  Functional data are ubiquitous in scientific modeling. For instance,
quantities of interest are modeled as functions of time, space, energy,
density, etc. Uncertainty quantification methods for computer models with
functional response have resulted in tools for emulation, sensitivity analysis,
and calibration that are widely used. However, many of these tools do not
perform well when the model's parameters control both the amplitude variation
of the functional output and its alignment (or phase variation). This paper
introduces a framework for Bayesian model calibration when the model responses
are misaligned functional data. The approach generates two types of data out of
the misaligned functional responses: one that isolates the amplitude variation
and one that isolates the phase variation. These two types of data are created
for the computer simulation data (both of which may be emulated) and the
experimental data. The calibration approach uses both types so that it seeks to
match both the amplitude and phase of the experimental data. The framework is
careful to respect constraints that arise especially when modeling phase
variation, but also in a way that it can be done with readily available
calibration software. We demonstrate the techniques on a simulated data example
and on two dynamic material science problems: a strength model calibration
using flyer plate experiments and an equation of state model calibration using
experiments performed on the Sandia National Laboratories' Z-machine.
