用物理约束的神经算子网络，从稀疏数据精准还原交通状态演化。
Physics-informed deep operator network for traffic state estimation
- 将交通状态估计建模为算子学习问题，直接映射输入到全时空状态场。
- 在NGSIM数据集上优于现有方法，准确捕捉拥堵传播与时空关联。
- 适合需要高精度动态交通建模的智能交通系统研究者使用。
交通状态估计（TSE）本质上是从有限、含噪观测中求解高维时空偏微分方程（PDE），描述交通流动力学。传统物理信息神经网络（PINNs）在点上施加PDE约束，本文提出物理信息深度算子网络（PI-DeepONet），将TSE重构成算子学习问题。该方法训练一个参数化神经算子，将稀疏输入数据映射至完整的时空交通状态场，受交通流守恒律约束。关键在于，相较于PINNs逐点施加约束，PI-DeepONet将交通流守恒模型与基本图模型直接融入算子学习过程，确保物理一致性，同时捕捉拥堵传播、空间相关性与时间演化。在NGSIM数据集上的实验表明，其性能优于当前最优基线。进一步分析揭示了最优函数生成策略及分支网络复杂度的影响。此外，输入函数生成方法与函数数量对模型表现的影响也被探讨，凸显所提框架的鲁棒性与有效性。
原文摘要 · Abstract (English)
Traffic state estimation (TSE) fundamentally involves solving high-dimensional spatiotemporal partial differential equations (PDEs) governing traffic flow dynamics from limited, noisy measurements. While Physics-Informed Neural Networks (PINNs) enforce PDE constraints point-wise, this paper adopts a physics-informed deep operator network (PI-DeepONet) framework that reformulates TSE as an operator learning problem. Our approach trains a parameterized neural operator that maps sparse input data to the full spatiotemporal traffic state field, governed by the traffic flow conservation law. Crucially, unlike PINNs that enforce PDE constraints point-wise, PI-DeepONet integrates traffic flow conservation model and the fundamental diagram directly into the operator learning process, ensuring physical consistency while capturing congestion propagation, spatial correlations, and temporal evolution. Experiments on the NGSIM dataset demonstrate superior performance over state-of-the-art baselines. Further analysis reveals insights into optimal function generation strategies and branch network complexity. Additionally, the impact of input function generation methods and the number of functions on model performance is explored, highlighting the robustness and efficacy of proposed framework.
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