Swarm Modeling With Dynamic Mode Decomposition

Abstract

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 parameterisations that do not generalise 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 believe the proposed swarmDMD approach will be useful for studying multi-agent systems found in biology, physics, and engineering.

Keywords

• Swarms
• multi-agent systems
• reduced-order models
• dynamic mode decomposition
• control
• optimisation