{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,2]],"date-time":"2026-03-02T22:49:15Z","timestamp":1772491755828,"version":"3.50.1"},"reference-count":56,"publisher":"Springer Science and Business Media LLC","issue":"7","license":[{"start":{"date-parts":[[2025,5,7]],"date-time":"2025-05-07T00:00:00Z","timestamp":1746576000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,5,7]],"date-time":"2025-05-07T00:00:00Z","timestamp":1746576000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"name":"Sichuan Provincial Key Laboratory of Philosophy and Social Science for Language Intelligence in Special Education","award":["YYZN-2024-4"],"award-info":[{"award-number":["YYZN-2024-4"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Supercomput"],"DOI":"10.1007\/s11227-025-07328-1","type":"journal-article","created":{"date-parts":[[2025,5,7]],"date-time":"2025-05-07T11:14:57Z","timestamp":1746616497000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["MapsTSF: efficient traffic prediction via hybrid Mamba 2-transformer spatiotemporal modeling and cross adaptive periodic sparse forecasting"],"prefix":"10.1007","volume":"81","author":[{"given":"Bing","family":"Wang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chaoqi","family":"Cai","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xingpeng","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chunlan","family":"Zhao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chi","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Youming","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,5,7]]},"reference":[{"issue":"2194","key":"7328_CR1","doi-asserted-by":"publisher","first-page":"20200209","DOI":"10.1098\/rsta.2020.0209","volume":"379","author":"B Lim","year":"2021","unstructured":"Lim B, Zohren S (2021) Time-series forecasting with deep learning: a survey. Phil Trans R Soc A 379(2194):20200209","journal-title":"Phil Trans R Soc A"},{"key":"7328_CR2","doi-asserted-by":"publisher","first-page":"106181","DOI":"10.1016\/j.asoc.2020.106181","volume":"90","author":"OB Sezer","year":"2020","unstructured":"Sezer OB, Gudelek MU, Ozbayoglu AM (2020) Financial time series forecasting with deep learning: a systematic literature review: 2005\u20132019. Appl Soft Comput 90:106181","journal-title":"Appl Soft Comput"},{"issue":"1","key":"7328_CR3","doi-asserted-by":"publisher","first-page":"13","DOI":"10.1186\/s43067-023-00081-6","volume":"10","author":"SA Sayed","year":"2023","unstructured":"Sayed SA, Abdel-Hamid Y, Hefny HA (2023) Artificial intelligence-based traffic flow prediction: a comprehensive review. J Electr Syst Inf Technol 10(1):13","journal-title":"J Electr Syst Inf Technol"},{"key":"7328_CR4","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/s40537-021-00542-7","volume":"8","author":"NAM Razali","year":"2021","unstructured":"Razali NAM, Shamsaimon N, Ishak KK, Ramli S, Amran MFM, Sukardi S (2021) Gap, techniques and evaluation: traffic flow prediction using machine learning and deep learning. J Big Data 8:1\u201325","journal-title":"J Big Data"},{"key":"7328_CR5","first-page":"17766","volume":"33","author":"D Cao","year":"2020","unstructured":"Cao D, Wang Y, Duan J, Zhang C, Zhu X, Huang C, Tong Y, Xu B, Bai J, Tong J et al (2020) Spectral temporal graph neural network for multivariate time-series forecasting. Adv Neural Inf Process Syst 33:17766\u201317778","journal-title":"Adv Neural Inf Process Syst"},{"key":"7328_CR6","doi-asserted-by":"crossref","unstructured":"Diao Z, Wang X, Zhang D, Liu Y, Xie K, He S (2019) Dynamic spatial-temporal graph convolutional neural networks for traffic forecasting. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol 33, pp 890\u2013897","DOI":"10.1609\/aaai.v33i01.3301890"},{"key":"7328_CR7","doi-asserted-by":"crossref","unstructured":"Li M, Zhu Z (2021) Spatial-temporal fusion graph neural networks for traffic flow forecasting. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol 35, pp 4189\u20134196","DOI":"10.1609\/aaai.v35i5.16542"},{"key":"7328_CR8","doi-asserted-by":"crossref","unstructured":"Zhou H, Zhang S, Peng J, Zhang S, Li J, Xiong H, Zhang W (2021) Informer: beyond efficient transformer for long sequence time-series forecasting. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol 35, pp 11106\u201311115","DOI":"10.1609\/aaai.v35i12.17325"},{"key":"7328_CR9","unstructured":"Zhou T, Ma Z, Wen Q, Wang X, Sun L, Jin R (2022) Fedformer: frequency enhanced decomposed transformer for long-term series forecasting. In: International Conference on Machine Learning, PMLR. pp 27268\u201327286"},{"key":"7328_CR10","unstructured":"Vaswani A (2017) Attention is all you need. In: Advances in Neural Information Processing Systems"},{"key":"7328_CR11","doi-asserted-by":"crossref","unstructured":"Guo S, Lin Y, Feng N, Song C, Wan H (2019) Attention based spatial-temporal graph convolutional networks for traffic flow forecasting. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol 33, pp 922\u2013929","DOI":"10.1609\/aaai.v33i01.3301922"},{"key":"7328_CR12","unstructured":"Liu S, Yu H, Liao C, Li J, Lin W, Liu AX, Dustdar S (2022) Pyraformer: low-complexity pyramidal attention for long-range time series modeling and forecasting. In: International Conference on Learning Representations"},{"key":"7328_CR13","doi-asserted-by":"crossref","unstructured":"Cui Y, Xie J, Zheng K (2021) Historical inertia: a neglected but powerful baseline for long sequence time-series forecasting. In: Proceedings of the 30th ACM International Conference on Information & Knowledge Management, pp 2965\u20132969","DOI":"10.1145\/3459637.3482120"},{"key":"7328_CR14","doi-asserted-by":"crossref","unstructured":"Cirstea RG, Yang B, Guo C, Kieu T, Pan S (2022) Towards spatio-temporal aware traffic time series forecasting. In: 2022 IEEE 38th International Conference on Data Engineering (ICDE), IEEE. pp 2900\u20132913","DOI":"10.1109\/ICDE53745.2022.00262"},{"key":"7328_CR15","first-page":"22419","volume":"34","author":"H Wu","year":"2021","unstructured":"Wu H, Xu J, Wang J, Long M (2021) Autoformer: decomposition transformers with auto-correlation for long-term series forecasting. Adv Neural Inf Process Syst 34:22419\u201322430","journal-title":"Adv Neural Inf Process Syst"},{"key":"7328_CR16","unstructured":"Gu A, Goel K, R\u00e9 C (2021) Efficiently modeling long sequences with structured state spaces. arXiv preprint arXiv:2111.00396"},{"key":"7328_CR17","unstructured":"Gu A, Dao T (2023) Mamba: linear-time sequence modeling with selective state spaces. arXiv preprint arXiv:2312.00752 (2023)"},{"key":"7328_CR18","unstructured":"Dao T, Gu A (2024) Transformers are SSMS: generalized models and efficient algorithms through structured state space duality. In: Forty-first International Conference on Machine Learning"},{"key":"7328_CR19","unstructured":"Zivot E, Wang J (2006) Vector autoregressive models for multivariate time series. In: Modeling financial time series with S-PLUS\u00ae, pp 385\u2013429"},{"key":"7328_CR20","doi-asserted-by":"crossref","unstructured":"M\u00fcller KR, Smola AJ, R\u00e4tsch G, Sch\u00f6lkopf B, Kohlmorgen J, Vapnik V (1997) Predicting time series with support vector machines. In: International Conference on Artificial Neural Networks, Springer, pp 999\u20131004","DOI":"10.1007\/BFb0020283"},{"key":"7328_CR21","unstructured":"Sutskever I (2024) Sequence to sequence learning with neural net-works. In: Advances in Neural Information Processing, p 3104"},{"key":"7328_CR22","doi-asserted-by":"crossref","unstructured":"Wu Z, Pan S, Long G, Jiang J, Zhang C (2019) Graph wavenet for deep spatial-temporal graph modeling. In: Proceedings of the 28th International Joint Conference on Artificial Intelligence, pp 1907\u20131913","DOI":"10.24963\/ijcai.2019\/264"},{"key":"7328_CR23","unstructured":"Li Y, Yu R, Shahabi C, Liu Y (2018) Diffusion convolutional recurrent neural network: data-driven traffic forecasting. In: International Conference on Learning Representations"},{"key":"7328_CR24","doi-asserted-by":"crossref","unstructured":"Yu B, Yin H, Zhu Z (2018) Spatio-temporal graph convolutional networks: a deep learning framework for traffic forecasting. In: Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence. International Joint Conferences on Artificial Intelligence Organization","DOI":"10.24963\/ijcai.2018\/505"},{"key":"7328_CR25","first-page":"17804","volume":"33","author":"L Bai","year":"2020","unstructured":"Bai L, Yao L, Li C, Wang X, Wang C (2020) Adaptive graph convolutional recurrent network for traffic forecasting. Adv Neural Inf Process Syst 33:17804\u201317815","journal-title":"Adv Neural Inf Process Syst"},{"key":"7328_CR26","unstructured":"Shang C, Chen J (2021) Discrete graph structure learning for forecasting multiple time series. In: Proceedings of International Conference on Learning Representations"},{"key":"7328_CR27","doi-asserted-by":"crossref","unstructured":"Wu Z, Pan S, Long G, Jiang J, Chang X, Zhang C (2020) Connecting the dots: multivariate time series forecasting with graph neural networks. In: Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, pp 753\u2013763","DOI":"10.1145\/3394486.3403118"},{"key":"7328_CR28","doi-asserted-by":"crossref","unstructured":"Song C, Lin Y, Guo S, Wan H (2020) Spatial-temporal synchronous graph convolutional networks: a new framework for spatial-temporal network data forecasting. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol 34, pp 914\u2013921","DOI":"10.1609\/aaai.v34i01.5438"},{"key":"7328_CR29","doi-asserted-by":"crossref","unstructured":"Deng J, Chen X, Jiang R, Song X, Tsang IW (2021) St-norm: spatial and temporal normalization for multi-variate time series forecasting. In: Proceedings of the 27th ACM SIGKDD Conference on Knowledge Discovery & Data Mining, pp 269\u2013278","DOI":"10.1145\/3447548.3467330"},{"key":"7328_CR30","doi-asserted-by":"crossref","unstructured":"Shao Z, Zhang Z, Wang F, Wei W, Xu Y (2022) Spatial-temporal identity: a simple yet effective baseline for multivariate time series forecasting. In: Proceedings of the 31st ACM International Conference on Information & Knowledge Management, pp 4454\u20134458","DOI":"10.1145\/3511808.3557702"},{"key":"7328_CR31","unstructured":"Lan S, Ma Y, Huang W, Wang W, Yang H, Li P (2022) DSTAGNN: dynamic spatial-temporal aware graph neural network for traffic flow forecasting. In: International Conference on Machine Learning, PMLR, pp 11906\u201311917"},{"key":"7328_CR32","doi-asserted-by":"crossref","unstructured":"Zheng C, Fan X, Wang C, Qi J (2020) GMAN: a graph multi-attention network for traffic prediction. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol 34, pp 1234\u20131241","DOI":"10.1609\/aaai.v34i01.5477"},{"key":"7328_CR33","doi-asserted-by":"crossref","unstructured":"Jiang J, Han C, Zhao WX, Wang J (2023) PDFormer: propagation delay-aware dynamic long-range transformer for traffic flow prediction. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol 37, pp 4365\u20134373","DOI":"10.1609\/aaai.v37i4.25556"},{"key":"7328_CR34","doi-asserted-by":"crossref","unstructured":"Wang C, Hu J, Tian R, Gao X, Ma Z (2023) ISTnet: inception spatial temporal transformer for traffic prediction. In: International Conference on Database Systems for Advanced Applications, Springer, pp 414\u2013430","DOI":"10.1007\/978-3-031-30637-2_27"},{"key":"7328_CR35","doi-asserted-by":"crossref","unstructured":"Liu H, Dong Z, Jiang R, Deng J, Deng J, Chen Q, Song X (2023) Spatio-temporal adaptive embedding makes vanilla transformer SOTA for traffic forecasting. In: Proceedings of the 32nd ACM International Conference on Information and Knowledge Management, pp 4125\u20134129","DOI":"10.1145\/3583780.3615160"},{"key":"7328_CR36","doi-asserted-by":"publisher","first-page":"103066","DOI":"10.1016\/j.simpat.2025.103066","volume":"140","author":"S Cheng","year":"2025","unstructured":"Cheng S, Qu S, Zhang J (2025) Transfer-mamba: Selective state space models with spatio-temporal knowledge transfer for few-shot traffic prediction across cities. Simul Model Pract Theory 140:103066","journal-title":"Simul Model Pract Theory"},{"issue":"1","key":"7328_CR37","doi-asserted-by":"publisher","first-page":"153","DOI":"10.1186\/s40537-024-01001-9","volume":"11","author":"Q Li","year":"2024","unstructured":"Li Q, Qin J, Cui D, Sun D, Wang D (2024) CMMamba: channel mixing mamba for time series forecasting. J Big Data 11(1):153","journal-title":"J Big Data"},{"key":"7328_CR38","doi-asserted-by":"crossref","unstructured":"Fang Y, Liang Y, Hui B, Shao Z, Deng L, Liu X, Jiang X, Zheng K (2024) Efficient large-scale traffic forecasting with transformers: A spatial data management perspective. arXiv preprint arXiv:2412.09972","DOI":"10.1145\/3690624.3709177"},{"key":"7328_CR39","unstructured":"Zhao Y, Luo X, Wen H, Xiao Z, Ju W, Zhang M (2024) Embracing large language models in traffic flow forecasting. arXiv preprint arXiv:2412.12201"},{"key":"7328_CR40","doi-asserted-by":"publisher","first-page":"100150","DOI":"10.1016\/j.commtr.2024.100150","volume":"4","author":"X Guo","year":"2024","unstructured":"Guo X, Zhang Q, Jiang J, Peng M, Zhu M, Yang HF (2024) Towards explainable traffic flow prediction with large language models. Commun Transp Res 4:100150","journal-title":"Commun Transp Res"},{"key":"7328_CR41","doi-asserted-by":"crossref","unstructured":"Arman A, Bellini P, Nesi P, Paolucci M (2019) Analyzing public transportation offer wrt mobility demand. In: Proceedings of the 1st ACM International Workshop on Technology Enablers and Innovative Applications for Smart Cities and Communities, pp 30\u201337 (2019)","DOI":"10.1145\/3364544.3364828"},{"issue":"18","key":"7328_CR42","doi-asserted-by":"publisher","first-page":"8982","DOI":"10.3390\/app12188982","volume":"12","author":"A Arman","year":"2022","unstructured":"Arman A, Badii C, Bellini P, Bilotta S, Nesi P, Paolucci M (2022) Analyzing demand with respect to offer of mobility. Appl Sci 12(18):8982","journal-title":"Appl Sci"},{"issue":"6088","key":"7328_CR43","doi-asserted-by":"publisher","first-page":"533","DOI":"10.1038\/323533a0","volume":"323","author":"DE Rumelhart","year":"1986","unstructured":"Rumelhart DE, Hinton GE, Williams RJ (1986) Learning representations by back-propagating errors. Nature 323(6088):533\u2013536","journal-title":"Nature"},{"key":"7328_CR44","doi-asserted-by":"crossref","unstructured":"Peng B, Alcaide E, Anthony Q, Albalak A, Arcadinho S, Biderman S, Cao H, Cheng X, Chung M, Grella M, et al (2023) RWKV: reinventing RNNs for the transformer era. arXiv preprint arXiv:2305.13048","DOI":"10.18653\/v1\/2023.findings-emnlp.936"},{"key":"7328_CR45","unstructured":"Waleffe R, Byeon W, Riach D, Norick B, Korthikanti V, Dao T, Gu A, Hatamizadeh A, Singh S, Narayanan D, et al (2024) An empirical study of mamba-based language models. arXiv preprint arXiv:2406.07887"},{"issue":"1867","key":"7328_CR46","doi-asserted-by":"publisher","first-page":"342","DOI":"10.1038\/072342a0","volume":"72","author":"K Pearson","year":"1905","unstructured":"Pearson K (1905) The problem of the random walk. Nature 72(1867):342\u2013342","journal-title":"Nature"},{"issue":"2","key":"7328_CR47","doi-asserted-by":"publisher","first-page":"146","DOI":"10.1137\/0201010","volume":"1","author":"R Tarjan","year":"1972","unstructured":"Tarjan R (1972) Depth-first search and linear graph algorithms. SIAM J Comput 1(2):146\u2013160","journal-title":"SIAM J Comput"},{"key":"7328_CR48","unstructured":"Moore EF (1959) The shortest path through a maze. In: Proc. of the International Symposium on the Theory of Switching, Harvard University Press, pp 285\u2013292"},{"key":"7328_CR49","unstructured":"Lin S, Lin W, Wu W, Chen H, Yang J (2024) SparseTSF: modeling long-term time series forecasting with 1k parameters. In: Salakhutdinov R, Kolter Z, Heller K, Weller A, Oliver N, Scarlett J, Berkenkamp F (eds) Proceedings of the 41st International Conference on Machine Learning. Proceedings of Machine Learning Research, PMLR, vol 235, pp 30211\u201330226. https:\/\/proceedings.mlr.press\/v235\/lin24n.html"},{"issue":"1","key":"7328_CR50","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1109\/TE.1969.4320436","volume":"12","author":"JW Cooley","year":"1969","unstructured":"Cooley JW, Lewis PA, Welch PD (1969) The fast Fourier transform and its applications. IEEE Trans Educ 12(1):27\u201334","journal-title":"IEEE Trans Educ"},{"key":"7328_CR51","first-page":"28341","volume":"36","author":"M Kollovieh","year":"2023","unstructured":"Kollovieh M, Ansari AF, Bohlke-Schneider M, Zschiegner J, Wang H, Wang YB (2023) Predict, refine, synthesize: self-guiding diffusion models for probabilistic time series forecasting. Adv Neural Inf Process Syst 36:28341\u201328364","journal-title":"Adv Neural Inf Process Syst"},{"key":"7328_CR52","unstructured":"Alcaraz JML, Strodthoff N (2022) Diffusion-based time series imputation and forecasting with structured state space models. arXiv preprint arXiv:2208.09399"},{"key":"7328_CR53","unstructured":"Wang M, Zheng D, Ye Z, Gan Q, Li M, Song X, Zhou J, Ma C, Yu L, Gai Y, et al (2019) Deep graph library: a graph-centric, highly-performant package for graph neural networks. arXiv preprint arXiv:1909.01315"},{"key":"7328_CR54","unstructured":"Paszke A, Gross S, Massa F, Lerer A, Bradbury J, Chanan G, Killeen T, Lin Z, Gimelshein N, Antiga L et al (2019) PyTorch: an imperative style, high-performance deep learning library. Adv Neural Inf Processing Syst 32"},{"key":"7328_CR55","unstructured":"Kingma DP (2014) Adam: a method for stochastic optimization. arXiv preprint arXiv:1412.6980"},{"key":"7328_CR56","unstructured":"Bai S, Kolter JZ, Koltun V (2018) An empirical evaluation of generic convolutional and recurrent networks for sequence modeling. arXiv preprint arXiv:1803.01271"}],"container-title":["The Journal of Supercomputing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11227-025-07328-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11227-025-07328-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11227-025-07328-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,7]],"date-time":"2025-05-07T23:03:17Z","timestamp":1746658997000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11227-025-07328-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,5,7]]},"references-count":56,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2025,5]]}},"alternative-id":["7328"],"URL":"https:\/\/doi.org\/10.1007\/s11227-025-07328-1","relation":{},"ISSN":["1573-0484"],"issn-type":[{"value":"1573-0484","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,5,7]]},"assertion":[{"value":"20 April 2025","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 May 2025","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"Ethical and informed consent for data use not applicable to this article as no datasets were generated during the current study.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical approval"}}],"article-number":"838"}}