We present a physics-informed deep learning (PIDL) approach to tackle the challenge of data sparsity and sensor noise in traffic state estimation (TSE). PIDL strengthens a deep learning (DL) neural network with the knowledge of traffic flow theory to accurately estimate traffic conditions. The ‘physics’—a priori information of the system—acts as a regularization agent during training. We illustrate the implementation of the proposed approach with two commonly used models representing traffic physics: Lighthill-Whitham-Richards (LWR) model and the cell transmission model (CTM). The LWR implementation is illustrated with Greenshields’ and inverse-lambda fundamental diagrams; whereas, CTM model implementation works with any fundamental diagram of choice. Two case studies validate the approach by reconstructing the velocity-field. Case study-I uses synthetic data generated to resemble the trajectory of connected and autonomous vehicles as captured by roadside units. Case study-II employs NGSIM data mimicking scant probe vehicle observations. We observe that the proposed PIDL approach is particularly better in state estimation with a lower amount of training data, illustrating the capability of PIDL in making precise and timely TSE even with sparse input. E.g., With 10% CAV penetration rate and a 15% added-noise, relative error for PIDL was at 22.9% compared to 30.8% for DL.

中文翻译：

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用于交通状态估计的基于物理的深度学习：LWR 和 CTM 模型的说明


我们提出了一种基于物理的深度学习（PIDL）方法来应对交通状态估计（TSE）中数据稀疏和传感器噪声的挑战。 PIDL 利用交通流理论知识强化深度学习 (DL) 神经网络，以准确估计交通状况。 “物理”（系统的先验信息）在训练期间充当正则化代理。我们用两个代表交通物理的常用模型来说明所提出方法的实现：Lighthill-Whitham-Richards (LWR) 模型和信元传输模型 (CTM)。 LWR 的实现用 Greenshields 和逆 lambda 基本图来说明；然而，CTM 模型实现适用于选择的任何基本图。两个案例研究通过重建速度场验证了该方法。案例研究-I 使用生成的合成数据来模拟路边单元捕获的联网自动驾驶车辆的轨迹。案例研究-II 采用 NGSIM 数据模拟少量探测车辆的观测结果。我们观察到，所提出的 PIDL 方法在训练数据量较少的状态估计方面尤其出色，这说明了 PIDL 即使在稀疏输入的情况下也能做出精确且及时的 TSE 的能力。例如，在 CAV 渗透率为 10% 且附加噪声为 15% 的情况下，PIDL 的相对误差为 22.9%，而 DL 的相对误差为 30.8%。