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

TL;DR

This paper introduces a data-driven method that uses coarse-graining, spectral analysis, and sparse regression to learn hydrodynamic equations from particle simulations, capturing collective behaviors in active matter.

Contribution

It develops a novel framework combining spectral methods and sparse regression to derive PDEs from microscopic particle data for active matter systems.

Findings

Successfully applied to Vicsek model and Active Brownian particles

Effectively captures flocking and phase separation behaviors

Demonstrates potential for uncovering universal collective 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.