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. 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.

Bridging scales in a multiscale pattern-forming system

“…( 6) to obtain a closed set of equations for the redistribution of mass between slices. Such "physics-informed neural networks" have received significant attention in recent years [44,45,46]. Mass conservation is an important and ubiquitous physical constraint that might help to further develop physics-informed machine learning approaches in future work.…”

Learning Mean-Field Equations from Particle Data Using WSINDy

“…In other fields this is described as coarse-graining. A related line of study is inference of 2nd-order particle systems, as explored in [48], which often lead to an infinite hierachy of mean-field equations. Our weak-form approach may provide a principled method for truncated and closing such hierarchies using particle data.…”

“…There are two works that are most closely related to the current work. In [48], the authors learn local hydrodynamic equations from active matter particle systems using the SINDy algorithm in the strong-form PDE setting. In contrast to [48], our approach learns nonlocal equations using the weak-form, however similarly to [48] we perform model selection and inference of parameters using sparse regression at the continuum level.…”

“…In [48], the authors learn local hydrodynamic equations from active matter particle systems using the SINDy algorithm in the strong-form PDE setting. In contrast to [48], our approach learns nonlocal equations using the weak-form, however similarly to [48] we perform model selection and inference of parameters using sparse regression at the continuum level. The weak form provides an advantage because no smoothness is required on the particle density (for requisite smoothness the authors of [48] use a Gaussian kernel, which is more expensive to compute than simple particle binning as done here).…”

“…In contrast to [48], our approach learns nonlocal equations using the weak-form, however similarly to [48] we perform model selection and inference of parameters using sparse regression at the continuum level. The weak form provides an advantage because no smoothness is required on the particle density (for requisite smoothness the authors of [48] use a Gaussian kernel, which is more expensive to compute than simple particle binning as done here). In [31], the authors apply the maximum likelihood approach in the continuum setting on the underlying nonlocal Fokker-Planck equation and learn directly the nonlocal PDE using strong-form discretizations of the dynamics.…”