Data-driven discovery of active nematic hydrodynamics

TL;DR

This paper introduces a data-driven method to automatically identify and optimize continuum models for active nematic hydrodynamics directly from experimental and simulation data, revealing key dynamics and parameters.

Contribution

It adapts a sparse fitting approach to derive continuum PDE models for active nematics from spatio-temporal data, including experimental microtubule-based systems.

Findings

Orientation dynamics are mainly governed by flow coupling.

Flow equations fitted to data estimate the activity parameter.

Negligible role of free-energy gradients in orientation dynamics.

Abstract

Two-dimensional active nematics are often modeled using phenomenological continuum theories that describe the dynamics of the nematic director and fluid velocity through partial differential equations (PDEs). While these models provide a statistically accurate description of the experiments, the identification of the relevant terms in the PDEs and their parameters is usually indirect. Here, we adapt a recently developed method to automatically identify optimal continuum models for active nematics directly from the spatio-temporal director and velocity data, via sparse fitting of the coarse-grained fields onto generic low order PDEs. We test the method extensively on computational models, and then apply it to data from experiments on microtubule-based active nematics. Thereby, we identify the optimal models for microtubule-based active nematics, along with the relevant phenomenological parameters. We find that the dynamics of the orientation field are largely governed by its coupling to the underlying flow, with free-energy gradients playing a negligible role. Furthermore, by fitting the flow equation to experimental data, we estimate a key parameter quantifying the `activity' of the nematic.