{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,15]],"date-time":"2026-06-15T14:47:36Z","timestamp":1781534856640,"version":"3.54.5"},"reference-count":31,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2026,5,8]],"date-time":"2026-05-08T00:00:00Z","timestamp":1778198400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004608","name":"Natural Science Foundation of Jiangsu Province","doi-asserted-by":"publisher","award":["BK20241326"],"award-info":[{"award-number":["BK20241326"]}],"id":[{"id":"10.13039\/501100004608","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Ministry of Education Humanities and Social Sciences","award":["24YJCZH455"],"award-info":[{"award-number":["24YJCZH455"]}]},{"name":"Intelligent Policing Key Laboratory of Sichuan Province","award":["ZNJW2025KFQN007"],"award-info":[{"award-number":["ZNJW2025KFQN007"]}]},{"DOI":"10.13039\/501100008081","name":"Southeast University","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100008081","id-type":"DOI","asserted-by":"crossref"}]},{"id":[{"id":"https:\/\/ror.org\/00cf0ab87","id-type":"ROR","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["2242025F10009"],"award-info":[{"award-number":["2242025F10009"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Systems"],"abstract":"<jats:p>Accurate trajectory data are fundamental to traffic modeling and autonomous vehicle development. However, reconstructing trajectories in cut-in scenarios is challenging due to complex multi-vehicle interactions and frequently sparse, noisy observations. Existing model-based methods require extensive parameter tuning, while purely data-driven methods depend on densely labeled trajectory datasets and may violate physical consistency. To address these limitations, this paper proposes CI-PINN (cut-in physics-informed neural network), a self-supervised framework for trajectory reconstruction under severe data degradation. By integrating a longitudinal interaction model that captures anticipation and relaxation behaviors, CI-PINN ensures kinematic plausibility by jointly minimizing data-fitting and physics residual losses. Experiments on the NGSIM dataset demonstrate robust performance across missing rates of 80\u201390%, achieving a mean absolute error of 0.91 m and a mean squared error of 2.17 m2, which are 63.2% and 78.1% lower than the best baseline method, respectively. These results demonstrate a label-efficient and physically consistent framework for trajectory reconstruction in cut-in scenarios. Beyond improving microscopic trajectory fidelity, the proposed method preserves system-level traffic metrics more reliably, facilitating more accurate safety assessments and intelligent transportation applications.<\/jats:p>","DOI":"10.3390\/systems14050535","type":"journal-article","created":{"date-parts":[[2026,5,8]],"date-time":"2026-05-08T20:11:13Z","timestamp":1778271073000},"page":"535","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Physics-Informed Neural Network for Vehicle Trajectory Reconstruction in Cut-In Scenarios with Sparse and Noisy Observations"],"prefix":"10.3390","volume":"14","author":[{"given":"Chenyi","family":"Xie","sequence":"first","affiliation":[{"name":"Department of Modern Urban Traffic Technologies and Urban Intelligent Transportation Systems, Southeast University, Nanjing 211189, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuan","family":"Zheng","sequence":"additional","affiliation":[{"name":"Department of Modern Urban Traffic Technologies and Urban Intelligent Transportation Systems, Southeast University, Nanjing 211189, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6486-0999","authenticated-orcid":false,"given":"Qingchao","family":"Liu","sequence":"additional","affiliation":[{"name":"Automotive Engineering Research Institute, Jiangsu University, Zhenjiang 212013, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jian","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Modern Urban Traffic Technologies and Urban Intelligent Transportation Systems, Southeast University, Nanjing 211189, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wenping","family":"Duan","sequence":"additional","affiliation":[{"name":"Intelligent Ecology Platform Seres Group Co., Ltd., Chongqing 400030, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yu","family":"Tang","sequence":"additional","affiliation":[{"name":"Intelligent Cockpit Evaluation Department, China Automotive Engineering Research Institute Co., Ltd., Jinyu Avenue 8, Liangjiang District, Chongqing 401122, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bin","family":"Ran","sequence":"additional","affiliation":[{"name":"Department of Modern Urban Traffic Technologies and Urban Intelligent Transportation Systems, Southeast University, Nanjing 211189, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,5,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"129503","DOI":"10.1016\/j.physa.2024.129503","article-title":"Lane Management for Mixed Traffic Flow on Roadways Considering the Car-Following Behaviors of Human-Driven Vehicles to Follow Connected and Automated Vehicles","volume":"635","author":"Zheng","year":"2024","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_2","first-page":"5","article-title":"Multiclass Multilane Model for Freeway Traffic Mixed with Connected Automated Vehicles and Regular Human-Piloted Vehicles","volume":"17","author":"Pan","year":"2021","journal-title":"Transp. A Transp. Sci."},{"key":"ref_3","first-page":"849","article-title":"Long-Term Prediction for High-Resolution Lane-Changing Data Using Temporal Convolution Network","volume":"10","author":"Zhang","year":"2022","journal-title":"Transp. B Transp. Dyn."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"2353","DOI":"10.1109\/TITS.2017.2787101","article-title":"Vehicle Tracking Using Surveillance with Multimodal Data Fusion","volume":"19","author":"Zhang","year":"2018","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"105367","DOI":"10.1016\/j.aap.2019.105367","article-title":"Optimal Jam-Absorption Driving Strategy for Mitigating Rear-End Collision Risks with Oscillations on Freeway Straight Segments","volume":"135","author":"Zheng","year":"2020","journal-title":"Accid. Anal. Prev."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"20854","DOI":"10.1109\/TITS.2024.3467213","article-title":"Maximum Platoon Size for Platoon-Based Cooperative Signal-Free Control at Intersections","volume":"25","author":"Zheng","year":"2024","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"103521","DOI":"10.1016\/j.trc.2021.103521","article-title":"Autonomous Intersection Management with Pedestrians Crossing","volume":"135","author":"Wu","year":"2022","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1186\/s40537-020-0285-1","article-title":"Sensor Data Quality: A Systematic Review","volume":"7","author":"Teh","year":"2020","journal-title":"J. Big Data"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"04024108","DOI":"10.1061\/JTEPBS.TEENG-8569","article-title":"Vehicle Trajectory Reconstruction from Sparse Data Using a Hybrid Approach","volume":"151","author":"Ma","year":"2025","journal-title":"J. Transp. Eng. Part A Syst."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"104768","DOI":"10.1016\/j.trc.2024.104768","article-title":"Developing Platooning Systems of Connected and Automated Vehicles with Guaranteed Stability and Robustness against Degradation Due to Communication Disruption","volume":"168","author":"Zheng","year":"2024","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"106500","DOI":"10.1016\/j.aap.2021.106500","article-title":"A Proactive Lane-Changing Risk Prediction Framework Considering Driving Intention Recognition and Different Lane-Changing Patterns","volume":"164","author":"Shangguan","year":"2022","journal-title":"Accid. Anal. Prev."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"99","DOI":"10.3141\/2390-11","article-title":"Making NGSIM Data Usable for Studies on Traffic Flow Theory: Multistep Method for Vehicle Trajectory Reconstruction","volume":"2390","author":"Montanino","year":"2013","journal-title":"Transp. Res. Rec. J. Transp. Res. Board"},{"key":"ref_13","first-page":"2163207","article-title":"Vehicle Trajectory Reconstruction for Intersections: An Integrated Wavelet Transform and Savitzky-Golay Filter Approach","volume":"20","author":"Zhao","year":"2024","journal-title":"Transp. A Transp. Sci."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1016\/j.trb.2015.06.010","article-title":"Trajectory Data Reconstruction and Simulation-Based Validation against Macroscopic Traffic Patterns","volume":"80","author":"Montanino","year":"2015","journal-title":"Transp. Res. Part B Methodol."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2071","DOI":"10.1109\/TITS.2020.3031282","article-title":"Platoon Trajectories Generation: A Unidirectional Interconnected LSTM-based Car-Following Model","volume":"23","author":"Lin","year":"2022","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"960","DOI":"10.1049\/itr2.12319","article-title":"Car-Following Trajectory Data Imputation with Adversarial Convolutional Neural Network","volume":"17","author":"Zhao","year":"2023","journal-title":"IET Intell. Transp. Syst."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"11701","DOI":"10.1109\/TITS.2024.3373774","article-title":"A Joint Spatiotemporal Prediction and Image Confirmation Model for Vehicle Trajectory Concatenation with Low Detection Rates","volume":"25","author":"Feng","year":"2024","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Qiu, X., Pan, Y., Zhu, M., Yang, L., and Zheng, X. (2024, January 2\u20135). Driving Style-Aware Car-Following Considering Cut-in Tendencies of Adjacent Vehicles with Inverse Reinforcement Learning. Proceedings of the 2024 IEEE Intelligent Vehicles Symposium (IV), Jeju Island, Republic of Korea.","DOI":"10.1109\/IV55156.2024.10588574"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"3264","DOI":"10.3934\/era.2023165","article-title":"Human-like Car-Following Modeling Based on Online Driving Style Recognition","volume":"31","author":"Ma","year":"2023","journal-title":"Electron. Res. Arch."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Tu, D., Wu, Y., Li, L., Jiang, Y., Wang, Y., and Yao, Z. (2026). Analysis of the Impact of Heterogeneous Platoon for Mixed Traffic Flow: Stability and Safety. Systems, 14.","DOI":"10.3390\/systems14030304"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"422","DOI":"10.1038\/s42254-021-00314-5","article-title":"Physics-Informed Machine Learning","volume":"3","author":"Karniadakis","year":"2021","journal-title":"Nat. Rev. Phys."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1727","DOI":"10.1007\/s10409-021-01148-1","article-title":"Physics-Informed Neural Networks (PINNs) for Fluid Mechanics: A Review","volume":"37","author":"Cai","year":"2021","journal-title":"Acta Mech. Sin."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"060801","DOI":"10.1115\/1.4050542","article-title":"Physics-Informed Neural Networks for Heat Transfer Problems","volume":"143","author":"Cai","year":"2021","journal-title":"J. Heat. Transf."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"104224","DOI":"10.1016\/j.trc.2023.104224","article-title":"Physics-Informed Neural Networks for Integrated Traffic State and Queue Profile Estimation: A Differentiable Programming Approach on Layered Computational Graphs","volume":"153","author":"Lu","year":"2023","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"103240","DOI":"10.1016\/j.trc.2021.103240","article-title":"A Physics-Informed Deep Learning Paradigm for Car-Following Models","volume":"130","author":"Mo","year":"2021","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"104110","DOI":"10.1016\/j.trc.2023.104110","article-title":"Modeling the Impact of Lane-Changing\u2019s Anticipation on Car-Following Behavior","volume":"150","author":"Chen","year":"2023","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1016\/j.trc.2016.04.011","article-title":"A Global Optimization Algorithm for Trajectory Data Based Car-Following Model Calibration","volume":"68","author":"Li","year":"2016","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"761047","DOI":"10.1155\/2014\/761047","article-title":"New Algorithms for Computing the Time-to-Collision in Freeway Traffic Simulation Models","volume":"2014","author":"Hou","year":"2014","journal-title":"Comput. Intell. Neurosci."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"106051","DOI":"10.1016\/j.aap.2021.106051","article-title":"Comparison of Threshold Determination Methods for the Deceleration Rate to Avoid a Crash (DRAC)-Based Crash Estimation","volume":"153","author":"Fu","year":"2021","journal-title":"Accid. Anal. Prev."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"135793","DOI":"10.1016\/j.energy.2025.135793","article-title":"Multiobjective Eco-Driving Speed Optimisation with Real-Time Traffic: Balancing Fuel, NOx, and Travel Time","volume":"324","author":"Liu","year":"2025","journal-title":"Energy"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1016\/S1361-9209(03)00054-3","article-title":"Development of VT-micro Model for Estimating Hot Stabilized Light Duty Vehicle and Truck Emissions","volume":"9","author":"Rakha","year":"2004","journal-title":"Transp. Res. Part D Transp. Environ."}],"container-title":["Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-8954\/14\/5\/535\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,10]],"date-time":"2026-05-10T04:24:59Z","timestamp":1778387099000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-8954\/14\/5\/535"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,5,8]]},"references-count":31,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2026,5]]}},"alternative-id":["systems14050535"],"URL":"https:\/\/doi.org\/10.3390\/systems14050535","relation":{},"ISSN":["2079-8954"],"issn-type":[{"value":"2079-8954","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,5,8]]}}}