Adaptive Domain Decomposition Physics-Informed Neural Networks for Traffic State Estimation with Sparse Sensor Data
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914545373544448 |
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| author | Ka, Eunhan Leclercq, Ludovic Ukkusuri, Satish V. |
| author_facet | Ka, Eunhan Leclercq, Ludovic Ukkusuri, Satish V. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_08028 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Adaptive Domain Decomposition Physics-Informed Neural Networks for Traffic State Estimation with Sparse Sensor Data Ka, Eunhan Leclercq, Ludovic Ukkusuri, Satish V. Machine Learning Systems and Control 35L65, 65M99, 68T07, 90B20 I.2.6; G.1.8; J.2 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. |
| title | Adaptive Domain Decomposition Physics-Informed Neural Networks for Traffic State Estimation with Sparse Sensor Data |
| topic | Machine Learning Systems and Control 35L65, 65M99, 68T07, 90B20 I.2.6; G.1.8; J.2 |
| url | https://arxiv.org/abs/2605.08028 |