{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,16]],"date-time":"2026-07-16T03:26:39Z","timestamp":1784172399633,"version":"3.55.0"},"reference-count":41,"publisher":"MDPI AG","issue":"21","license":[{"start":{"date-parts":[[2025,11,4]],"date-time":"2025-11-04T00:00:00Z","timestamp":1762214400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Nantong University Base of the Jiangsu Research Center for Xi Jinping Thought on Socialism with Chinese Characteristics for a New Era","award":["25jdyb010"],"award-info":[{"award-number":["25jdyb010"]}]},{"name":"2025 Jiangsu Provincial Science and Technology Think Tank Youth Initiative Program","award":["JSKX 0125 086"],"award-info":[{"award-number":["JSKX 0125 086"]}]},{"name":"Engineering Research Center of Sustainable Urban Intelligent Transportation, Ministry of Education Open Project Funding","award":["KCX2024-KF02"],"award-info":[{"award-number":["KCX2024-KF02"]}]},{"name":"2025 Nantong Social Science Research Project","award":["ET25-3"],"award-info":[{"award-number":["ET25-3"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This study develops a recent model proposed by Zhang et al. to predict bus short-term origin-destination (OD) demand based on a small-scale dataset (i.e., one week\u2019s data per 30 mins\u2019 collecting interval). We distinctively use sole input sequence by introducing a multi-head attention mechanism while simultaneously ensuring prediction accuracy. Extensive experiments demonstrate that one-layer bidirectional LSTMs (BiLSTMs) perform better than multi-layer ones. A modified deep learning model integrating physics-guided mechanisms, adaptive graph convolution, attention networks, and spatiotemporal encoder\u2013decoder is constructed. We retained the original name, i.e., physics-guided adaptive graph spatio-temporal attention network (PAG-STAN) model. The model uses an encoder\u2013decoder architecture, where the encoder captures spatiotemporal correlations via an adaptive graph convolutional LSTM (AGC-LSTM), enhanced by an attention mechanism that adjusts the importance of different spatiotemporal features. The decoder utilizes bidirectional LSTM to reconstruct the periodic patterns and predict the full OD matrix for the next interval. A masked physics-guided loss function, which embeds the quantitative relationship between boarding passenger volume and OD demand, is adopted for training. The Adam optimizer and early stopping technique are used to enhance training efficiency and avoid overfitting. Experimental results show that PAG-STAN outperforms other deep learning models in prediction accuracy. Compared with the suboptimal model, the proposed model achieved reductions of 6.19% in RMSE, 6.59% in MAE, and 8.20% in WMAPE, alongside a 1.13% improvement in R2.<\/jats:p>","DOI":"10.3390\/s25216739","type":"journal-article","created":{"date-parts":[[2025,11,4]],"date-time":"2025-11-04T12:13:08Z","timestamp":1762258388000},"page":"6739","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Deep Learning-Driven Bus Short-Term OD Demand Prediction via a Physics-Guided Adaptive Graph Spatio-Temporal Attention Network"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7815-3889","authenticated-orcid":false,"given":"Zhichao","family":"Cao","sequence":"first","affiliation":[{"name":"School of Transportation and Civil Engineering, Nantong University, Nantong 226019, China"},{"name":"Engineering Research Center of Sustainable Urban Intelligent Transportation, Ministry of Education, Chengdu 610041, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0007-4880-7355","authenticated-orcid":false,"given":"Longfei","family":"Song","sequence":"additional","affiliation":[{"name":"School of Transportation and Civil Engineering, Nantong University, Nantong 226019, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7363-4045","authenticated-orcid":false,"given":"Silin","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Transportation and Civil Engineering, Nantong University, Nantong 226019, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jingxuan","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Transportation and Civil Engineering, Nantong University, Nantong 226019, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,11,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"36","DOI":"10.3311\/PPtr.12072","article-title":"Public Transport Accessibility: A Literature Review","volume":"47","author":"Saif","year":"2019","journal-title":"Period. Polytech. Transp. Eng."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1016\/j.ijtst.2022.03.002","article-title":"Origin\u2013Destination Inference in Public Transportation Systems: A Comprehensive Review","volume":"12","author":"Mohammed","year":"2023","journal-title":"Int. J. Transp. Sci. Technol."},{"key":"ref_3","first-page":"865","article-title":"Traffic Flow Prediction with Big Data: A Deep Learning Approach","volume":"16","author":"Lv","year":"2014","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Fan, Q., Yu, C., and Zuo, J. (2025). Predicting Urban Rail Transit Network Origin-Destination Matrix under Operational Incidents with Deep Counterfactual Inference. Appl. Sci., 15.","DOI":"10.3390\/app15126398"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"276","DOI":"10.1016\/j.eng.2024.04.020","article-title":"Physics Guided Deep Learning-Based Model for Short-Term Origin-Destination Demand Prediction in Urban Rail Transit Systems Under Pandemic","volume":"41","author":"Zhang","year":"2024","journal-title":"Engineering"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1061\/(ASCE)0733-947X(1997)123:4(261)","article-title":"Traffic Flow Forecasting: Comparison of Modeling Approaches","volume":"123","author":"Smith","year":"1997","journal-title":"J. Transp. Eng."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"179","DOI":"10.3141\/1678-22","article-title":"Application of Subset Autoregressive Integrated Moving Average Model for Short-Term Freeway Traffic Volume Forecasting","volume":"1678","author":"Lee","year":"1999","journal-title":"Transp. Res. Rec."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1109\/TITS.2008.2011693","article-title":"An Aggregation Approach to Short-Term Traffic Flow Prediction","volume":"10","author":"Tan","year":"2009","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"664","DOI":"10.1061\/(ASCE)0733-947X(2003)129:6(664)","article-title":"Modeling and Forecasting Vehicular Traffic Flow as a Seasonal ARIMA Process: Theoretical Basis and Empirical Results","volume":"129","author":"Williams","year":"2003","journal-title":"J. Transp. Eng."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"222","DOI":"10.1007\/s40534-019-0193-2","article-title":"Using Kalman Filter Algorithm for Short-Term Traffic Flow Prediction in a Connected Vehicle Environment","volume":"27","author":"Emami","year":"2019","journal-title":"J. Mod. Transp."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"122219","DOI":"10.1016\/j.eswa.2023.122219","article-title":"A Fundamental Diagram Based Hybrid Framework for Traffic Flow Estimation and Prediction by Combining a Markovian Model with Deep Learning","volume":"238","author":"Pan","year":"2024","journal-title":"Expert Syst. Appl."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"192","DOI":"10.1177\/0361198120926504","article-title":"A Novel Three-Stage Framework for Prioritizing and Selecting Feature Variables for Short-Term Metro Passenger Flow Prediction","volume":"Volume 2674","author":"Zhao","year":"2020","journal-title":"Proceedings of the Transportation Research Board 99th Annual Meeting"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Wang, D., Zhang, Q., Wu, S., Li, X., and Wang, R. (2016, January 20\u201322). Traffic Flow Forecast with Urban Transport Network. Proceedings of the 2016 IEEE International Conference on Intelligent Transportation Engineering, Singapore.","DOI":"10.1109\/ICITE.2016.7581322"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"332","DOI":"10.1155\/2020\/3247847","article-title":"Urban Traffic Travel Time Short-Term Prediction Model Based on Spatio-Temporal Feature Extraction","volume":"2020","author":"Kang","year":"2020","journal-title":"J. Adv. Transp."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2096","DOI":"10.1016\/j.neucom.2010.12.032","article-title":"Traffic Flow Forecasting by Seasonal SVR with Chaotic Simulated Annealing Algorithm","volume":"74","author":"Hong","year":"2011","journal-title":"Neurocomputing"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1016\/j.trc.2015.11.002","article-title":"A Spatiotemporal Correlative k-Nearest Neighbor Model for Short-Term Traffic Multistep Forecasting","volume":"62","author":"Cai","year":"2016","journal-title":"Transp. Res. Part C"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"14317","DOI":"10.1109\/JSEN.2020.3007809","article-title":"Sensing Data Supported Traffic Flow Prediction via Denoising Schemes and ANN: A Comparison","volume":"20","author":"Chen","year":"2020","journal-title":"IEEE Sens. J."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"108780","DOI":"10.1016\/j.comnet.2022.108780","article-title":"Metaheuristic Enabled Modified Hidden Markov Model for Traffic Flow Prediction","volume":"206","author":"Raskar","year":"2022","journal-title":"Comput. Netw."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1038","DOI":"10.4028\/www.scientific.net\/AMM.397-400.1038","article-title":"Prediction of the Metro Section Passenger Flow Based on Time-Space Characteristic","volume":"397","author":"Jin","year":"2013","journal-title":"Appl. Mech. Mater."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1599","DOI":"10.1049\/itr2.12352","article-title":"A Deep Neural Network Model with GCN and 3D Convolutional Network for Short-Term Metro Passenger Flow Forecasting","volume":"17","author":"Zhang","year":"2023","journal-title":"IET Intell. Transp. Syst."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"122381","DOI":"10.1016\/j.eswa.2023.122381","article-title":"Dynamic Spatial\u2013Temporal Graph Convolutional Recurrent Networks for Traffic Flow Forecasting","volume":"240","author":"Xia","year":"2024","journal-title":"Expert Syst. Appl."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1210","DOI":"10.1049\/iet-its.2019.0873","article-title":"Multi-Graph Convolutional Network for Short-Term Passenger Flow Forecasting in Urban Rail Transit","volume":"14","author":"Zhang","year":"2020","journal-title":"IET Intell. Transp. Syst."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"101230","DOI":"10.1016\/j.cstp.2024.101230","article-title":"Origin-Destination Demand Prediction of Public Transit Using Graph Convolutional Neural Network","volume":"17","author":"Shanthappa","year":"2024","journal-title":"Case Stud. Transp. Policy"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"125838","DOI":"10.1016\/j.physa.2021.125838","article-title":"Short-Term Demand Forecasting for Online Car-Hailing Using ConvLSTM Networks","volume":"570","author":"Lu","year":"2021","journal-title":"Phys. A"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"11518","DOI":"10.1109\/JIOT.2023.3243122","article-title":"Spatiotemporal Residual Graph Attention Network for Traffic Flow Forecasting","volume":"10","author":"Zhang","year":"2023","journal-title":"IEEE Internet Things J."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"18155","DOI":"10.1109\/TITS.2022.3150600","article-title":"Multi-Graph Convolutional-Recurrent Neural Network (MGC-RNN) for Short-Term Forecasting of Transit Passenger Flow","volume":"23","author":"He","year":"2022","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"123982","DOI":"10.1016\/j.eswa.2024.123982","article-title":"Parallel Framework of a Multi-Graph Convolutional Network and Gated Recurrent Unit for Spatial\u2013Temporal Metro Passenger Flow Prediction","volume":"251","author":"Zhan","year":"2024","journal-title":"Expert Syst. Appl."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"119144","DOI":"10.1016\/j.ins.2023.119144","article-title":"Short-Term Passenger Flow Prediction for Multi-Traffic Modes: A Transformer and Residual Network Based Multi-Task Learning Method","volume":"642","author":"Yang","year":"2023","journal-title":"Inf. Sci."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"121989","DOI":"10.1016\/j.eswa.2023.121989","article-title":"An Origin\u2013Destination Passenger Flow Prediction System Based on Convolutional Neural Network and Passenger Source-Based Attention Mechanism","volume":"238","author":"Lv","year":"2024","journal-title":"Expert Syst. Appl."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"6913","DOI":"10.1109\/TNNLS.2022.3183903","article-title":"Bidirectional Spatial-Temporal Adaptive Transformer for Urban Traffic Flow Forecasting","volume":"34","author":"Chen","year":"2023","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"3219","DOI":"10.1109\/TITS.2019.2924971","article-title":"Deep Multi-Scale Convolutional LSTM Network for Travel Demand and Origin-Destination Predictions","volume":"21","author":"Chu","year":"2019","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"3848","DOI":"10.1109\/TITS.2019.2935152","article-title":"T-GCN: A Temporal Graph Convolutional Network for Traffic Prediction","volume":"21","author":"Zhao","year":"2019","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"6910","DOI":"10.1109\/TITS.2020.2997352","article-title":"A Hybrid Deep Learning Model with Attention-Based Conv-LSTM Networks for Short-Term Traffic Flow Prediction","volume":"22","author":"Zheng","year":"2020","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"5106","DOI":"10.1109\/TITS.2020.3047047","article-title":"Dynamic Origin-Destination Prediction in Urban Rail Systems: A Multi-Resolution Spatio-Temporal Deep Learning Approach","volume":"23","author":"Noursalehi","year":"2021","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"102928","DOI":"10.1016\/j.trc.2020.102928","article-title":"Short-Term Origin-Destination Demand Prediction in Urban Rail Transit Systems: A Channel-Wise Attentive Split-Convolutional Neural Network Method","volume":"124","author":"Zhang","year":"2021","journal-title":"Transp. Res. Part C"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"102858","DOI":"10.1016\/j.trc.2020.102858","article-title":"Predicting Origin-Destination Ride-Sourcing Demand with a Spatio-Temporal Encoder-Decoder Residual Multi-Graph Convolutional Network","volume":"122","author":"Ke","year":"2021","journal-title":"Transp. Res. Part C"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"25115","DOI":"10.1109\/TITS.2021.3122541","article-title":"A Spatiotemporal Bidirectional Attention-Based Ride-Hailing Demand Prediction Model: A Case Study in Beijing During COVID-19","volume":"23","author":"Huang","year":"2022","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"806","DOI":"10.1080\/15472450.2023.2209913","article-title":"Adaptive Graph Convolutional Network-Based Short-Term Passenger Flow Prediction for Metro","volume":"28","author":"Zhao","year":"2024","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"106435","DOI":"10.1016\/j.cie.2020.106435","article-title":"An Optimized Model Using LSTM Network for Demand Forecasting","volume":"143","author":"Abbasimehr","year":"2020","journal-title":"Comput. Ind. Eng."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Yu, B., Yin, H., and Zhu, Z. (2018, January 13\u201319). Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting. Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence, Stockholm, Sweden.","DOI":"10.24963\/ijcai.2018\/505"},{"key":"ref_41","first-page":"388","article-title":"A Novel Hybrid Deep Learning Model with ARIMA Conv-LSTM Networks and Shuffle Attention Layer for Short-Term Traffic Flow Prediction","volume":"21","author":"Sattarzadeh","year":"2025","journal-title":"Transp. A Transp. Sci."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/25\/21\/6739\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,4]],"date-time":"2025-11-04T12:23:16Z","timestamp":1762258996000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/25\/21\/6739"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,11,4]]},"references-count":41,"journal-issue":{"issue":"21","published-online":{"date-parts":[[2025,11]]}},"alternative-id":["s25216739"],"URL":"https:\/\/doi.org\/10.3390\/s25216739","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,11,4]]}}}