Adaptive Domain Decomposition Physics-Informed Neural Networks for Traffic State Estimation with Sparse Sensor Data

• URL: http://arxiv.org/abs/2605.08028v1
• Date: Fri, 08 May 2026 17:13:53 GMT
• Title: Adaptive Domain Decomposition Physics-Informed Neural Networks for Traffic State Estimation with Sparse Sensor Data
• Abstract summary: ADD-PINN is a two-stage residual-guided framework for offline speed-field reconstruction.<n>It attains the lowest relative L2 error in 18 of 25 configurations and in 14 of 15 sparse-sensing cases.
• Score: 4.048935037437864
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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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