Recovering Population Dynamics from a Single Point Cloud Snapshot

Discovering population dynamics from point cloud data has experienced increased popularity in various applications, including GPS behavior prediction, multi-target tracking, and single cell analysis. Existing methods require data in multiple time periods. However, to address privacy concerns and observational restrictions, our method estimates trajectories solely from a single snapshot without time series information or features other than coordinates. We propose a model that recovers vector fields by solving an optimal transport problem and introducing the smoothness of point movements as regularization terms. Experiments with point cloud data generated from typical vector fields show that our method can accurately recover the original vector fields and predict the trajectories at arbitrary coordinates from just one point cloud snapshot.