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Estimation of spatial and time scales of collective behaviors of active matter through learning hydrodynamic equations from particle dynamics

Bappaditya Roy1,2,* and Natsuhiko Yoshinaga1,2,3,†

  • 1Department of Complex and Intelligent Systems, Future University Hakodate, Kamedanakano-cho 116-2, Hakodate 041-8655, Japan
  • 2Mathematics for Advanced Materials-OIL (MathAM-OIL), AIST, Katahira 2-1-1, Sendai 980-8577, Japan
  • 3WPI-Advanced Institute for Materials Research (WPI-AIMR), Tohoku University, Katahira 2-1-1, Sendai 980-8577, Japan

  • *Contact author: physicsbapai@gmail.com
  • †Contact author: yoshinaga@fun.ac.jp
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Phys. Rev. E 113, 025406 – Published 4 February, 2026

DOI: https://doi.org/10.1103/h7n7-4vsq

Abstract

We present a data-driven framework for learning hydrodynamic equations from particle-based simulations of active matter. Our method leverages coarse graining in both space and time to bridge microscopic particle dynamics with macroscopic continuum models. By employing spectral representations and sparse regression, we efficiently estimate partial differential equations that capture collective behaviors such as flocking and phase separation. This approach, validated using hydrodynamic descriptions of the Vicsek model and active Brownian particles, demonstrates the potential of data-driven strategies to uncover the universal features of collective dynamics in active matter systems.

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Phys. Rev. E 113, 025406– Published 4 February, 2026
  • Received 6 November 2024
  • Accepted 14 January 2026
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