Learning anisotropic interaction rules from individual trajectories in a heterogeneous cellular population

Interacting particle system (IPS) models have proven to be highly successful for describing the spatial movement of organisms. However, it is challenging infer interaction rules directly from data. In field equation discovery, weak-form sparse identification nonlinear dynamics (WSINDy) methodology has been shown computationally efficient identifying governing equations complex systems noisy Motivated by success IPS describe organisms, we develop WSINDy second-order learn communities cells. Our approach learns directional each individual cell that in aggregate govern a heterogeneous population migrating To sort according active classes present its model, also novel ad hoc classification scheme (which accounts fact some cells do not enough evidence accurately model). Aggregated are then constructed hierarchically simultaneously identify different species and determine best-fit species. We demonstrate efficiency proficiency method on several test scenarios, motivated common migration experiments.