Abstract

In the study of collective behaviour, a central question is to understand how group properties emerge from simple individual interactions at the level of the individuals. Usually, one defines an order parameter that quantifies some property of the group, and is interested in studying the dynamics of this order parameter. Often, the group-level dynamical equations are analytically derived from first principles, based on assumptions on the local interactions. However, there are two main difficulties to this approach. First, analytical derivations are often based on many simplifying assumptions on the individual interactions, as all but the simplest of models become analytically intractable. Second, when studying collective behaviour in the real world (e.g. collective animal behaviour), the group sizes are typically small, where the individual-level stochasticity can have observable effects on the order parameter. Indeed, in real world systems, the exact individual interactions are usually unknown, adding another layer of difficulty. We circumvent these difficulties with a novel data-driven approach to directly derive stochastic differential equations (SDEs) from observed time series data. By combining techniques from machine learning with physical understanding of the system (such as inherent symmetries), we are able to derive accurate SDE models from observed or simulated time series data. I will present some of our recent work on characterizing the mesoscale dynamics of both real-world and simulated fish schools. In real fish schooling experiments, we observe both unifying and differentiating aspects in the group dynamics of different species. The determinstic dynamics of the group differs across species, and can promote or destroy group-level order depending on species. On the other hand, the stochastic dynamics typically have a characteristic structure that promote order in small- to intermediate-sized groups. By connecting these observations to the mesoscale group dynamics of simulated fish schools, we make putative inferences about how the inter-individual interactions differ across different species.