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

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 (PDEs) 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.

13 pages, 12 figures

References in corpus (9)

• Novel type of phase transition in a system of self-driven particles
• Motility-Induced Phase Separation
• Hydrodynamic equations for self-propelled particles: microscopic derivation and stability analysis
• Pattern formation of microtubules and motors: inelastic interaction of polar rods
• Learning hydrodynamic equations for active matter from particle simulations and experiments
• Dry Active Matter exhibits a self-organized 'Cross Sea' Phase
• Data-driven discovery of active nematic hydrodynamics
• Bayesian Modelling of Pattern Formation from One Snapshot of Pattern
• Inverse problems of inhomogeneous fracture toughness using phase-field models