Learning collective motion dynamics from trajectory data with physics-regularized graph neural networks

Learning collective motion from trajectory data requires models that reproduce individual trajectories, remain stable under recursive deployment, and preserve macroscopic group organization. A persistent difficulty is that models trained on short-horizon transitions can accumulate errors in closed-loop rollout, distorting long-horizon collective behavior. We propose a Physics-Regularized Graph Neural Network (PR-GNN) that addresses this problem by incorporating physical structure at multiple levels. PR-GNN constructs focal-centered dynamic interaction graphs, estimates neighbor importance through a learned attention mechanism, and organizes the predicted acceleration around three physically motivated components derived from motion features: self-motion, velocity alignment, and spatial interaction. A multi-step rollout training objective, augmented by collective behavior regularization, shifts learning toward long-horizon fidelity rather than short-horizon accuracy. On six self-propelled-particle datasets, PR-GNN achieves lower closed-loop position errors than all five evaluated baseline methods while preserving key macroscopic indicators, including polarization, rotational organization, mean speed, and spatial spread. The learned attention distributions and response-channel signatures provide post-hoc evidence of behaviorally relevant neighbor relations and dominant physical response modes.