A recent development in machine learning - physics-informed deep learning (PIDL) - presents unique advantages in transportation applications such as traffic state estimation. Consolidating the benefits of deep learning (DL) and the governing physical equations, it shows the potential to complement traditional sensing methods in obtaining traffic states. In this paper, we first explain the conservation law from the traffic flow theory as ``physics'', then present the architecture of a PIDL neural network and demonstrate its effectiveness in learning traffic conditions of unobserved areas. In addition, we also exhibit the data collection scenario using fog computing infrastructure. A case study on estimating the vehicle velocity is presented and the result shows that PIDL surpasses the performance of a regular DL neural network with the same learning architecture, in terms of convergence time and reconstruction accuracy. The encouraging results showcase the broad potential of PIDL for real-time applications in transportation with a low amount of training data.

翻译：机器学习领域的最新发展——物理信息深度学习（PIDL）——在交通状态估计等交通应用中展现出独特优势。它融合了深度学习（DL）的优势与物理控制方程，有望补充传统传感方法在获取交通状态方面的不足。本文首先从交通流理论中阐释守恒定律作为“物理”约束，随后介绍PIDL神经网络的架构，并证明其在学习未观测区域交通状况方面的有效性。此外，我们还展示了利用雾计算基础设施的数据收集场景。通过一个车速估计案例研究，结果表明，在相同学习架构下，PIDL在收敛时间和重构精度方面均优于常规深度学习神经网络。这些令人鼓舞的结果展示了PIDL在训练数据量较少的情况下用于交通实时应用的广阔潜力。