SwarmDMD: A Data-driven Method for Swarm Modeling and Analysis

Biological and engineering swarms often exhibit fluid-like behaviors that are challenging to model due to the high-dimensional dynamics, despite the emergence of low-dimensional patterns. Most existing swarm modelling approaches are based on first principles and result in swarm-specific parameterizations that do not generalize to a broad range of applications. In this work, we adapt the dynamic mode decomposition (DMD) from fluid mechanics to (1) learn approximate local interactions of homogeneous swarms through observation data and (2) generate similar swarming behavior using the learned model. The proposed swarmDMD algorithm is developed and tested on a canonical swarm model, where we show that (1) swarmDMD can faithfully reconstruct the swarm dynamics; and (2) swarmDMD allows for the prediction of nonlinear swarm dynamics from different initial conditions. We believe swarmDMD approach will be useful for studying multi-agent systems found in biology, physics, and engineering, and may provide additional insights into the understanding and control in the collective dynamics of vortices in multiscale turbulence.