Discovering mesoscopic descriptions of collective movement with neural stochastic modelling

Abstract: Collective motion is an ubiquitous phenomenon in nature, inspiring engineers, physicists and mathematicians to develop mathematical models and bio-inspired designs. Collective motion at small to medium group sizes ($\sim$10-1000 individuals, also called the `mesoscale'), can show nontrivial features due to stochasticity. Therefore, characterizing both the deterministic and stochastic aspects of the dynamics is crucial in the study of mesoscale collective phenomena. Here, we use a physics-inspired, neural-network based approach to characterize the stochastic group dynamics of interacting individuals, through a stochastic differential equation (SDE) that governs the collective dynamics of the group. We apply this technique on both synthetic and real-world datasets, and identify the deterministic and stochastic aspects of the dynamics using drift and diffusion fields, enabling us to make novel inferences about the nature of order in these systems.