Interpretable inference of collective models from trajectory data with two-stage rule learning

Inferring collective models from trajectory data is important for understanding coordinated behaviors in swarming systems, yet remains challenging because observed trajectories are jointly shaped by neighbor selection and response dynamics. Here we propose a Two-Stage Interpretable Rule Inference (TIRI) framework for recovering explicit collective models from trajectory data. In Stage I, template-based cooperative coevolution is used to infer the neighbor selection rule and determine the interaction inputs of each individual. In Stage II, the inferred neighbor selection rule is fixed and analytical response rules are discovered by automatically defined function-based strongly typed genetic programming. Experiments on six collective models show that TIRI infers effective neighbor selection rules and recovers response rules that preserve the main structural components of the original motion update equations. The inferred models further reproduce collective trajectories and macroscopic behavioral indicators, including group polarization and angular momentum, more faithfully than the template-constrained Stage I models. These results show that TIRI provides an interpretable data-driven framework for recovering rule-level collective models from trajectory observations.