Data-driven discovery of stochastic dynamical equations of collective motion

Nabeel, A and Jadhav, V and M, DR and Sire, C and Theraulaz, G and Escobedo, R and Iyer, SK and Guttal, V (2023) Data-driven discovery of stochastic dynamical equations of collective motion. In: Physical biology, 20 (5).

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Abstract

oarse-grained descriptions of collective motion of flocking systems are often derived for the macroscopic or the thermodynamic limit. However, the size of many real flocks falls within 'mesoscopic' scales (10 to 100 individuals), where stochasticity arising from the finite flock sizes is important. Previous studies on mesoscopic models have typically focused on non-spatial models. Developing mesoscopic scale equations, typically in the form of stochastic differential equations, can be challenging even for the simplest of the collective motion models that explicitly account for space. To address this gap, here, we take a novel data-driven equation learning approach to construct the stochastic mesoscopic descriptions of a simple, spatial, self-propelled particle (SPP) model of collective motion. In the spatial model, a focal individual can interact withkrandomly chosen neighbours within an interaction radius. We considerk = 1 (called stochastic pairwise interactions),k = 2 (stochastic ternary interactions), andkequalling all available neighbours within the interaction radius (equivalent to Vicsek-like local averaging). For the stochastic pairwise interaction model, the data-driven mesoscopic equations reveal that the collective order is driven by a multiplicative noise term (hence termed, noise-induced flocking). In contrast, for higher order interactions (k > 1), including Vicsek-like averaging interactions, models yield collective order driven by a combination of deterministic and stochastic forces. We find that the relation between the parameters of the mesoscopic equations describing the dynamics and the population size are sensitive to the density and to the interaction radius, exhibiting deviations from mean-field theoretical expectations. We provide semi-analytic arguments potentially explaining these observed deviations. In summary, our study emphasises the importance of mesoscopic descriptions of flocking systems and demonstrates the potential of the data-driven equation discovery methods for complex systems studies.

Item Type:	Journal Article
Publication:	Physical biology
Publisher:	NLM (Medline)
Additional Information:	The copyright for this article belongs to the NLM (Medline)
Keywords:	data-driven equation discovery; finite size effects; langevin dynamics; mesoscale modelling; noise-induced transitions; physics-informed machine learning; self organization
Department/Centre:	Division of Biological Sciences > Centre for Ecological Sciences Division of Mechanical Sciences > Chemical Engineering Others Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	01 Aug 2023 05:11
Last Modified:	01 Aug 2023 05:11
URI:	https://eprints.iisc.ac.in/id/eprint/82724

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