Data-driven continuum modeling of active nematics via sparse identification of nonlinear dynamics

Data-driven modeling methods have recently shown great potential in determining accurate continuum models for complex systems directly from experimental measurements. One such complex system is the active nematic liquid crystal system consisting of microtubule-motor protein assemblies immersed in a fluid. This system exhibits rich non-equilibrium behavior, including spontaneous creation and annihilation of topological defects. Although several models have been proposed for the system, the governing equations remain under debate.

We here present a model extracted directly from experimental image data via the "sparse identification of nonlinear dynamics" (SINDy) data-driven modeling technique. This model discovery process includes extracting appropriate data for a continuum model from experimental data, constructing a plausible library of model terms, and solving a sparse regression problem. A number of issues arise in this process, including strong correlations between library terms and instabilities in the discovered models. We present numerical simulations and the results of some modern statistical and classical pen-and-paper analyses which combine to clarify the discovery results. We then discuss the physical implications of the learned model, and compare the model with those proposed previously.