Learning hydrodynamic equations for active matter from particle simulations and experiments

TL;DR

This paper introduces a data-driven framework that uses spectral basis and sparse regression to learn hydrodynamic equations for active matter directly from microscopic simulations and experiments, capturing collective behaviors accurately.

Contribution

It presents a novel method for deriving macroscopic hydrodynamic PDEs from particle and experimental data, incorporating physical symmetries and enabling parameter measurement from videos.

Findings

Successfully learned hydrodynamic equations for active matter models.

Reproduced collective dynamics quantitatively in simulations and experiments.

Enabled measurement of multiple hydrodynamic parameters from video data.

Abstract

Recent advances in high-resolution imaging techniques and particle-based simulation methods have enabled the precise microscopic characterization of collective dynamics in various biological and engineered active matter systems. In parallel, data-driven algorithms for learning interpretable continuum models have shown promising potential for the recovery of underlying partial differential equations (PDEs) from continuum simulation data. By contrast, learning macroscopic hydrodynamic equations for active matter directly from experiments or particle simulations remains a major challenge. Here, we present a framework that leverages spectral basis representations and sparse regression algorithms to discover PDE models from microscopic simulation and experimental data, while incorporating the relevant physical symmetries. We illustrate the practical potential through applications to a chiral active particle model mimicking swimming cells and to recent microroller experiments. In both cases, our scheme learns hydrodynamic equations that reproduce quantitatively the self-organized collective dynamics observed in the simulations and experiments. This inference framework makes it possible to measure a large number of hydrodynamic parameters in parallel and directly from video data.