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.
自适应区域分解物理信息神经网络用于稀疏传感器数据的交通状态估计 / Adaptive Domain Decomposition Physics-Informed Neural Networks for Traffic State Estimation with Sparse Sensor Data
该论文提出了一种自适应区域分解物理信息神经网络方法，通过先训练一个粗略的全局网络，再利用其残差分布自动划分子区域并初始化子网络，从而在稀疏传感器数据下更高效、更准确地重构交通速度场，避免传统方法对交通冲击波的过度平滑问题。
源自 arXiv: 2605.08028
