Agent-Guided Hypothesis-Driven Symbolic Regression for Car-Following Dynamics Discovery

Traffic congestion remains a persistent problem for modern cities, and the growing presence of autonomous vehicles has made understanding driving behaviors more essential than ever. Car-following models are fundamental to analyzing these dynamics. Their formulas have traditionally been derived by professionals guided by physical intuition and data fitting, yielding models that are both interpretable and transferable. Discovering such a model from trajectory data follows the classic scientific loop: generating a hypothesis, collecting data, analyzing it, validating the hypothesis, and repeating. The steps from analysis, to validation, to regeneration are professionally driven but labor-intensive, often demanding many rounds of validating and revising the hypothesis. This paper asks whether these steps can be automated. We propose agent-guided hypothesis-driven symbolic regression (AHSR), a framework that couples a large language model (LLM) with a deep reinforcement-learning symbolic regression (DRL-SR) engine to discover car-following dynamics directly from vehicle trajectories. Informed by car-following literature and an initial skim of the trajectory data, the LLM proposes a hypothesis template that specifies the hypothesis structure, the candidate variables with their bounds, and the physical units. DRL-SR then explores expression candidates within this template, and the LLM revises the hypothesis in light of DRL-SR's findings and returns an updated template. This iteration repeats until a concise and explainable expression is found, ensuring that every explored expression is physically feasible, explainable, and accurate. Experiments show that AHSR is capable to recover classical and most widely-used car-following models on synthetic data with noise. These results suggest that AHSR can automate the discovery of explainable car-following models, reducing the manual effort of the traditional scientific loop while preserving physical interpretability.