  We present a data-driven nonintrusive model order reduction method for
dynamical systems with moving boundaries. The proposed method draws on the
proper orthogonal decomposition, Gaussian process regression, and moving least
squares interpolation. It combines several attributes that are not
simultaneously satisfied in the existing model order reduction methods for
dynamical systems with moving boundaries. Specifically, the method requires
only snapshot data of state variables at discrete time instances and the
parameters that characterize the boundaries, but not further knowledge of the
full-order model and the underlying governing equations. The dynamical systems
can be generally nonlinear. The movements of boundaries are not limited to
prescribed or periodic motions but can be free motions. In addition, we
numerically investigate the ability of the reduced order model constructed by
the proposed method to forecast the full-order solutions for future times
beyond the range of snapshot data. The error analysis for the proposed reduced
order modeling and the criteria to determine the furthest forecast time are
also provided. Through numerical experiments, we assess the accuracy and
efficiency of the proposed method in several benchmark problems. The snapshot
data used to construct and validate the reduced order model are from
analytical/numerical solutions and experimental measurements.
