学习环形道路中的“前瞻”非局部交通动力学
Learning "Look-Ahead" Nonlocal Traffic Dynamics in a Ring Road
- The Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））
- The Hong Kong University of Science and Technology（香港科技大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文利用环形道路轨迹数据和物理信息神经网络学习非局部 LWR 模型的基本图与前瞻核，证实“前瞻”效应存在，并提升三类交通场景的波传播预测精度。
AI中文摘要：
宏观交通流模型被广泛用于交通控制与管理。为纳入驾驶员的预期行为，并消除经典 Lighthill-Whitham-Richards（LWR）交通模型中固有的不切实际的速度不连续性，具有“前瞻”动力学的非局部偏微分方程（PDE）模型已被提出，这类模型假设速度是下游加权交通密度的函数。然而，在两个重要问题上仍缺乏数据验证：非局部动力学是否存在，以及“前瞻”窗口的长度和权重如何影响交通密度的时空传播。本文采用环形道路实验中的交通轨迹数据，设计了一种物理信息神经网络，用于学习最符合数据的基本图和前瞻核，并通过最小化结合数据偏差与非局部模型偏差的损失函数，重构了一个数据增强的非局部 LWR 模型。结果表明，学习得到的非局部 LWR 在三种不同场景下对交通波传播给出了更准确的预测：停走振荡、拥堵和自由流交通。我们首次利用真实交通数据证明了“前瞻”效应的存在。研究发现，最优非局部核的长度约为 35 至 50 米，而 5 米以内的核权重占据了非局部效应的大部分。我们的结果还强调了在机器学习模型中选择先验物理规律的重要性。
英文摘要：
The macroscopic traffic flow model is widely used for traffic control and management. To incorporate drivers' anticipative behaviors and to remove impractical speed discontinuity inherent in the classic Lighthill-Whitham-Richards (LWR) traffic model, nonlocal partial differential equation (PDE) models with ``look-ahead" dynamics have been proposed, which assume that the speed is a function of weighted downstream traffic density. However, it lacks data validation on two important questions: whether there exist nonlocal dynamics, and how the length and weight of the ``look-ahead" window affect the spatial temporal propagation of traffic densities. In this paper, we adopt traffic trajectory data from a ring-road experiment and design a physics-informed neural network to learn the fundamental diagram and look-ahead kernel that best fit the data, and reinvent a data-enhanced nonlocal LWR model via minimizing the loss function combining the data discrepancy and the nonlocal model discrepancy. Results show that the learned nonlocal LWR yields a more accurate prediction of traffic wave propagation in three different scenarios: stop-and-go oscillations, congested, and free traffic. We first demonstrate the existence of ``look-ahead" effect with real traffic data. The optimal nonlocal kernel is found out to take a length of around 35 to 50 meters, and the kernel weight within 5 meters accounts for the majority of the nonlocal effect. Our results also underscore the importance of choosing a priori physics in machine learning models.
