  We use video footage of a water tunnel experiment to construct a
two-dimensional reduced-order model of the flapping dynamics of an inverted
flag in uniform flow. The model is obtained as the reduced dynamics on an
attracting spectral submanifold (SSM) that emanates from the two slowest modes
of the unstable fixed point of the flag. Beyond an unstable fixed point and a
limit cycle expected from observations, our SSM-reduced model also confirms the
existence of two unstable fixed points for the flag, which were found by
previous studies. Importantly, the model correctly reconstructs the dynamics
from a small number of general trajectories and no further information on the
system. In the chaotic flapping regime, we construct a 4D SSM-reduced model
that captures the system's chaotic attractor.
