{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T17:37:16Z","timestamp":1762364236810,"version":"build-2065373602"},"reference-count":39,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T00:00:00Z","timestamp":1762300800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["52432010","52372314","52202399"],"award-info":[{"award-number":["52432010","52372314","52202399"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Systems"],"abstract":"<jats:p>Long-sequence traffic flow forecasting plays a crucial role in intelligent transportation systems. However, existing Transformer-based approaches face a quadratic complexity bottleneck in computation and are prone to over-smoothing in deep architectures. This results in overly averaged predictions that fail to capture the peaks and troughs of traffic flow. To address these issues, we propose a State-Space Generative Adversarial Network (SSGAN) with a state-space generator and a multi-scale convolutional discriminator. Specifically, a bidirectional Mamba-2 model was designed as the generator to leverage the linear complexity and efficient forecasting capability of state-space models for long-sequence modeling. Meanwhile, the discriminator incorporates a multi-scale convolutional structure to extract traffic features from the frequency domain, thereby capturing flow patterns across different scales, alleviating the over-smoothing issue and enhancing discriminative ability. Through adversarial training, the model is able to better approximate the true distribution of traffic flow. Experiments conducted on four real-world public traffic flow datasets demonstrate that the proposed method outperformed the baselines in both forecasting accuracy and computational efficiency.<\/jats:p>","DOI":"10.3390\/systems13110991","type":"journal-article","created":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T17:06:06Z","timestamp":1762362366000},"page":"991","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["State-Space and Multi-Scale Convolutional Generative Adversarial Network for Traffic Flow Forecasting"],"prefix":"10.3390","volume":"13","author":[{"given":"Wenxie","family":"Lin","sequence":"first","affiliation":[{"name":"School of Transportation, Southeast University, Jiulonghu Campus, Nanjing 211100, China"},{"name":"Jiangsu Key Laboratory of Urban ITS, Jiangsu Province Collaborative Innovation Center of Modern Urban Traffic Technologies, Nanjing 211100, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhe","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Transportation, Southeast University, Jiulonghu Campus, Nanjing 211100, China"},{"name":"Jiangsu Key Laboratory of Urban ITS, Jiangsu Province Collaborative Innovation Center of Modern Urban Traffic Technologies, Nanjing 211100, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yangzhen","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Transportation, Southeast University, Jiulonghu Campus, Nanjing 211100, China"},{"name":"Jiangsu Key Laboratory of Urban ITS, Jiangsu Province Collaborative Innovation Center of Modern Urban Traffic Technologies, Nanjing 211100, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-7231-3368","authenticated-orcid":false,"given":"Jinyu","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Transportation, Southeast University, Jiulonghu Campus, Nanjing 211100, China"},{"name":"Jiangsu Key Laboratory of Urban ITS, Jiangsu Province Collaborative Innovation Center of Modern Urban Traffic Technologies, Nanjing 211100, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gang","family":"Ren","sequence":"additional","affiliation":[{"name":"School of Transportation, Southeast University, Jiulonghu Campus, Nanjing 211100, China"},{"name":"Jiangsu Key Laboratory of Urban ITS, Jiangsu Province Collaborative Innovation Center of Modern Urban Traffic Technologies, Nanjing 211100, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,11,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"114187","DOI":"10.1016\/j.knosys.2025.114187","article-title":"Interaction-Aware Vehicle Trajectory Prediction Using Spatial-Temporal Dynamic Graph Neural Network","volume":"327","author":"Wang","year":"2025","journal-title":"Knowl.-Based Syst."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"103656","DOI":"10.1016\/j.tre.2024.103656","article-title":"A data-driven optimization-based approach for freeway traffic state estimation based on heterogeneous sensor data fusion","volume":"189","author":"Zhang","year":"2024","journal-title":"Transp. Res. Part E Logist. Transp. Rev."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"104105","DOI":"10.1016\/j.tre.2025.104105","article-title":"Prescriptive analytics for freeway traffic state estimation by multi-source data fusion","volume":"198","author":"Huang","year":"2025","journal-title":"Transp. Res. Part E Logist. Transp. Rev."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"108121","DOI":"10.1016\/j.aap.2025.108121","article-title":"Safety and efficiency-oriented adaptive strategy controls for connected and automated vehicles in unstable communication environment","volume":"220","author":"Zhao","year":"2025","journal-title":"Accid. Anal. Prev."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"103611","DOI":"10.1016\/j.tre.2024.103611","article-title":"A novel ranking method based on semi-SPO for battery swapping allocation optimization in a hybrid electric transit system","volume":"188","author":"Huang","year":"2024","journal-title":"Transp. Res. Part E Logist. Transp. Rev."},{"key":"ref_6","first-page":"5999","article-title":"Attention is all you need","volume":"30","author":"Vaswani","year":"2017","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref_7","unstructured":"Zhou, T., Ma, Z., Wen, Q., Wang, X., Sun, L., and Jin, R. (2022, January 23\u201329). Fedformer: Frequency enhanced decomposed transformer for long-term series forecasting. Proceedings of the International Conference on Machine Learning, Honolulu, HI, USA."},{"key":"ref_8","unstructured":"Zhang, Y., and Yan, J. (2023, January 1\u20135). Crossformer: Transformer utilizing cross-dimension dependency for multivariate time series forecasting. Proceedings of the Eleventh International Conference on Learning Representations, Kigali, Rwanda."},{"key":"ref_9","unstructured":"Nie, Y., Nguyen, N.H., Sinthong, P., and Kalagnanam, J. (2023, January 1\u20135). A Time Series is Worth 64 Words: Long-term Forecasting with Transformers. Proceedings of the Eleventh International Conference on Learning Representations, Kigali, Rwanda."},{"key":"ref_10","unstructured":"Liu, Y., Hu, T., Zhang, H., Wu, H., Wang, S., Ma, L., and Long, M. (2024, January 7\u201311). iTransformer: Inverted Transformers Are Effective for Time Series Forecasting. Proceedings of the Twelfth International Conference on Learning Representations, Vienna, Austria."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"111637","DOI":"10.1016\/j.knosys.2024.111637","article-title":"LSTTN: A long-short term transformer-based spatiotemporal neural network for traffic flow forecasting","volume":"293","author":"Luo","year":"2024","journal-title":"Knowl. Based Syst."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"120648","DOI":"10.1016\/j.ins.2024.120648","article-title":"A multi-channel spatial-temporal transformer model for traffic flow forecasting","volume":"671","author":"Xiao","year":"2024","journal-title":"Inf. Sci."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Fang, Y., Liang, Y., Hui, B., Shao, Z., Deng, L., Liu, X., Jiang, X., and Zheng, K. (2025, January 3\u20137). Efficient large-scale traffic forecasting with transformers: A spatial data management perspective. Proceedings of the 31st ACM SIGKDD Conference on Knowledge Discovery and Data Mining V. 1, Toronto, ON, Canada.","DOI":"10.1145\/3690624.3709177"},{"key":"ref_14","first-page":"21297","article-title":"Soft: Softmax-free transformer with linear complexity","volume":"34","author":"Lu","year":"2021","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref_15","first-page":"1474","article-title":"Hippo: Recurrent memory with optimal polynomial projections","volume":"33","author":"Gu","year":"2020","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref_16","unstructured":"Gu, A., Goel, K., and R\u00e9, C. (2021). Efficiently modeling long sequences with structured state spaces. arXiv."},{"key":"ref_17","unstructured":"Gu, A., and Dao, T. (2023). Mamba: Linear-time sequence modeling with selective state spaces. arXiv."},{"key":"ref_18","unstructured":"Dao, T., and Gu, A. (2024). Transformers are SSMs: Generalized models and efficient algorithms through structured state space duality. arXiv."},{"key":"ref_19","first-page":"20743","article-title":"Hierarchical classification auxiliary network for time series forecasting","volume":"39","author":"Sun","year":"2025","journal-title":"Proc. AAAI Conf. Artif. Intell."},{"key":"ref_20","first-page":"1","article-title":"Generative adversarial nets","volume":"27","author":"Goodfellow","year":"2014","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Wen, Q., Zhou, T., Zhang, C., Chen, W., Ma, Z., Yan, J., and Sun, L. (2023, January 19\u201325). Transformers in time series: A survey. Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence, Macao, China.","DOI":"10.24963\/ijcai.2023\/759"},{"key":"ref_22","first-page":"11121","article-title":"Are transformers effective for time series forecasting?","volume":"37","author":"Zeng","year":"2023","journal-title":"Proc. AAAI Conf. Artif. Intell."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1869","DOI":"10.1109\/TASE.2021.3077537","article-title":"A hybrid prediction method for realistic network traffic with temporal convolutional network and LSTM","volume":"19","author":"Bi","year":"2021","journal-title":"IEEE Trans. Autom. Sci. Eng."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Eldele, E., Ragab, M., Chen, Z., Wu, M., and Li, X. (2024). TSLANet: Rethinking transformers for time series representation learning. arXiv.","DOI":"10.1109\/TAI.2024.3430236"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"111986","DOI":"10.1016\/j.knosys.2024.111986","article-title":"MDCNet: Long-term time series forecasting with mode decomposition and 2D convolution","volume":"299","author":"Su","year":"2024","journal-title":"Knowl.-Based Syst."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"107897","DOI":"10.1016\/j.neunet.2025.107897","article-title":"Enhancing intelligent transportation systems with a more efficient model for long-term traffic predictions based on an attention mechanism and a residual temporal convolutional network","volume":"192","author":"Reza","year":"2025","journal-title":"Neural Netw."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Lee, M., Yoon, H., and Kang, M. (2025). CASA: CNN Autoencoder-based Score Attention for Efficient Multivariate Long-term Time-series Forecasting. arXiv.","DOI":"10.24963\/ijcai.2025\/619"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"129178","DOI":"10.1016\/j.neucom.2024.129178","article-title":"Is mamba effective for time series forecasting?","volume":"619","author":"Wang","year":"2025","journal-title":"Neurocomputing"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"112875","DOI":"10.1016\/j.knosys.2024.112875","article-title":"MGCN: Mamba-integrated spatiotemporal graph convolutional network for long-term traffic forecasting","volume":"309","author":"Lin","year":"2025","journal-title":"Knowl.-Based Syst."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"113416","DOI":"10.1016\/j.knosys.2025.113416","article-title":"iTransMamba: A lightweight spatio-temporal network based on long-term traffic flow forecasting","volume":"317","author":"Cao","year":"2025","journal-title":"Knowl.-Based Syst."},{"key":"ref_31","unstructured":"Hamad, M., Mabrok, M., and Zorba, N. (2025). MCST-Mamba: Multivariate Mamba-Based Model for Traffic Prediction. arXiv."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"103495","DOI":"10.1016\/j.inffus.2025.103495","article-title":"ST-Camba: A decoupled-free spatiotemporal graph fusion state space model with linear complexity for efficient traffic forecasting","volume":"126","author":"Wang","year":"2025","journal-title":"Inf. Fusion"},{"key":"ref_33","first-page":"552","article-title":"SATP-GAN: Self-attention based generative adversarial network for traffic flow prediction","volume":"9","author":"Zhang","year":"2021","journal-title":"Transp. B Transp. Dyn."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"108990","DOI":"10.1016\/j.knosys.2022.108990","article-title":"TFGAN: Traffic forecasting using generative adversarial network with multi-graph convolutional network","volume":"249","author":"Khaled","year":"2022","journal-title":"Knowl.-Based Syst."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Zhang, Z., Cao, Q., Lin, W., Song, J., Chen, W., and Ren, G. (2024). Estimation of arterial path flow considering flow distribution consistency: A data-driven semi-supervised method. Systems, 12.","DOI":"10.3390\/systems12110507"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"96","DOI":"10.3141\/1748-12","article-title":"Freeway performance measurement system: Mining loop detector data","volume":"1748","author":"Chen","year":"2001","journal-title":"Transp. Res. Rec."},{"key":"ref_37","unstructured":"Das, A., Kong, W., Leach, A., Mathur, S., Sen, R., and Yu, R. (2023). Long-term forecasting with tide: Time-series dense encoder. arXiv."},{"key":"ref_38","unstructured":"Li, Z., Qi, S., Li, Y., and Xu, Z. (2023). Revisiting long-term time series forecasting: An investigation on linear mapping. arXiv."},{"key":"ref_39","unstructured":"Wu, H., Hu, T., Liu, Y., Zhou, H., Wang, J., and Long, M. (2023, January 1\u20135). TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis. Proceedings of the Eleventh International Conference on Learning Representations, Kigali, Rwanda."}],"container-title":["Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-8954\/13\/11\/991\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T17:32:58Z","timestamp":1762363978000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-8954\/13\/11\/991"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,11,5]]},"references-count":39,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2025,11]]}},"alternative-id":["systems13110991"],"URL":"https:\/\/doi.org\/10.3390\/systems13110991","relation":{},"ISSN":["2079-8954"],"issn-type":[{"value":"2079-8954","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,11,5]]}}}