Learning hydrodynamic equations for active matter from particle simulations and experiments.

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. The inference framework makes it possible to measure hydrodynamic parameters directly and simultaneously from video data.