  This study is devoted to the construction of a multifidelity Monte Carlo
(MFMC) method for the uncertainty quantification of a nonlocal,
non-mass-conserving Cahn-Hilliard model for phase transitions with an obstacle
potential. We are interested in the estimation of the expected value of an
output of interest (OoI) that depends on the solution of the nonlocal
Cahn-Hilliard model. As opposed to its local counterpart, the nonlocal model
captures sharp interfaces without the need for significant mesh refinement.
However, the computational cost of the nonlocal Cahn-Hilliard model is higher
than that of its local counterpart with similar mesh refinement, inhibiting its
use for outer-loop applications such as uncertainty quantification. The MFMC
method augments the desired high-fidelity, high-cost OoI with a set of
lower-fidelity, lower-cost OoIs to alleviate the computational burden
associated with nonlocality. Most of the computational budget is allocated to
sampling the cheap surrogate models to achieve speedup, whereas the
high-fidelity model is sparsely sampled to maintain accuracy. For the
non-mass-conserving nonlocal Cahn-Hilliard model, the use of the MFMC method
results in, for a given computational budget, about one-order-of-magnitude
reduction in the mean-squared error of the expected value of the OoI relative
to that of the Monte Carlo method.
