  Dynamic mode decomposition (DMD) has recently become a popular tool for the
non-intrusive analysis of dynamical systems. Exploiting Proper Orthogonal
Decomposition (POD) as a dimensionality reduction technique, DMD is able to
approximate a dynamical system as a sum of spatial basis evolving linearly in
time, thus enabling a better understanding of the physical phenomena and
forecasting of future time instants. In this work we propose an extension of
DMD to parameterized dynamical systems, focusing on the future forecasting of
the output of interest in a parametric context. Initially all the snapshots --
for different parameters and different time instants -- are projected to a
reduced space; then DMD, or one of its variants, is employed to approximate
reduced snapshots for future time instants. Exploiting the low dimension of the
reduced space the predicted reduced snapshots are then combined using
regression techniques, thus enabling the possibility to approximate any
untested parametric configuration in future. This paper depicts in detail the
algorithmic core of this method; we also present and discuss three test cases
for our algorithm: a simple dynamical system with a linear parameter
dependency, a heat problem with nonlinear parameter dependency and a fluid
dynamics problem with nonlinear parameter dependency.
