Observation-Aligned Two-Stage Domain Decomposition for Physics-Informed Traffic State Estimation with Sparse Fixed Sensors
Lyles School of Civil and Construction Engineering, Purdue University（普渡大学土木与建设工程学院）
Eunhan Ka, Ludovic Leclercq, Satish V. Ukkusuri
备注：
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
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.
Physics-informed deep operator network for traffic state estimation
The Key Laboratory of Road and Traffic Engineering, Ministry of Education, Tongji University, Shanghai 201804, China（交通工程重点实验室，教育部，同济大学，上海201804，中国）；College of Transportation Engineering, Tongji University, Shanghai 201804, China（交通工程学院，同济大学，上海201804，中国）
Macroscopic transport patterns of UAV traffic in 3D anisotropic wind fields: A constraint-preserving hybrid PINN-FVM approach
Nanophotonics and Biophotonics Key Laboratory of Jilin Province, School of Physics, Changchun University of Science and Technology（吉林省纳米光子学与生物光子学重点实验室，物理学院，长春理工大学）
HypNO: A Graph-Based Neural Operator with Physics-Informed Message Passing for Hyperbolic Conservation Laws
Laboratory of Computer Science (LIX), École Polytechnique（计算机科学实验室（LIX），巴黎综合理工学院）；Department of Electrical Engineering and Computer Sciences, University of California, Berkeley（电气工程与计算机科学系，加利福尼亚大学伯克利分校）
SAMSGL: Series-Aligned Multi-Scale Graph Learning for Spatio-Temporal Forecasting
East China University of Science and Technology（华东理工大学）；Potsdam Institute for Climate Impact Research（波茨坦气候影响研究所）；Humboldt University of Berlin（柏林洪堡大学）
CIWI-CKT: Chaos-Informed Wave Interference Feature Fusion and Cross-City Knowledge Transfer for Traffic Flow Forecasting
Griffith University（格里菲斯大学）；School of Information and Communication Technology, Griffith University（格里菲斯大学信息与通信技术学院）；School of Information Engineering, Chang’an University（长安大学信息工程学院）
Informed along the road: roadway capacity driven graph convolution network for network-wide traffic prediction
Tandon School of Engineering, New York University（纽约大学工程学院）；State Key Laboratory of Internet of Things for Smart City, University of Macau（澳门大学物联网智能城市国家重点实验室）
Physics-Informed Teacher-Student Ensemble Learning for Traffic State Estimation with a Varying Speed Limit Scenario
Department of Building, Civil and Environmental Engineering, Concordia University（康科迪亚大学建筑、土木和环境工程系）；Urban Artificial Intelligence Laboratory, University of Florida（佛罗里达大学城市人工智能实验室）；Department of Civil, Environmental and Construction Engineering, University of Central Florida（中央佛罗里达大学土木、环境和建设工程系）
Potential failures of physics-informed machine learning in traffic flow modeling: theoretical and experimental analysis
University of Maryland, College Park, MD 20742, United States（马里兰大学学院公园分校）；Florida Atlantic University, Boca Raton, FL 33431, United States（佛罗里达 Atlantic 大学）
Evolutionary Physics-Informed Temporal Fusion for Lane-Change Intention Prediction
Tandon School of Engineering（工程学院）；New York University（纽约大学）；Khoury College of Computer Science（计算机科学学院）；Northeastern University（东北大学）；School of Business（商学院）；Wake Forest University（威克森林大学）；Independent Researcher（独立研究者）；University of Massachusetts Amherst（马萨诸塞大学阿默斯特分校）；Carnegie Mellon University（卡内基梅隆大学）；University of Pennsylvania（宾夕法尼亚大学）；Qualcomm CDMA Technologies（高通CDMA技术）；University of Michigan（密歇根大学）
