Learning hydrodynamic equations for active matter from particle simulations and experiments

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, especially when continuum models are not known a priori or analytic coarse graining fails, as often is the case for nondilute and heterogeneous systems. 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 a range of applications, from a chiral active particle model mimicking nonidentical swimming cells to recent microroller experiments and schooling fish. In all these cases, our scheme learns hydrodynamic equations that reproduce 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.

Learning mean-field equations from particle data using WSINDy

“…To the best of our knowledge, we present here the first weak-form sparse regression approach for inference of interacting particle systems, however we now review several related approaches that have recently been developed. In [ 32 ], the authors learn local hydrodynamic equations from active matter particle systems using the SINDy algorithm in the strong-form PDE setting. In contrast to [ 32 ], our approach learns nonlocal equations using the weak-form, however similarly to [ 32 ] we perform model selection and inference of parameters using sparse regression at the continuum level.…”

Learning dynamical models of single and collective cell migration: a review

“…Beyond these models of cells as discrete entities, active polar or nematic hydrodynamic models provide important conceptual frameworks to describe cellular assemblies. To learn such models from observed data, inference and machine learning approaches for active nematics have been developed and applied in the context of in vitro microtubule assays [318,319], and active polar particle experiments [320]. These approaches use the observed velocity fields or cell tracking data to uncover the hydrodynamic equations governing these active matter systems, which could provide a promising approach for inference from collective cellular systems.…”

Pushing coarse-grained models beyond the continuum limit using equation learning

“…Mathematical models of population dynamics are often constructed by considering both discrete and continuous descriptions, allowing for both microscopic and macroscopic details to be considered [1]. This approach has been applied to several kinds of discrete models, including cellular Potts models [2][3][4][5], exclusion processes [6][7][8][9], mechanical models of epithelial tissues [10][11][12][13][14][15][16][17], hydrodynamics [18,19] and a variety of other types of individual-based models [1,[20][21][22][23][24][25][26][27]. Continuum models are useful for describing collective behaviour, especially because the computational requirement of discrete models increases with the size of the population, and this can become computationally prohibitive for large populations, which is particularly problematic for parameter inference [28].…”