{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,18]],"date-time":"2026-04-18T05:50:15Z","timestamp":1776491415333,"version":"3.51.2"},"reference-count":42,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T00:00:00Z","timestamp":1775001600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T00:00:00Z","timestamp":1775001600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62476230"],"award-info":[{"award-number":["62476230"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"New Chongqing Youth Innovation Talent Project","award":["CSTB2024NSCQ-QCXMX0070"],"award-info":[{"award-number":["CSTB2024NSCQ-QCXMX0070"]}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["SWU-KR22046"],"award-info":[{"award-number":["SWU-KR22046"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Computing"],"published-print":{"date-parts":[[2026,4]]},"DOI":"10.1007\/s00607-026-01644-x","type":"journal-article","created":{"date-parts":[[2026,4,7]],"date-time":"2026-04-07T08:28:14Z","timestamp":1775550494000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["ADCformer: multivariate time series forecasting with adaptive differential channels transformer"],"prefix":"10.1007","volume":"108","author":[{"given":"Yutao","family":"Xia","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yue","family":"Zhou","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaofang","family":"Hu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shukai","family":"Duan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2026,4,7]]},"reference":[{"key":"1644_CR1","doi-asserted-by":"crossref","unstructured":"Koprinska I, Wu D, Wang Z (2018) Convolutional neural networks for energy time series forecasting. In: 2018 international joint conference on neural networks (IJCNN). IEEE. pp. 1\u20138","DOI":"10.1109\/IJCNN.2018.8489399"},{"issue":"2","key":"1644_CR2","doi-asserted-by":"publisher","first-page":"246","DOI":"10.1109\/TITS.2009.2021448","volume":"10","author":"B Ghosh","year":"2009","unstructured":"Ghosh B, Basu B, O\u2019Mahony M (2009) Multivariate short-term traffic flow forecasting using time-series analysis. IEEE Trans Intell Transp Syst 10(2):246\u2013254","journal-title":"IEEE Trans Intell Transp Syst"},{"key":"1644_CR3","doi-asserted-by":"publisher","DOI":"10.1016\/j.knosys.2025.113115","volume":"311","author":"F Jiang","year":"2025","unstructured":"Jiang F, Han X, Wen S, Tian T (2025) Spatiotemporal interactive learning dynamic adaptive graph convolutional network for traffic forecasting. Knowl Based Syst 311:113115","journal-title":"Knowl Based Syst"},{"key":"1644_CR4","doi-asserted-by":"crossref","unstructured":"Tian G, Huang T, Peng C, Yang Y, Wen S (2025) BiMT-TCN: a cutting-edge hybrid model for enhanced stock price prediction. Knowl-Based Syst 114263.","DOI":"10.1016\/j.knosys.2025.114263"},{"key":"1644_CR5","doi-asserted-by":"publisher","DOI":"10.1016\/j.knosys.2025.114383","author":"Y Cao","year":"2025","unstructured":"Cao Y, Sheng Z, Zhu H, Huang T, Wen S (2025) Prostate cancer forecasting in small samples based on lightweight neural networks using ensemble learning. Knowl-Based Syst. https:\/\/doi.org\/10.1016\/j.knosys.2025.114383","journal-title":"Knowl-Based Syst"},{"key":"1644_CR6","doi-asserted-by":"publisher","DOI":"10.1016\/j.energy.2023.127350","volume":"274","author":"SF Stefenon","year":"2023","unstructured":"Stefenon SF, Seman LO, Aquino LS, dos Santos Coelho L (2023) Wavelet-seq2seq-lstm with attention for time series forecasting of level of dams in hydroelectric power plants. Energy 274:p127350","journal-title":"Energy"},{"issue":"1","key":"1644_CR7","doi-asserted-by":"publisher","first-page":"419","DOI":"10.1109\/JIOT.2021.3124673","volume":"9","author":"J Han","year":"2021","unstructured":"Han J, Lee GH, Park S, Lee J, Choi JK (2021) A multivariatetime-series-prediction-based adaptive data transmission period control algorithm for IoT networks. IEEE Internet Things J 9(1):419\u2013436","journal-title":"IEEE Internet Things J"},{"key":"1644_CR8","first-page":"1551","volume":"2023","author":"Q Hua","year":"2023","unstructured":"Hua Q, Yang D, Qian S, Hu H, Cao J, Xue G (2023) Kae-informer: a knowledge auto-embedding informer for forecasting long-term workloads of microservices. Proc ACM Web Conf 2023:1551\u20131561","journal-title":"Proc ACM Web Conf"},{"key":"1644_CR9","doi-asserted-by":"crossref","unstructured":"Lai G, Chang W-C, Yang Y, Liu H (2018) Modeling long-and short-term temporal patterns with deep neural networks. In: The 41st international ACM SIGIR conference on research & development in information retrieval, pp. 95\u2013104","DOI":"10.1145\/3209978.3210006"},{"key":"1644_CR10","doi-asserted-by":"publisher","first-page":"113971","DOI":"10.1016\/j.knosys.2025.113971","volume":"325","author":"J Jiang","year":"2025","unstructured":"Jiang J, Jiang B, Wang Y, Miao D (2025) mLANet: an efficient recurrent neural network for long-term time series forecasting. Knowl-Based Syst 325:113971","journal-title":"Knowl-Based Syst"},{"key":"1644_CR11","unstructured":"Wu H, Hu T, Liu Y, Zhou H, Wang J, Long M (2023) Timesnet: temporal 2d-variation modeling for general time series analysis. In: International conference on learning representations"},{"key":"1644_CR12","doi-asserted-by":"crossref","unstructured":"Lai G, Chang WC, Yang Y, Liu H (2018) Modeling long-and short-term temporal patterns with deep neural networks. In: The 41st international ACM SIGIR conference on research & development in information retrieval, pp. 95\u2013104.","DOI":"10.1145\/3209978.3210006"},{"key":"1644_CR13","unstructured":"Zhang Y, Yan J (2023) Crossformer: transformer utilizing crossdimension dependency for multivariate time series forecasting. In: International conference on learning representations"},{"key":"1644_CR14","unstructured":"Gao J, Hu W, Chen Y. Client: \u201cCross-variable linear integrated enhanced transformer for multivariate long-term time series forecasting.\u201d arXiv preprint arXiv:2305.18838, 2023."},{"key":"1644_CR15","unstructured":"Liu Y, Hu T, Zhang H, Wu H, Wang S, Ma L, Long M (2024) itransformer: Inverted transformers are effective for time series forecasting. In: The eleventh international conference on learning representations"},{"key":"1644_CR16","doi-asserted-by":"publisher","DOI":"10.1016\/j.neunet.2025.107769","author":"Y Yu","year":"2025","unstructured":"Yu Y, Yu W, Nie F et al (2025) PRformer: pyramidal recurrent transformer for multivariate time series forecasting. Neural Netw. https:\/\/doi.org\/10.1016\/j.neunet.2025.107769","journal-title":"Neural Netw"},{"key":"1644_CR17","unstructured":"Nie Y, Nguyen NH, Sinthong P, et al. (2023) A time series is worth 64 words: Long-term forecasting with transformers. In: The eleventh international conference on learning representations"},{"key":"1644_CR18","first-page":"43322","volume":"36","author":"T Zhou","year":"2023","unstructured":"Zhou T, Niu P, Sun L et al (2023) One fits all: power general time series analysis by pretrained lm. Adv Neural Inf Process Syst 36:43322\u201343355","journal-title":"Adv Neural Inf Process Syst"},{"key":"1644_CR19","doi-asserted-by":"publisher","DOI":"10.1109\/TKDE.2024.3400008","author":"L Han","year":"2024","unstructured":"Han L, Ye HJ, Zhan DC (2024) The capacity and robustness trade-off: Revisiting the channel independent strategy for multivariate time series forecasting. IEEE Trans Knowl Data Eng. https:\/\/doi.org\/10.1109\/TKDE.2024.3400008","journal-title":"IEEE Trans Knowl Data Eng"},{"key":"1644_CR20","unstructured":"Franceschi JY, Dieuleveut A, Jaggi M (2019) Unsupervised scalable representation learning for multivariate time series. Advances in neural information processing systems, 32."},{"issue":"3","key":"1644_CR21","doi-asserted-by":"publisher","first-page":"1181","DOI":"10.1016\/j.ijforecast.2019.07.001","volume":"36","author":"D Salinas","year":"2020","unstructured":"Salinas D, Flunkert V, Gasthaus J, Januschowski T (2020) Deepar: probabilistic forecasting with autoregressive recurrent networks. Int J Forecast 36(3):1181\u20131191","journal-title":"Int J Forecast"},{"key":"1644_CR22","unstructured":"Rangapuram SS, Seeger MW, Gasthaus J, Stella L, Wang Y, Januschowski T (2018) Deep state space models for time series forecasting. Advances in neural information processing systems, 31"},{"key":"1644_CR23","doi-asserted-by":"crossref","unstructured":"Lea C, Flynn MD, Vidal R, Reiter A, Hager GD (2017) Temporal convolutional networks for action segmentation and detection. In: proceedings of the IEEE conference on computer vision and pattern recognition, pp. 156\u2013165","DOI":"10.1109\/CVPR.2017.113"},{"key":"1644_CR24","doi-asserted-by":"publisher","first-page":"11106","DOI":"10.1609\/aaai.v35i12.17325","volume":"35","author":"H Zhou","year":"2021","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 35:11106\u201311115","journal-title":"In Proceedings of the AAAI conference on artificial intelligence"},{"key":"1644_CR25","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":"1644_CR26","unstructured":"Li S, Jin X, Xuan Y, Zhou X, Chen W, Wang Y-X, Yan X (2019) Enhancing the locality and breaking the memory bottleneck of transformer on time series forecasting. Advances in neural information processingsystems, 32"},{"key":"1644_CR27","unstructured":"Haixu W, Jiehui X, Jianmin W, Mingsheng L (2021) Autoformer: Decomposition transformers with auto-correlation for long-term series forecasting. NeurIPS"},{"key":"1644_CR28","doi-asserted-by":"crossref","unstructured":"Chen M, Peng H, Fu J, Ling H (2021) Autoformer: searching transformers for visual recognition. In: Proceedings of the IEEE\/CVF international conference on computer vision, pp. 12270\u201312280","DOI":"10.1109\/ICCV48922.2021.01205"},{"key":"1644_CR29","unstructured":"Murphy WMJ, Chen K (2023) Univariate vs multivariate time series forecasting with transformers"},{"issue":"9","key":"1644_CR30","first-page":"11121","volume":"37","author":"A Zeng","year":"2023","unstructured":"Zeng A, Chen M, Zhang L et al (2023) Are transformers effective for time series forecasting? Proc AAAI Conf Artif Intell 37(9):11121\u201311128","journal-title":"Proc AAAI Conf Artif Intell"},{"key":"1644_CR31","unstructured":"Zhao L, Shen Y (2024) Rethinking channel dependence for multivariate time series forecasting: learning from leading indicators. arXiv preprint arXiv:2401.17548"},{"key":"1644_CR32","unstructured":"Liu S, Yu H, Liao C, Li J, Lin W, Liu AX, Dustdar S (2021) Pyraformer: low-complexity pyramidal attention for long-range time series modeling and forecasting. In: International conference on learning representations"},{"key":"1644_CR33","unstructured":"Lu H, Han-Jia Y, De-Chuan Z (2023) The capacity and robustness trade-off: revisiting the channel independent strategy for multivariate time series forecasting. arXiv preprint arXiv:2304.05206"},{"key":"1644_CR34","unstructured":"Li Z, Qi S, Li Y, Xu Z (2023a) Revisiting long-term time series forecasting: an investigation on linear mapping. arXiv preprint arXiv:2305.10721"},{"key":"1644_CR35","doi-asserted-by":"publisher","first-page":"28320","DOI":"10.1109\/JIOT.2024.3401697","volume":"11","author":"W Han","year":"2024","unstructured":"Han W, Zhu T, Chen L et al (2024) MCformer: multivariate time series forecasting with mixed-channels transformer. IEEE Internet Things J 11:28320\u201328329","journal-title":"IEEE Internet Things J"},{"key":"1644_CR36","doi-asserted-by":"publisher","first-page":"130258","DOI":"10.1016\/j.eswa.2025.130258","volume":"300","author":"Z Huang","year":"2025","unstructured":"Huang Z, Zhang F, Liu Y (2025) Dual-channel transformer: integrating independence and dependence for time series forecasting. Expert Syst Appl 300:130258","journal-title":"Expert Syst Appl"},{"key":"1644_CR37","first-page":"4356","volume":"37","author":"J Ji","year":"2023","unstructured":"Ji J, Wang J, Huang C, Wu J, Xu B, Wu Z, Zhang J, Zheng Y (2023) Spatio-temporal self-supervised learning for traffic flow prediction. Proc AAAI Conf artificial Intell 37:4356\u20134364","journal-title":"Proc AAAI Conf artificial Intell"},{"key":"1644_CR38","doi-asserted-by":"crossref","unstructured":"Chen J, Lenssen J E, Feng A, et al. (2024) From similarity to superiority: channel clustering for time series forecasting. arXiv preprint arXiv:2404.01340","DOI":"10.52202\/079017-4152"},{"key":"1644_CR39","unstructured":"Kim T, Kim J, Tae Y, Park C, Choi JH, Choo J (2021) Reversible instance normalization for accurate time-series forecasting against distribution shift. In: International conference on learning representations. [Online]. :https:\/\/openreview.net\/forum?id=cGDAkQo1C0p"},{"issue":"0","key":"1644_CR40","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1007\/bf02546511","volume":"55","author":"N Wiener","year":"1930","unstructured":"Wiener N (1930) Generalized harmonic analysis. Acta Math 55(0):117\u2013258. https:\/\/doi.org\/10.1007\/bf02546511","journal-title":"Acta Math"},{"key":"1644_CR41","unstructured":"Ailing Z, Muxi C, Lei Z, Qiang X (2023) Are transformers effective for time series forecasting? AAAI"},{"key":"1644_CR42","unstructured":"Abhimanyu D, Weihao K, Andrew L, Rajat S, Rose Y (2023) Long-term forecasting with tide: time-series dense encoder. arXiv preprint arXiv:2304.08424"}],"container-title":["Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00607-026-01644-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00607-026-01644-x","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00607-026-01644-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,18]],"date-time":"2026-04-18T05:13:09Z","timestamp":1776489189000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00607-026-01644-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,4]]},"references-count":42,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2026,4]]}},"alternative-id":["1644"],"URL":"https:\/\/doi.org\/10.1007\/s00607-026-01644-x","relation":{},"ISSN":["0010-485X","1436-5057"],"issn-type":[{"value":"0010-485X","type":"print"},{"value":"1436-5057","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,4]]},"assertion":[{"value":"21 November 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 March 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 April 2026","order":3,"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 no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"64"}}