approach to numerical examples in higher model parameter dimensions and
interpret the resulting posterior under uncertainty. In the examples, we
investigate coupled multi-physics models of fluid-structure interaction effects
in biofilms and find that the model parameters affect the results in a coupled
manner.
