  Modelling biological or engineering swarms is challenging due to the
inherently high dimension of the system, despite the often low-dimensional
emergent dynamics. Most existing swarm modelling approaches are based on first
principles and often result in swarm-specific parameterizations that do not
generalize to a broad range of applications. In this work, we apply a purely
data-driven method to (1) learn local interactions of homogeneous swarms
through observation data and to (2) generate similar swarming behaviour using
the learned model. In particular, a modified version of dynamic mode
decomposition with control, called swarmDMD, is developed and tested on the
canonical Vicsek swarm model. The goal is to use swarmDMD to learn inter-agent
interactions that give rise to the observed swarm behaviour. We show that
swarmDMD can faithfully reconstruct the swarm dynamics, and the model learned
by swarmDMD provides a short prediction window for data extrapolation with a
trade-off between prediction accuracy and prediction horizon. We also provide a
comprehensive analysis on the efficacy of different observation data types on
the modelling, where we find that inter-agent distance yields the most accurate
models. We believe the proposed swarmDMD approach will be useful for studying
multi-agent systems found in biology, physics, and engineering.
