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This research introduces TSDD-PINN, a two-stage domain decomposition framework that improves physics-informed neural networks for traffic state estimation using sparse sensors. By refining spatial domains based on residual profiles, the method reduces training time by 2.4x while achieving lower $L_2$ errors compared to standard PINNs and interpolation baselines. The findings highlight that model advantages are most pronounced in sparse sensing scenarios, offering a more efficient approach for reconstructing speed fields from limited fixed sensor data.
Observation-Aligned Two-Stage Domain Decomposition for Physics-Informed Traffic State Estimation with Sparse Fixed Sensors
arXiv:2605.08028v2 Announce Type: replace Abstract: Traffic state estimation from sparse fixed sensors is challenging because physics-informed neural networks (PINNs) tend to over-smooth sharp transitions admitted by the Lighthill-Whitham--Richards (LWR) model. This study proposes Two-Stage Domain Decomposition Physics-Informed Neural Networks (TSDD-PINN), an observation-aligned framework for LWR-based offline speed-field reconstruction. The framework supports spatial, temporal, and space--time refinement. Matched direction analysis shows that spatial refinement has the lowest mean error and less than half the training time of space--time refinement in the tested setting, while temporal refinement is faster. A global parent PINN is first trained. In the controlled spatial implementation, its residual profile guides a deterministic partition for warm-started child networks. An optional operational safeguard retains Stage~1 when the prespecified screen does not activate. The primary I-24 MOTION evaluation spans five days, five sensor configurations, and ten seeds per configuration, yielding 1{,}500 runs. Controlled TSDD-PINN attains the lowest relative $L_2$ error in 18 of 25 configurations and 14 of 15 sparse-sensing cases, while training 2.4 times faster than the extended PINN (XPINN) baseline under the evaluated implementations and training budgets. Non-neural comparisons show that the advantage over interpolation is concentrated under sparse sensing, whereas dense sensing often favors interpolation. A separate 250-run operational evaluation finds infrequent activation and motivates the Stage-1-preserving safeguard. The residual is treated as an indicator of model difficulty rather than a validated shock detector. The evidence supports a sensing-density-dependent operating range rather than uniform improvement.
Abstract:Traffic state estimation from sparse fixed sensors is challenging because physics-informed neural networks (PINNs) tend to over-smooth sharp transitions admitted by the Lighthill-Whitham--Richards (LWR) model. This study proposes Two-Stage Domain Decomposition Physics-Informed Neural Networks (TSDD-PINN), an observation-aligned framework for LWR-based offline speed-field reconstruction. The framework supports spatial, temporal, and space--time refinement. Matched direction analysis shows that spatial refinement has the lowest mean error and less than half the training time of space--time refinement in the tested setting, while temporal refinement is faster. A global parent PINN is first trained. In the controlled spatial implementation, its residual profile guides a deterministic partition for warm-started child networks. An optional operational safeguard retains Stage~1 when the prespecified screen does not activate. The primary I-24 MOTION evaluation spans five days, five sensor configurations, and ten seeds per configuration, yielding 1{,}500 runs. Controlled TSDD-PINN attains the lowest relative $L_2$ error in 18 of 25 configurations and 14 of 15 sparse-sensing cases, while training 2.4 times faster than the extended PINN (XPINN) baseline under the evaluated implementations and training budgets. Non-neural comparisons show that the advantage over interpolation is concentrated under sparse sensing, whereas dense sensing often favors interpolation. A separate 250-run operational evaluation finds infrequent activation and motivates the Stage-1-preserving safeguard. The residual is treated as an indicator of model difficulty rather than a validated shock detector. The evidence supports a sensing-density-dependent operating range rather than uniform improvement.
52 pages, 7 figures, 11 tables. Revised after peer review and accepted for publication in Transportation Research Part C: Emerging Technologies. The title and method name were updated, with additional classical TSE comparisons, sensitivity and component analyses, and decomposition-direction evaluation
Machine Learning (cs.LG); Systems and Control (eess.SY)
I.2.6; G.1.8; J.2
arXiv:2605.08028 [cs.LG]
(or arXiv:2605.08028v2 [cs.LG] for this version)
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