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Living systems display complex behaviors driven by physical forces as well as decision-making. Hydrodynamic theories hold promise for simplified universal descriptions of socially generated collective behaviors. However, the construction of such theories is often divorced from the data they should describe. Here, we develop and apply a data-driven pipeline that links micromotives to macrobehavior by augmenting hydrodynamics with individual preferences that guide motion. We illustrate this pipeline on a case study of residential dynamics in the United States, for which census and sociological data are available. Guided by Census data, sociological surveys, and neural network analysis, we systematically assess standard hydrodynamic assumptions to construct a sociohydrodynamic model. Solving our minimal hydrodynamic model, calibrated using statistical inference, qualitatively captures key features of residential dynamics at the level of individual US counties. We highlight that a social memory, akin to hysteresis in magnets, emerges in the segregation–integration transition even with memory-less agents. While residential segregation is a multifactorial phenomenon, this physics analogy suggests a simple mechanistic explanation for the phenomenon of neighborhood tipping, whereby a small change in a neighborhood’s population leads to a rapid demographic shift. Beyond residential segregation, our work paves the way for systematic investigations of decision-guided motility in real space, from micro-organisms to humans, as well as fitness-mediated motion in more abstract spaces.
PNAS
By: Daniel S. Seara , Jonathan Colen, Michel Fruchart, Yael Avni, David G. Martin and Vincenzo Vitelli.
Edited by Jean-Philippe Bouchaud, Academie des Sciences, Paris, France; received April 14, 2025; accepted July 20, 2025 by Editorial Board Member Paul Chaikin
DOI: https://doi.org/10.1073/pnas.2508692122