Physics-informed deep learning (PIDL) neural networks have shown their capability as a useful instrument for transportation practitioners in utilizing the underlying relationship between the state variables for traffic state estimation (TSE). Another efficient traffic management approach is implementing varying speed limits (VSLs) on transportation corridors to control traffic and mitigate congestion. However, the existing training architecture of PIDL in the literature cannot accommodate the changing traffic characteristics on a freeway with VSL. To tackle this challenge, we propose a novel framework integrating teacher-student ensemble training with PIDL neural networks for TSE under VSL scenarios. The physics of flow conservation law is encoded locally in the teacher models by PIDL, and the student model uses a multi-layer perceptron classifier (MLP) to identify traffic characteristics and selects the ensemble member of PIDL neural networks for TSE. This integrated framework provides a natural solution for capturing the heterogeneity of VSL and accurately addressing the TSE problem. The case study results validate the proposed ensemble approach, demonstrating its superior performance in TSE compared to other popular baseline methods, as indicated by relative L2 error.

翻译：物理信息深度学习神经网络已展现出作为交通工程实践者利用状态变量间内在关系进行交通状态估计的有效工具。另一种高效的交通管理方法是在交通走廊实施可变速度限制以控制交通流并缓解拥堵。然而，现有文献中物理信息深度学习的训练架构无法适应设置可变速度限制的高速公路上变化的交通特性。针对这一挑战，我们提出了一种新颖的框架，将教师-学生集成训练与物理信息深度学习神经网络相结合，用于可变速度限制场景下的交通状态估计。教师模型通过物理信息深度学习局部编码流量守恒定律的物理机制，学生模型采用多层感知机分类器识别交通特性，并选择物理信息深度学习神经网络的集成成员进行交通状态估计。该集成框架为捕捉可变速度限制的异质性并准确解决交通状态估计问题提供了天然解决方案。案例研究结果验证了所提集成方法的有效性，表明其在交通状态估计方面的性能优于其他主流基准方法，相对L2误差指标证明了这一点。