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.

翻译：集体运动是自然界中普遍存在的现象，启发工程师、物理学家和数学家开发数学模型和仿生设计。中小组群规模（约10-1000个体，也称为“介观尺度”）的集体运动，由于随机性可能表现出非平凡特征。因此，在介观集体现象研究中，刻画动力学中确定性和随机性方面至关重要。本文采用基于物理学启发的神经网络方法，通过控制群体集体运动的随机微分方程（SDE）来表征相互作用个体的随机群体动力学。我们将该技术应用于合成数据集和真实世界数据集，并利用漂移场和扩散场识别动力学中的确定性和随机性成分，从而对这些系统中的有序性本质做出新颖推断。