Learning accurate closures of a kinetic theory of an active fluid.

Recent advances in experimental control of active matter have inspired many theoretical efforts for identifying relevant control inputs to steer non-equilibrium dynamics. Large classes of active matter systems of interest can be modeled with kinetic theories derived from first principles, however the high-dimensionality of the kinetic model poses a huge challenge to simulate. Reduced-order representation based on low-order moments of the kinetic model serve as an efficient means to simulate and control active fluids, but rely on closure assumptions to approximate unresolved higher-order moments. Still, the accuracy and differentiability of the closures determine the precision with which active fluids can be controlled. Here, we present a learning framework that relies on invariant representation of tensor-valued isotropic functions to learn the closure models directly from kinetic simulations. Using a combination of sparse and nonlinear regression techniques we learn a differentiable nonlinear map between the invariants of participating tensors and coefficients of the corresponding independent tensors. The learned expressions demonstrate excellent approximation power in comparison with commonly used closure models and approximate well beyond the parameter regime in which they were inferred.