用残差引导的分域方法，提升稀疏传感器下交通状态估计精度。
Adaptive Domain Decomposition Physics-Informed Neural Networks for Traffic State Estimation with Sparse Sensor Data
- 基于残差分布动态划分区域，分块训练提升模型对突变区的捕捉能力。
- 在25组配置中18组误差最低，比扩展PINN快2.4倍，稀疏传感下表现更优。
- 适合固定传感器、存在局部交通突变的离线交通重建任务。
基于稀疏固定传感器的交通状态估计面临挑战，因物理信息神经网络（PINNs）常过度平滑Lighthill-Whitham-Richards（LWR）模型中的激波。本文提出自适应域分解物理信息神经网络（ADD-PINN），一种两阶段残差引导框架，用于基于LWR模型的离线速度场重建。先训练粗粒度全局PINN，其空间残差分布用于定位子域边界并初始化子网络；当局部过渡证据不足时，数据驱动的激波指示器可启用单域回退机制。主实验基于I-24 MOTION数据集，覆盖五天、五种传感器配置及每配置十次随机种子，共1,500次运行。相较于神经网络与物理信息基线，ADD-PINN在25组配置中18组相对L2误差最低，在15组稀疏传感场景中14组最优，且训练速度为扩展PINN（XPINN）的2.4倍。消融实验表明仅空间分解即为有效默认策略。补充的下一代仿真（NGSIM）实验作为负向对照：激波指示器在全部50次运行中抑制分解，单域回退在所有配置中排名第一。结果支持残差引导的空间分解是稀疏固定传感与局部过渡区域共现时有效的PINN家族设计。
原文摘要 · Abstract (English)
Traffic state estimation from sparse fixed sensors is challenging because physics-informed neural networks (PINNs) tend to over-smooth the shockwaves admitted by the Lighthill-Whitham-Richards (LWR) model. This study proposes Adaptive Domain Decomposition Physics-Informed Neural Networks (ADD-PINN), a two-stage residual-guided framework for LWR-based offline speed-field reconstruction. A coarse global PINN is first trained; its spatial residual profile is then used to place subdomain boundaries and initialize child subnetworks in a decomposition-enabled mode, while a data-driven shock indicator can retain a single-domain fallback when localized evidence of transition is weak. The primary offline I-24 MOTION evaluation spans five days, five sensor configurations, and ten seeds per configuration, yielding 1,500 runs in total. Against neural and physics-informed baselines, ADD-PINN attains the lowest relative L2 error in 18 of 25 configurations and in 14 of 15 sparse-sensing cases, while training 2.4 times faster than the extended PINN (XPINN) baseline. An ablation study supports spatial-only decomposition as an effective default for fixed-sensor traffic reconstruction in the evaluated settings. Supplementary Next Generation Simulation (NGSIM) experiments serve as a negative control: the shock indicator suppresses decomposition in all 50 runs, and the default single-domain fallback ranks first across all sensor configurations. These results support residual-guided spatial decomposition as an effective PINN-family design for offline reconstruction when sparse fixed sensing coincides with localized transition regions.
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