Car-following models (CFMs) are fundamental to traffic flow analysis and autonomous driving. Although calibrated physics-based and trained data-driven CFMs can replicate human driving behavior, their reliance on specific datasets limits generalization across diverse scenarios and reduces reliability in real-world deployment. In addition to behavioral fidelity, ensuring traffic stability is increasingly critical for the safe and efficient operation of autonomous vehicles (AVs), requiring CFMs that jointly address both objectives. However, existing models generally do not support a systematic integration of these goals. To bridge this gap, we propose a knowledge-informed deep learning (KIDL) paradigm that distills the generalization capabilities of pre-trained large language models (LLMs) into a lightweight and stability-aware neural architecture. LLMs are used to extract fundamental car-following knowledge beyond dataset-specific patterns, and this knowledge is transferred to a reliable, tractable, and computationally efficient model through knowledge distillation. KIDL also incorporates stability constraints directly into its training objective, ensuring that the resulting model not only emulates human-like behavior but also satisfies the local and string stability requirements essential for real-world AV deployment. We evaluate KIDL on the real-world NGSIM and HighD datasets, comparing its performance with representative physics-based, data-driven, and hybrid CFMs. Both empirical and theoretical results consistently demonstrate KIDL’s superior behavioral generalization and traffic flow stability, offering a robust and scalable solution for next-generation traffic systems.
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