Learning Interaction Dynamics from Particle Trajectories and Density Evolution

Abstract

We consider the problem of understanding the coordinated movements of biological or artificial swarms. In this regard, we propose a learning scheme to estimate the coordination laws of the interacting agents from observations of the swarm's density over time. We describe the dynamics of the swarm based on pairwise interactions according to a Cucker-Smale flocking model, and express the swarm's density evolution as the solution to a system of mean-field hydrodynamic equations. We propose a new family of parametric functions to model the pairwise interactions, which allows for the meanfield macroscopic system of integro-differential equations to be efficiently solved as an augmented system of PDEs. Finally, we incorporate the augmented system in an iterative optimization scheme to learn the dynamics of the interacting agents from observations of the swarm's density evolution over time. The results of this work can offer an alternative approach to study how animal flocks coordinate, create new control schemes for large networked systems, and serve as a central part of defense mechanisms against adversarial drone attacks.

Semi-linear Poisson-mediated Flocking in a Cucker-Smale Model

“…which is the Green's function corresponding to L x in an infinite domain. We note that the parameters (k, λ , L) generate a family of interaction functions (see also (Mavridis et al, 2020)) that can simulate widely used interaction functions as the one found in the original Cucker-Smale model (Cucker and Smale, 2007):…”

“…In the BVP of the augmented system of PDEs (21) with the initial and boundary conditions (26), we select the linear differential operator (see also (Mavridis et al, 2020)): (66)…”