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Data-Driven Stochastic Modeling of Schooling Fish: From Collective Dynamics to Individual Fluctuations

Collective motion in animal groups emerges from the interplay between individual variability and social coordination, yet connecting these scales quantitatively has remained a major challenge.Using high-resolution trajectories of schooling fish, we infer a data-driven stochastic framework that reproduces with remarkable accuracy the behavior of real fish schools. We decompose motion into two coupled components: the dynamics of the school's center of mass (or centroid), modeled as an active Brownian particle confined by the tank, and individual motions relative to that center, described by stochastic equations with data-inferred mean-field potentials and multiplicative noise. Simulations of these equations produce synthetic schools that quantitatively match real ones across multiple observables, including burst-and-coast dynamics, polarization, and spatial cohesion. This minimal, predictive framework bridges experiment and theory, showing that the collective dynamics of animal groups can be faithfully reconstructed from first principles directly from data.