{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,21]],"date-time":"2026-09-21T11:01:37Z","timestamp":1789988497267,"version":"4.0.1"},"reference-count":44,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2026,9,19]],"date-time":"2026-09-19T00:00:00Z","timestamp":1789776000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Multivariate time series forecasting requires models to infer future values and how the temporal structure evolves beyond the observation boundary. A central challenge is to define this evolution as an intermediate prediction and connect it to value forecasting. We propose explicit future pattern (EFP)-enhanced forecasting, which represents evolution as a multiscale change from the last observed pattern. A separately supervised predictor estimates this change from history, and a decoder combines the predicted pattern with historical behavior and variable relations. A mixed training strategy exposes the decoder to supervised, predicted, and perturbed patterns; inference requires only historical input. Experiments on nine public datasets and four forecasting horizons evaluate the forecasting accuracy and the contribution of explicit future patterns. Predicted patterns outperform shuffled patterns on all nine datasets, and the error increases in aggregate as sample alignment is weakened. Ablations support the roles of dynamic multiscale evolution, frequency information, and mixed training. These results indicate that explicit future patterns can provide useful, inspectable guidance for multivariate forecasting when their estimates remain aligned with the current sample.<\/jats:p>","DOI":"10.3390\/e28091031","type":"journal-article","created":{"date-parts":[[2026,9,21]],"date-time":"2026-09-21T08:03:47Z","timestamp":1789977827000},"page":"1031","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Explicit Future Pattern-Enhanced Multivariate Time Series Forecasting"],"prefix":"10.3390","volume":"28","author":[{"given":"Yaokang","family":"Li","sequence":"first","affiliation":[{"name":"School of Artificial Intelligence, Guangzhou Institute of Science and Technology, Guangzhou 510540, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"conceptualization","vocabulary":"credit"},{"role":"methodology","vocabulary":"credit"},{"role":"software","vocabulary":"credit"},{"role":"data-curation","vocabulary":"credit"},{"role":"writing-original-draft","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"}]},{"given":"Yunan","family":"Wei","sequence":"additional","affiliation":[{"name":"School of Computer, Zhuhai College of Science and Technology, Zhuhai 519041, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"validation","vocabulary":"credit"},{"role":"formal-analysis","vocabulary":"credit"},{"role":"investigation","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"}]},{"given":"Jing","family":"Cai","sequence":"additional","affiliation":[{"name":"School of Artificial Intelligence, Guangzhou Institute of Science and Technology, Guangzhou 510540, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"resources","vocabulary":"credit"},{"role":"data-curation","vocabulary":"credit"},{"role":"writing-original-draft","vocabulary":"credit"},{"role":"visualization","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0009-0003-4786-4121","authenticated-orcid":false,"given":"Wenbin","family":"Cheng","sequence":"additional","affiliation":[{"name":"University of Electronic Science and Technology of China, Zhongshan Institute, Zhongshan 528402, China"},{"name":"University of Electronic Science and Technology of China, Chengdu 611731, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"visualization","vocabulary":"credit"},{"role":"resources","vocabulary":"credit"},{"role":"investigation","vocabulary":"credit"},{"role":"funding-acquisition","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4159-3132","authenticated-orcid":false,"given":"Yiting","family":"Lin","sequence":"additional","affiliation":[{"name":"University of Electronic Science and Technology of China, Zhongshan Institute, Zhongshan 528402, China"},{"name":"University of Electronic Science and Technology of China, Chengdu 611731, China"},{"name":"Guangdong Provincial\/Zhuhai Key Laboratory of Interdisciplinary Research and Application for Data Science, Beijing Normal-Hong Kong Baptist University, Zhuhai 519087, China"},{"name":"Department of Computer Science, Hong Kong Baptist University, Hong Kong, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"supervision","vocabulary":"credit"},{"role":"resources","vocabulary":"credit"},{"role":"project-administration","vocabulary":"credit"},{"role":"funding-acquisition","vocabulary":"credit"},{"role":"writing-original-draft","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"}]}],"member":"1968","published-online":{"date-parts":[[2026,9,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Tj\u00f8stheim, D. 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