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.
| Comments: | 56 pages, 5 figures, 12 tables. Submitted to Transportation Research Part C |
| Subjects: | Machine Learning (cs.LG); Systems and Control (eess.SY) |
| MSC classes: | 35L65, 65M99, 68T07, 90B20 |
| ACM classes: | I.2.6; G.1.8; J.2 |
| Cite as: | arXiv:2605.08028 [cs.LG] |
| (or arXiv:2605.08028v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.08028 arXiv-issued DOI via DataCite (pending registration) |
From: Eunhan Ka [view email]
[v1]
Fri, 8 May 2026 17:13:53 UTC (7,114 KB)
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