  Dynamic Mode Decomposition (DMD) is a powerful data-driven method used to
extract spatio-temporal coherent structures that dictate a given dynamical
system. The method consists of stacking collected temporal snapshots into a
matrix and mapping the nonlinear dynamics using a linear operator. The standard
procedure considers that snapshots possess the same dimensionality for all the
observable data. However, this often does not occur in numerical simulations
with adaptive mesh refinement/coarsening schemes (AMR/C). This paper proposes a
strategy to enable DMD to extract features from observations with different
mesh topologies and dimensions, such as those found in AMR/C simulations. For
this purpose, the adaptive snapshots are projected onto the same reference
function space, enabling the use of snapshot-based methods such as DMD. The
present strategy is applied to challenging AMR/C simulations: a continuous
diffusion-reaction epidemiological model for COVID-19, a density-driven gravity
current simulation, and a bubble rising problem. We also evaluate the DMD
efficiency to reconstruct the dynamics and some relevant quantities of
interest. In particular, for the SEIRD model and the bubble rising problem, we
evaluate DMD's ability to extrapolate in time (short-time future estimates).
