发表机构
KTH Royal Institute of Technology（瑞典皇家理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出物理信息神经细胞自动机（PI-NCA），通过保证车辆守恒的架构学习交通流动态，并在随机扩展中保持约束，实验表明其优于标准NCA。
AI 中文摘要
交通流建模对于理解和预测道路网络上车辆的集体动态至关重要。细胞自动机通过局部交互规则提供了一种简单、可解释且强大的框架来表示这些动态，同时保留再现复杂宏观交通现象的能力。然而，在保持物理上有意义的约束的同时从数据中学习局部转换规则仍然具有挑战性，特别是对于随机模型。在这项工作中，我们提出了一种物理信息神经细胞自动机（PI-NCA）用于数据驱动的交通流建模。在标准神经细胞自动机（NCA）的基础上，我们设计了一种与道路拓扑物理一致并保证车辆总数守恒的神经架构，从而将学习到的转换规则约束为物理上允许的动态。我们通过参数化概率转换规则同时保持相同的物理信息约束，进一步将该框架扩展到随机动态。我们在由成熟的Nagel-Schreckenberg和Kerner-Klenov-Wolf细胞自动机生成的多个交通场景上评估了所提出的模型。结果表明，PI-NCA成功学习了两种交通模型的动态，并且始终优于标准NCA，而随机扩展在不损害所施加的物理约束的情况下捕获了概率转换规则。
英文摘要
Traffic flow modeling is essential for understanding and predicting the collective dynamics of vehicles on road networks. Cellular automata provide a simple, interpretable yet powerful framework for representing these dynamics via local interaction rules, while retaining the ability to reproduce complex macroscopic traffic phenomena. However, learning local transition rules from data while preserving physically meaningful constraints remains challenging, particularly for stochastic models. In this work, we propose a physics-informed neural cellular automaton (PI-NCA) for data-driven traffic flow modeling. Building on the standard neural cellular automaton (NCA), we design a neural architecture that is physically consistent with the road topology and guarantees conservation of the total number of vehicles, thereby constraining the learned transition rules to physically admissible dynamics. We further extend this framework to stochastic dynamics by parameterizing probabilistic transition rules while preserving the same physics-informed constraints. We evaluate the proposed models on multiple traffic scenarios generated by the well-established Nagel-Schreckenberg and Kerner-Klenov-Wolf cellular automata. The results demonstrate that the PI-NCA successfully learns the dynamics of both traffic models and consistently outperforms a standard NCA, while the stochastic extension captures probabilistic transition rules without compromising the imposed physical constraints.
Comments45 pages, 16 figures
