{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,4]],"date-time":"2026-02-04T00:15:20Z","timestamp":1770164120909,"version":"3.49.0"},"reference-count":47,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2025,7,4]],"date-time":"2025-07-04T00:00:00Z","timestamp":1751587200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"2022 Open Research Project of the National Key Laboratory for Special Vehicle Design and Manufacturing Integration Technology","award":["2022.F.FQ. Process-0492"],"award-info":[{"award-number":["2022.F.FQ. Process-0492"]}]},{"name":"2022 Open Research Project of the National Key Laboratory for Special Vehicle Design and Manufacturing Integration Technology","award":["No. 2024C008-7"],"award-info":[{"award-number":["No. 2024C008-7"]}]},{"name":"the Basic Construction Funds within the Budget of Jilin Province in 202","award":["2022.F.FQ. Process-0492"],"award-info":[{"award-number":["2022.F.FQ. Process-0492"]}]},{"name":"the Basic Construction Funds within the Budget of Jilin Province in 202","award":["No. 2024C008-7"],"award-info":[{"award-number":["No. 2024C008-7"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Time series forecasting serves a critical function in domains such as energy, meteorology, and power systems by leveraging historical data to predict future trends. However, existing methods often prioritize long-term dependencies while neglecting the integration of local features and global patterns, resulting in limited accuracy for short-term predictions of non-stationary multivariate sequences. To address these challenges, this paper proposes a time series forecasting model named VBTCKN based on variational mode decomposition and a dual-channel cross-attention network. First, the model employs variational mode decomposition (VMD) to decompose the time series into multiple frequency-complementary modal components, thereby reducing sequence volatility. Subsequently, the BiLSTM channel extracts temporal dependencies between sequences, while the transformer channel captures dynamic correlations between local features and global patterns. The cross-attention mechanism dynamically fuses features from both channels, enhancing complementary information integration. Finally, prediction results are generated through Kolmogorov\u2013Arnold networks (KAN). Experiments conducted on four public datasets demonstrated that VBTCKN outperformed other state-of-the-art methods in both accuracy and robustness. Compared with BiLSTM, VBTCKN reduced RMSE by 63.32%, 68.31%, 57.98%, and 90.76%, respectively.<\/jats:p>","DOI":"10.3390\/sym17071063","type":"journal-article","created":{"date-parts":[[2025,7,4]],"date-time":"2025-07-04T11:20:11Z","timestamp":1751628011000},"page":"1063","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["VBTCKN: A Time Series Forecasting Model Based on Variational Mode Decomposition with Two-Channel Cross-Attention Network"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6719-0652","authenticated-orcid":false,"given":"Zhiguo","family":"Xiao","sequence":"first","affiliation":[{"name":"School of Computer Science & Technology, Beijing Institute of Technology, Beijing 100811, China"},{"name":"College of Computer Science and Technology, Changchun University, Changchun 130022, China"},{"name":"National Key Laboratory of Special Vehicle Design and Manufacturing Integration Technology, Baotou 014000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0000-1580-5280","authenticated-orcid":false,"given":"Changgen","family":"Li","sequence":"additional","affiliation":[{"name":"College of Computer Science and Technology, Changchun University, Changchun 130022, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huihui","family":"Hao","sequence":"additional","affiliation":[{"name":"National Key Laboratory of Special Vehicle Design and Manufacturing Integration Technology, Baotou 014000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Siwen","family":"Liang","sequence":"additional","affiliation":[{"name":"National Key Laboratory of Special Vehicle Design and Manufacturing Integration Technology, Baotou 014000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qi","family":"Shen","sequence":"additional","affiliation":[{"name":"College of Computer Science and Technology, Changchun University, Changchun 130022, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dongni","family":"Li","sequence":"additional","affiliation":[{"name":"School of Computer Science & Technology, Beijing Institute of Technology, Beijing 100811, China"},{"name":"National Key Laboratory of Special Vehicle Design and Manufacturing Integration Technology, Baotou 014000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,7,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"48322","DOI":"10.1109\/ACCESS.2023.3276628","article-title":"Time series prediction based on LSTM-attention-LSTM model","volume":"11","author":"Wen","year":"2023","journal-title":"IEEE Access"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Zhao, C., Hu, P., Liu, X., Lan, X., and Zhang, H. 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