{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,31]],"date-time":"2026-07-31T18:51:39Z","timestamp":1785523899651,"version":"3.56.0"},"reference-count":106,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2026,4,16]],"date-time":"2026-04-16T00:00:00Z","timestamp":1776297600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Fundamental Research Funds for the Central Universities Special Fund Project","award":["LGZD202606"],"award-info":[{"award-number":["LGZD202606"]}]},{"name":"Youth Fund Project of Ministry of Education in China Humanities and Social Sciences Foundation","award":["25YJC760104"],"award-info":[{"award-number":["25YJC760104"]}]},{"name":"General Research Projects in Philosophy and Social Sciences of Colleges and Universities in Jiangsu Province","award":["2025SJYB0084"],"award-info":[{"award-number":["2025SJYB0084"]}]},{"name":"Research Project on Higher Education Teaching Reform of Jiangsu Association of Automation","award":["JSAAJG2025Y28"],"award-info":[{"award-number":["JSAAJG2025Y28"]}]},{"name":"General Project on Teaching Reform of Nanjing Police University","award":["YB26005"],"award-info":[{"award-number":["YB26005"]}]},{"name":"Harbin Xinguang Optic-electronics Technology Co., Ltd. Horizontal Research Project","award":["2024320107003397"],"award-info":[{"award-number":["2024320107003397"]}]},{"name":"Harbin Xinguang Optic-electronics Technology Co., Ltd. Horizontal Research Project","award":["2025320107003049"],"award-info":[{"award-number":["2025320107003049"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Traffic flow prediction is a key component of Intelligent Transportation Systems (ITS), crucial for alleviating urban congestion, optimizing traffic management, and improving the overall efficiency of road networks. With the rapid growth in vehicle numbers and the increasing complexity of urban traffic patterns, accurate short-term traffic flow prediction has become increasingly important. This paper comprehensively reviews the latest advancements in traffic flow prediction methods, focusing on graph neural network (GNN)-based approaches and hybrid deep learning frameworks. First, we introduce the fundamental theoretical foundations, including graph neural networks, deep learning algorithms, heuristic optimization methods, and attention mechanisms. Subsequently, we summarize GNN-based prediction methods into four paradigms: (1) federated learning and privacy-preserving methods, enabling cross-regional collaboration while protecting sensitive data; (2) dynamically adaptive graph structure methods, capturing time-varying spatial dependencies; (3) multi-graph fusion and attention mechanism methods, enhancing feature representations from multiple perspectives; and (4) cross-domain technology integration methods, fusing novel architectures and interdisciplinary technologies. Furthermore, we investigate hybrid methods combining signal decomposition, heuristic optimization, and attention mechanisms with LSTM networks to address challenges related to non-stationarity and model optimization. For each category, we analyzed representative works and summarized their core innovations, strengths, and limitations using a systematic comparative table. Finally, we discussed current challenges, including computational complexity, model interpretability, and generalization ability, and outlined future research directions such as lightweight model design, uncertainty quantification, multimodal data fusion, and integration with traffic control systems. This review provides researchers and practitioners with a systematic understanding of the latest advances in traffic flow prediction and offers guidance for methodological selection and future research.<\/jats:p>","DOI":"10.3390\/a19040310","type":"journal-article","created":{"date-parts":[[2026,4,16]],"date-time":"2026-04-16T07:37:19Z","timestamp":1776325039000},"page":"310","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Traffic Flow Prediction in Intelligent Transportation Systems: A Comprehensive Review of Graph Neural Networks and Hybrid Deep Learning Methods"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-4050-359X","authenticated-orcid":false,"given":"Zhenhua","family":"Wang","sequence":"first","affiliation":[{"name":"College of Information Technology, Nanjing Police University, Nanjing 210023, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xinmeng","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Information Technology, Nanjing Police University, Nanjing 210023, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lijun","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Information, Guangdong Communication Polytechnic, Guangzhou 510650, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zheng","family":"Wu","sequence":"additional","affiliation":[{"name":"College of Information Technology, Nanjing Police University, Nanjing 210023, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jiangang","family":"Hu","sequence":"additional","affiliation":[{"name":"College of Public Security, Nanjing Police University, Nanjing 210023, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-6990-6701","authenticated-orcid":false,"given":"Fujiang","family":"Yuan","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology, Taiyuan Normal University, Jinzhong 030619, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-2962-6334","authenticated-orcid":false,"given":"Zhen","family":"Tian","sequence":"additional","affiliation":[{"name":"James Watt School of Engineering, University of Glasgow, Glasgow G12 8QQ, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,4,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1109\/MVT.2009.935537","article-title":"Intelligent transportation systems","volume":"5","author":"Dimitrakopoulos","year":"2010","journal-title":"IEEE Veh. Technol. Mag."},{"key":"ref_2","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_3","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_4","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1016\/j.trc.2015.03.014","article-title":"Long short-term memory neural network for traffic speed prediction using remote microwave sensor data","volume":"54","author":"Ma","year":"2015","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.trc.2017.02.024","article-title":"Deep learning for short-term traffic flow prediction","volume":"79","author":"Polson","year":"2017","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/j.trc.2014.01.005","article-title":"Short-term traffic forecasting: Where we are and where we\u2019re going","volume":"43","author":"Vlahogianni","year":"2014","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1016\/S0968-090X(02)00009-8","article-title":"Comparison of parametric and nonparametric models for traffic flow forecasting","volume":"10","author":"Smith","year":"2002","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1590\/2238-1031.jtl.v9n2a6","article-title":"Recent trends in intelligent transportation systems: A review","volume":"9","author":"Singh","year":"2015","journal-title":"J. Transp. Lit."},{"key":"ref_9","first-page":"1544","article-title":"A survey on modern deep neural network for traffic prediction: Trends, methods and challenges","volume":"34","author":"Tedjopurnomo","year":"2020","journal-title":"IEEE Trans. Knowl. Data Eng."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1709","DOI":"10.1109\/TITS.2025.3636070","article-title":"Evaluating Scenario-Based Decision-Making for Interactive Autonomous Driving Using Rational Criteria: A Survey","volume":"27","author":"Tian","year":"2025","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Liu, R., and Shin, S.Y. (2025). A Review of Traffic Flow Prediction Methods in Intelligent Transportation System Construction. Appl. Sci., 15.","DOI":"10.20944\/preprints202503.0643.v1"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Attioui, M., and Lahby, M. (2025). Congestion Forecasting Using Machine Learning Techniques: A Systematic Review. Future Transp., 5.","DOI":"10.3390\/futuretransp5030076"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"5079","DOI":"10.1007\/s13042-025-02560-w","article-title":"Deep learning for time series forecasting: A survey","volume":"36","author":"Kong","year":"2025","journal-title":"Int. J. Mach. Learn. Cybern."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"848","DOI":"10.1109\/OJITS.2025.3580802","article-title":"Overview of Traffic Flow Forecasting Techniques","volume":"6","author":"Carianni","year":"2025","journal-title":"IEEE Open J. Intell. Transp. Syst."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"9981657","DOI":"10.1155\/2024\/9981657","article-title":"Deep Learning Algorithms for Traffic Forecasting: A Comprehensive Review and Comparison with Classical Ones","volume":"2024","author":"Afandizadeh","year":"2024","journal-title":"J. Adv. Transp."},{"key":"ref_16","first-page":"200268","article-title":"A survey on traffic flow prediction and classification","volume":"20","author":"Gomes","year":"2023","journal-title":"Intell. Syst. Appl."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Mystakidis, A., Koukaras, P., and Tjortjis, C. (2025). Advances in Traffic Congestion Prediction: An Overview of Emerging Techniques and Methods. Smart Cities, 8.","DOI":"10.3390\/smartcities8010025"},{"key":"ref_18","first-page":"2379377","article-title":"Congestion boundary approach for phase transitions in traffic flow","volume":"12","author":"Lee","year":"2024","journal-title":"Transp. B Transp. Dyn."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"117710","DOI":"10.1016\/j.chaos.2025.117710","article-title":"Congestion transition in a heterogeneous ring road car-following model incorporating visual angle defect and speed limit effects","volume":"204","author":"Peng","year":"2026","journal-title":"Chaos Solitons Fractals"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"103361","DOI":"10.1016\/j.trb.2025.103361","article-title":"Road price and capacity policies subject to a fiscal constraint in a city","volume":"204","author":"Kono","year":"2026","journal-title":"Transp. Res. Part B Methodol."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"4339","DOI":"10.1109\/TITS.2018.2883485","article-title":"Cooperative shock waves mitigation in mixed traffic flow environment","volume":"20","author":"Fiengo","year":"2019","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"109","DOI":"10.3141\/2088-12","article-title":"Empirical study of behavioral theory of traffic flow: Analysis of recurrent bottleneck","volume":"2088","author":"Altun","year":"2008","journal-title":"Transp. Res. Rec."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"9367","DOI":"10.1109\/TPAMI.2025.3583357","article-title":"CNN2GNN: How to bridge cnn with gnn","volume":"47","author":"Jiao","year":"2025","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Fan, Y., Cui, C., Wang, Z., Qi, H., and Tian, Z. (2025). Graph Anomaly Detection Algorithm Based on Multi-View Heterogeneity Resistant Network. Information, 16.","DOI":"10.3390\/info16110985"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"129001","DOI":"10.1016\/j.neucom.2024.129001","article-title":"A multi-view GNN-based network representation learning framework for recommendation systems","volume":"619","author":"Amara","year":"2025","journal-title":"Neurocomputing"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Gilmer, J., Schoenholz, S.S., Riley, P.F., Vinyals, O., and Dahl, G.E. (2020). Message passing neural networks. Machine Learning Meets Quantum Physics, Springer.","DOI":"10.1007\/978-3-030-40245-7_10"},{"key":"ref_27","unstructured":"Kipf, T.N., and Welling, M. (2017, January 24\u201326). Semi-Supervised Classification with Graph Convolutional Networks. Proceedings of the International Conference on Learning Representations, Toulon, France."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"111184","DOI":"10.1016\/j.patcog.2024.111184","article-title":"Exploring Latent Transferability of feature components","volume":"160","author":"Wang","year":"2025","journal-title":"Pattern Recognit."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"764","DOI":"10.1109\/TMI.2025.3605162","article-title":"Teacher-Student Instance-level Adversarial Augmentation for Single Domain Generalized Medical Image Segmentation","volume":"45","author":"Wang","year":"2025","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"3154","DOI":"10.1021\/acs.jcim.4c02441","article-title":"DeePMD-GNN: A DeePMD-kit Plugin for External Graph Neural Network Potentials","volume":"65","author":"Zeng","year":"2025","journal-title":"J. Chem. Inf. Model."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"124744","DOI":"10.1016\/j.apenergy.2024.124744","article-title":"DEST-GNN: A double-explored spatio-temporal graph neural network for multi-site intra-hour PV power forecasting","volume":"378","author":"Yang","year":"2025","journal-title":"Appl. Energy"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"100665","DOI":"10.1109\/ACCESS.2021.3096877","article-title":"Adaptative balanced distribution for domain adaptation with strong alignment","volume":"9","author":"Wang","year":"2021","journal-title":"IEEE Access"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Graves, A., Mohamed, A.r., and Hinton, G. (2013). Speech recognition with deep recurrent neural networks. Proceedings of the 2013 IEEE International Conference on Acoustics, Speech and signal Processing, IEEE.","DOI":"10.1109\/ICASSP.2013.6638947"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1550","DOI":"10.1109\/5.58337","article-title":"Backpropagation through time: What it does and how to do it","volume":"78","author":"Werbos","year":"2002","journal-title":"Proc. IEEE"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Zheng, L., Wang, X., Li, F., Mao, Z., Tian, Z., Peng, Y., Yuan, F., and Yuan, C. (2025). A Mean-Field-Game-Integrated MPC-QP Framework for Collision-Free Multi-Vehicle Control. Drones, 9.","DOI":"10.20944\/preprints202504.1889.v1"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"125878","DOI":"10.1016\/j.eswa.2024.125878","article-title":"Predicting flow status of a flexible rectifier using cognitive computing","volume":"264","author":"Peng","year":"2025","journal-title":"Expert Syst. Appl."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"671","DOI":"10.1126\/science.220.4598.671","article-title":"Optimization by simulated annealing","volume":"220","author":"Kirkpatrick","year":"1983","journal-title":"Science"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"529","DOI":"10.1137\/1018105","article-title":"Adaptation in natural and artificial systems (John H. Holland)","volume":"18","author":"Sampson","year":"1976","journal-title":"SIAM Rev."},{"key":"ref_39","unstructured":"Fogel, L., Owens, A., and Walsh, M. (1966). Artificial Intelligence Through, Wiley."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1287\/inte.20.4.74","article-title":"Tabu search: A tutorial","volume":"20","author":"Glover","year":"1990","journal-title":"Interfaces"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1109\/4235.585892","article-title":"Ant colony system: A cooperative learning approach to the traveling salesman problem","volume":"1","author":"Dorigo","year":"1997","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"102146","DOI":"10.1016\/j.inffus.2023.102146","article-title":"Traffic flow matrix-based graph neural network with attention mechanism for traffic flow prediction","volume":"104","author":"Chen","year":"2024","journal-title":"Inf. Fusion"},{"key":"ref_43","unstructured":"Li, Y., Yu, R., Shahabi, C., and Liu, Y. (2017). Diffusion convolutional recurrent neural network: Data-driven traffic forecasting. arXiv."},{"key":"ref_44","unstructured":"Varaiya, P. (2004). Freeway Performance Measurement System (PeMS), UC Berkeley. [4th ed.]."},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Tan, P., Shi, W., Shi, Z., and Wang, Y. (2024). LSTDNet: A Long-Range Spatio-Temporal Decoupling Network for Traffic Prediction. Proceedings of the 2024 7th International Conference on Pattern Recognition and Artificial Intelligence (PRAI), IEEE.","DOI":"10.1109\/PRAI62207.2024.10826651"},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Pareek, P.K., Al-Fatlawy, R.R., Manasa, R., Varma, P.R.K., and Kotla, N.R.D. (2024). Traffic Flow Prediction in Intelligent Transportation using Spatial-Temporal Graph Convolution Attention Module. Proceedings of the 2024 First International Conference on Software, Systems and Information Technology (SSITCON), IEEE.","DOI":"10.1109\/SSITCON62437.2024.10795987"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"922","DOI":"10.1609\/aaai.v33i01.3301922","article-title":"Attention based spatial-temporal graph convolutional networks for traffic flow forecasting","volume":"Volume 33","author":"Guo","year":"2019","journal-title":"Proceedings of the AAAI Conference on Artificial Intelligence"},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Hou, Y., and Zhang, D. (2025). Graph Neural Network-Enhanced Multivariate Time Series Forecasting with Series-Core Fusion. Proceedings of the 2025 8th International Conference on Advanced Algorithms and Control Engineering (ICAACE), IEEE.","DOI":"10.1109\/ICAACE65325.2025.11019045"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1177\/0361198105191700113","article-title":"Improved dual-loop detection system for collecting real-time truck data","volume":"1917","author":"Zhang","year":"2005","journal-title":"Transp. Res. Rec."},{"key":"ref_50","doi-asserted-by":"crossref","unstructured":"Zhang, J., Zheng, Y., and Qi, D. (2017). Deep spatio-temporal residual networks for citywide crowd flows prediction. Proceedings of the AAAI Conference on Artificial Intelligence, AAAI Press.","DOI":"10.1609\/aaai.v31i1.10735"},{"key":"ref_51","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_52","unstructured":"Stoyanovich, J., Gilbride, M., and Moffitt, V.Z. (2017). Zooming in on NYC taxi data with Portal. arXiv."},{"key":"ref_53","doi-asserted-by":"crossref","unstructured":"Yao, H., Wu, F., Ke, J., Tang, X., Jia, Y., Lu, S., Gong, P., Ye, J., and Li, Z. (2018). Deep multi-view spatial-temporal network for taxi demand prediction. Proceedings of the AAAI Conference on Artificial Intelligence, AAAI Press.","DOI":"10.1609\/aaai.v32i1.11836"},{"key":"ref_54","first-page":"75354","article-title":"Largest: A benchmark dataset for large-scale traffic forecasting","volume":"36","author":"Liu","year":"2023","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"16283","DOI":"10.1038\/s41598-019-51539-5","article-title":"Understanding traffic capacity of urban networks","volume":"9","author":"Loder","year":"2019","journal-title":"Sci. Rep."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"1243","DOI":"10.1016\/j.trc.2010.12.007","article-title":"On the assessment of vehicle trajectory data accuracy and application to the Next Generation SIMulation (NGSIM) program data","volume":"19","author":"Punzo","year":"2011","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_57","doi-asserted-by":"crossref","unstructured":"Yuan, J., Zheng, Y., Zhang, C., Xie, W., Xie, X., Sun, G., and Huang, Y. (2010). T-drive: Driving directions based on taxi trajectories. Proceedings of the 18th SIGSPATIAL International Conference on Advances in Geographic Information Systems, Association for Computing Machinery.","DOI":"10.1145\/1869790.1869807"},{"key":"ref_58","first-page":"1273","article-title":"Communication-efficient learning of deep networks from decentralized data","volume":"54","author":"McMahan","year":"2017","journal-title":"Proc. Mach. Learn. Res."},{"key":"ref_59","doi-asserted-by":"crossref","unstructured":"Feng, J., Du, C., and Mu, Q. (2024). Traffic Flow Prediction Based on Federated Learning and Spatio-Temporal Graph Neural Networks. ISPRS Int. J.-Geo-Inf., 13.","DOI":"10.3390\/ijgi13060210"},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"1191","DOI":"10.1109\/TITS.2022.3179391","article-title":"Short-Term Traffic Flow Prediction Based on Graph Convolutional Networks and Federated Learning","volume":"24","author":"Xia","year":"2023","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"6420","DOI":"10.1109\/TKDE.2025.3607895","article-title":"Federated Graph Neural Networks With Equivalent Hypergraph Construction for Traffic Flow Prediction","volume":"37","author":"Wang","year":"2025","journal-title":"IEEE Trans. Knowl. Data Eng."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"102079","DOI":"10.1016\/j.inffus.2023.102079","article-title":"Spatial-temporal graph neural network traffic prediction based load balancing with reinforcement learning in cellular networks","volume":"103","author":"Liu","year":"2024","journal-title":"Inf. Fusion"},{"key":"ref_63","doi-asserted-by":"crossref","unstructured":"Wu, Z., Pan, S., Long, G., Jiang, J., and Zhang, C. (2019). Graph wavenet for deep spatial-temporal graph modeling. arXiv.","DOI":"10.24963\/ijcai.2019\/264"},{"key":"ref_64","first-page":"17804","article-title":"Adaptive graph convolutional recurrent network for traffic forecasting","volume":"33","author":"Bai","year":"2020","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"573","DOI":"10.1177\/03611981251318339","article-title":"Traffic Flow Prediction Based on Spatio-Temporal Aggregated Graph Neural Networks","volume":"2679","author":"Wu","year":"2025","journal-title":"Transp. Res. Rec."},{"key":"ref_66","doi-asserted-by":"crossref","unstructured":"Gu, J., Jia, Z., Cai, T., Song, X., and Mahmood, A. (2023). Dynamic Correlation Adjacency-Matrix-Based Graph Neural Networks for Traffic Flow Prediction. Sensors, 23.","DOI":"10.3390\/s23062897"},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"26800","DOI":"10.1038\/s41598-024-78335-0","article-title":"Spatio-temporal envolutional graph neural network for traffic flow prediction in UAV-based urban traffic monitoring system","volume":"14","author":"Ma","year":"2024","journal-title":"Sci. Rep."},{"key":"ref_68","doi-asserted-by":"crossref","unstructured":"Hu, S., Gu, J., and Li, S. (2025). Research on Urban Road Traffic Flow Prediction Based on Sa-Dynamic Graph Convolutional Neural Network. Mathematics, 13.","DOI":"10.3390\/math13030416"},{"key":"ref_69","doi-asserted-by":"crossref","unstructured":"Jiang, M., and Liu, Z. (2023). Traffic Flow Prediction Based on Dynamic Graph Spatial-Temporal Neural Network. Mathematics, 11.","DOI":"10.3390\/math11112528"},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"121101","DOI":"10.1016\/j.eswa.2023.121101","article-title":"Dynamic multi-graph neural network for traffic flow prediction incorporating traffic accidents","volume":"234","author":"Ye","year":"2023","journal-title":"Expert Syst. Appl."},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"124430","DOI":"10.1016\/j.eswa.2024.124430","article-title":"Adaptive graph neural network for traffic flow prediction considering time variation","volume":"255","author":"Chen","year":"2024","journal-title":"Expert Syst. Appl."},{"key":"ref_72","doi-asserted-by":"crossref","unstructured":"Vrahatis, A.G., Lazaros, K., and Kotsiantis, S. (2024). Graph attention networks: A comprehensive review of methods and applications. Future Internet, 16.","DOI":"10.3390\/fi16090318"},{"key":"ref_73","doi-asserted-by":"crossref","first-page":"810","DOI":"10.1016\/j.jfa.2008.11.001","article-title":"Ricci curvature of Markov chains on metric spaces","volume":"256","author":"Ollivier","year":"2009","journal-title":"J. Funct. Anal."},{"key":"ref_74","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1142\/S0218126624502736","article-title":"Road Network Traffic Flow Prediction Method Based on Graph Attention Networks","volume":"33","author":"Wang","year":"2024","journal-title":"J. Circuits Syst. Comput."},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"386","DOI":"10.1109\/TITS.2023.3306559","article-title":"GMHANN: A Novel Traffic Flow Prediction Method for Transportation Management Based on Spatial-Temporal Graph Modeling","volume":"25","author":"Wang","year":"2024","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1016\/j.ins.2021.07.007","article-title":"Dynamic graph convolutional network for long-term traffic flow prediction with reinforcement learning","volume":"578","author":"Peng","year":"2021","journal-title":"Inf. Sci."},{"key":"ref_77","doi-asserted-by":"crossref","first-page":"47469","DOI":"10.1109\/ACCESS.2023.3257221","article-title":"Traffic Flow Prediction Based on Information Aggregation and Comprehensive Temporal-Spatial Synchronous Graph Neural Network","volume":"11","author":"Cheng","year":"2023","journal-title":"IEEE Access"},{"key":"ref_78","doi-asserted-by":"crossref","unstructured":"Han, X., Zhu, G., Zhao, L., Du, R., Wang, Y., Chen, Z., Liu, Y., and He, S. (2023). Ollivier-Ricci Curvature Based Spatio-Temporal Graph Neural Networks for Traffic Flow Forecasting. Symmetry, 15.","DOI":"10.3390\/sym15050995"},{"key":"ref_79","first-page":"81","article-title":"Channel attention-based spatial-temporal graph neural networks for traffic prediction","volume":"58","author":"Wang","year":"2024","journal-title":"Data Technol. Appl."},{"key":"ref_80","doi-asserted-by":"crossref","first-page":"102513","DOI":"10.1016\/j.displa.2023.102513","article-title":"RL-GCN: Traffic flow prediction based on graph convolution and reinforcement for smart cities","volume":"80","author":"Xing","year":"2023","journal-title":"Displays"},{"key":"ref_81","doi-asserted-by":"crossref","first-page":"4443","DOI":"10.1109\/TITS.2023.3329489","article-title":"Network-Wide Traffic Flow Dynamics Prediction Leveraging Macroscopic Traffic Flow Model and Deep Neural Networks","volume":"25","author":"Yang","year":"2024","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_82","doi-asserted-by":"crossref","first-page":"27476","DOI":"10.1038\/s41598-025-10794-5","article-title":"An efficient intelligent transportation system for traffic flow prediction using meta-temporal hyperbolic quantum graph neural networks","volume":"15","author":"Rajagopal","year":"2025","journal-title":"Sci. Rep."},{"key":"ref_83","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1016\/j.neunet.2021.05.035","article-title":"IGAGCN: Information geometry and attention-based spatiotemporal graph convolutional networks for traffic flow prediction","volume":"143","author":"An","year":"2021","journal-title":"Neural Netw."},{"key":"ref_84","doi-asserted-by":"crossref","first-page":"103251","DOI":"10.1016\/j.tre.2023.103251","article-title":"TS-STNN: Spatial-temporal neural network based on tree structure for traffic flow prediction","volume":"177","author":"Lv","year":"2023","journal-title":"Transp. Res. Part-E-Logist. Transp. Rev."},{"key":"ref_85","doi-asserted-by":"crossref","first-page":"34758","DOI":"10.1038\/s41598-025-18472-2","article-title":"A hybrid support vector machine and neural network model with fuzzy logic fusion for smart city traffic prediction","volume":"15","author":"Abbas","year":"2025","journal-title":"Sci. Rep."},{"key":"ref_86","doi-asserted-by":"crossref","first-page":"380","DOI":"10.5755\/j01.itc.54.2.39228","article-title":"A Prediction Method for Highway Traffic Flow Based on the IHPO-VMD-LSTM-Informer Model","volume":"54","author":"Wang","year":"2025","journal-title":"Inf. Technol. Control"},{"key":"ref_87","doi-asserted-by":"crossref","unstructured":"Vo, H.H.P., Nguyen, T.M., Bui, K.A., and Yoo, M. (2024). Traffic Flow Prediction in 5G-Enabled Intelligent Transportation Systems Using Parameter Optimization and Adaptive Model Selection. Sensors, 24.","DOI":"10.3390\/s24206529"},{"key":"ref_88","doi-asserted-by":"crossref","unstructured":"Zhou, R., Qiu, S., Li, M., Meng, S., and Zhang, Q. (2024). Short-Term Air Traffic Flow Prediction Based on CEEMD-LSTM of Bayesian Optimization and Differential Processing. Electronics, 13.","DOI":"10.3390\/electronics13101896"},{"key":"ref_89","doi-asserted-by":"crossref","unstructured":"Zhao, Z., Yuan, J., and Chen, L. (2024). Air Traffic Flow Management Delay Prediction Based on Feature Extraction and an Optimization Algorithm. Aerospace, 11.","DOI":"10.3390\/aerospace11020168"},{"key":"ref_90","doi-asserted-by":"crossref","first-page":"467","DOI":"10.1016\/j.aej.2023.05.015","article-title":"Short-term traffic flow prediction: An ensemble machine learning approach","volume":"74","author":"Dai","year":"2023","journal-title":"Alex. Eng. J."},{"key":"ref_91","doi-asserted-by":"crossref","unstructured":"Dong, Z., Zhou, Y., and Bao, X. (2024). A Short-Term Vessel Traffic Flow Prediction Based on a DBO-LSTM Model. Sustainability, 16.","DOI":"10.3390\/su16135499"},{"key":"ref_92","doi-asserted-by":"crossref","first-page":"e2215","DOI":"10.1002\/met.2215","article-title":"Pre-tactical convection prediction for air traffic flow management using LSTM neural network","volume":"31","author":"Jardines","year":"2024","journal-title":"Meteorol. Appl."},{"key":"ref_93","doi-asserted-by":"crossref","unstructured":"Guo, C., Zhu, J., and Wang, X. (2024). MVHS-LSTM: The Comprehensive Traffic Flow Prediction Based on Improved LSTM via Multiple Variables Heuristic Selection. Appl.-Sci., 14.","DOI":"10.3390\/app14072959"},{"key":"ref_94","doi-asserted-by":"crossref","unstructured":"Fu, F., Wang, D., Sun, M., Xie, R., and Cai, Z. (2024). Urban Traffic Flow Prediction Based on Bayesian Deep Learning Considering Optimal Aggregation Time Interval. Sustainability, 16.","DOI":"10.3390\/su16051818"},{"key":"ref_95","doi-asserted-by":"crossref","first-page":"12377","DOI":"10.1007\/s13369-023-08672-1","article-title":"A Deep Ensemble Approach for Long-Term Traffic Flow Prediction","volume":"49","author":"Cini","year":"2024","journal-title":"Arab. J. Sci. Eng."},{"key":"ref_96","doi-asserted-by":"crossref","unstructured":"Zhuang, W., and Cao, Y. (2023). Short-Term Traffic Flow Prediction Based on a K-Nearest Neighbor and Bidirectional Long Short-Term Memory Model. APplied Sci., 13.","DOI":"10.3390\/app13042681"},{"key":"ref_97","first-page":"216","article-title":"Multivariate Congestion Prediction using Stacked LSTM Autoencoder based Bidirectional LSTM Model","volume":"17","author":"Vijayalakshmi","year":"2023","journal-title":"KSII Trans. Internet Inf. Syst."},{"key":"ref_98","doi-asserted-by":"crossref","first-page":"126436","DOI":"10.1109\/ACCESS.2023.3330909","article-title":"Research on Regional Traffic Flow Prediction Based on MGCN-WOALSTM","volume":"11","author":"Cao","year":"2023","journal-title":"IEEE Access"},{"key":"ref_99","doi-asserted-by":"crossref","first-page":"58516","DOI":"10.1109\/ACCESS.2023.3270395","article-title":"Urban Traffic Flow Estimation System Based on Gated Recurrent Unit Deep Learning Methodology for Internet of Vehicles","volume":"11","author":"Hussain","year":"2023","journal-title":"IEEE Access"},{"key":"ref_100","doi-asserted-by":"crossref","unstructured":"Lan, T., Zhang, X., Qu, D., Yang, Y., and Chen, Y. (2023). Short-Term Traffic Flow Prediction Based on the Optimization Study of Initial Weights of the Attention Mechanism. Sustainability, 15.","DOI":"10.3390\/su15021374"},{"key":"ref_101","doi-asserted-by":"crossref","first-page":"80448","DOI":"10.1109\/ACCESS.2023.3299849","article-title":"Research on Tool Remaining Life Prediction Method Based on CNN-LSTM-PSO","volume":"11","author":"Wang","year":"2023","journal-title":"IEEE Access"},{"key":"ref_102","doi-asserted-by":"crossref","first-page":"1332","DOI":"10.1109\/TITS.2019.2939290","article-title":"An Improved Bayesian Combination Model for Short-Term Traffic Prediction With Deep Learning","volume":"21","author":"Gu","year":"2020","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_103","doi-asserted-by":"crossref","first-page":"e3224","DOI":"10.7717\/peerj-cs.3224","article-title":"Enhanced congestion prediction of traffic flow using a hybrid attention-based deep learning model","volume":"11","author":"Aburasain","year":"2025","journal-title":"PeerJ Comput. Sci."},{"key":"ref_104","doi-asserted-by":"crossref","unstructured":"Jia, X., Qu, J., Lyu, Y., Guo, M., Zhang, J., and Guo, F. (2025). A Prediction-Based Anomaly Detection Method for Traffic Flow Data with Multi-Domain Feature Extraction. Appl. Sci., 15.","DOI":"10.3390\/app15063234"},{"key":"ref_105","doi-asserted-by":"crossref","first-page":"41816","DOI":"10.1109\/ACCESS.2023.3270889","article-title":"Transformer Based Traffic Flow Forecasting in SDN-VANET","volume":"11","author":"Shuvro","year":"2023","journal-title":"IEEE Access"},{"key":"ref_106","doi-asserted-by":"crossref","first-page":"3","DOI":"10.4018\/JDM.325353","article-title":"TransFusion Model Fusion Mechanism Based on Transformer for Traffic Flow Prediction","volume":"34","author":"Song","year":"2023","journal-title":"J. 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