Learning active nematohydrodynamics with SINDy-PI

Active nematic liquid crystals exhibit a wide range of phenomena that cannot be observed in equilibrium systems. However, due to their complexity, lack of scale-separation and nonequilibrium dynamics, developing accurate, quantitative theoretical models for active materials by first principles approaches has been challenging. Further, it has generally not been possible to determine how the phenomenological parameters of such theories depend on the system parameters that control microscopic dynamics. As an alternative approach to obtain such models, we use Sparse Identification of Nonlinear Dynamics (the parallel implicit form, SINDy-PI), which is a regression technique that takes raw experimental or computational data as an input and returns a parsimonious partial differential equation.

In this talk, I will describe the application of SINDy-PI to identify a hydrodynamic theory for dry active nematics, meaning that long-range hydrodynamic interactions are negligible, such as in cell sheets or dense active nematics on a frictional substrate. Dry active nematics have received less theoretical study than the wet case and the appropriate theoretical model remains unclear. Our data was produced by particle-based simulations of dry active nematics over a wide range of activity and nematic stiffness. The collective dynamics vary widely over this range, from a highly uniform nematic with few defects to highly chaotic dynamics with nematic defects and large density fluctuations. By systematically applying SINDy-PI to this complete set of data, we identify a model for dry active nematics. Further, we learn how the hydrodynamic coefficients, such as the elastic moduli and the alignment free energy, scale with the microscopic parameters, such as the activity and nematic stiffness. Our results show that data-driven model discovery approaches such as SINDy-PI are powerful tools to determine quantitative models for a variety of soft matter systems, and to relate microscopic parameters to macroscale emergent behaviors.