Modeling active fluids via physically constrained machine learning

Active matter is abundant on Earth, especially in living systems, with examples ranging from~cell-division to bacterial suspensions.~We investigate a particular example of active matter -- a~fluid driven by chemically-driven molecular motors acting on a suspension of microtubules.~~Its dynamics should be described by a model including a pair of coupled partial differential equations:~one governing the fluid flow and another governing the orientation of microtubules.~These equations must capture all relevant forces and torques acting on the two components, both described by tensor fields.~Deriving these equations from first principles is difficult, as interactions occur over many length and time scales and not all the relevant physical processes are understood.~A data-driven model discovery offers a promising alternative.~We use~a hybrid approach which combines general physical constraints such as locality, causality, and symmetries to construct a library of candidate models with~symbolic regression to narrow it down. We show that this approach allows a parsimonious model of the system to be derived from experimental recordings.