Trajectory Inference

Trajectory inference aims to recover how people, vehicles, robots, or biological populations move and change over time when observations are sparse, incomplete, or unpaired. For population dynamics, common approaches include optimal transport, Schrödinger bridges, flow matching, and neural differential equations; geometric and lineage priors, along with second-order acceleration models, can constrain the inferred paths. For individual motion, researchers combine video, GPS, maps, and sensor data to reconstruct or predict trajectories, with applications in developmental biology, mobility, navigation, and robotics. A central challenge is that many dynamics can fit the observed snapshots, so methods must balance smoothness and physical or biological plausibility with uncertainty, branching, and reliable evaluation when intermediate states are unseen.