{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T22:31:35Z","timestamp":1773700295792,"version":"3.50.1"},"reference-count":40,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2026,1,31]],"date-time":"2026-01-31T00:00:00Z","timestamp":1769817600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Shanxi Province Application Basic Research Plan","award":["202403021222070"],"award-info":[{"award-number":["202403021222070"]}]},{"name":"Scientific and Technological Achievement Transformation Program of Shanxi Province","award":["202304021301035"],"award-info":[{"award-number":["202304021301035"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Accurate power load forecasting is crucial for ensuring the safety and economic operation of power systems. However, the complex, non-stationary, and heterogeneous nature of power load data presents significant challenges for traditional prediction methods, particularly in capturing instantaneous dynamics and effectively fusing multi-feature information. This paper proposes a novel framework\u2014Ensemble Entropy with Adaptive Deep Fusion (EEADF)\u2014for short-term multi-feature power load forecasting. The framework introduces an ensemble instantaneous entropy extraction module to compute and fuse multiple entropy types (approximate, sample, and permutation entropies) in real-time within sliding windows, creating a sensitive representation of system states. A task-adaptive hierarchical fusion mechanism is employed to balance computational efficiency and model expressivity. For time-series forecasting tasks with relatively structured patterns, feature concatenation fusion is used that directly combines LSTM sequence features with multimodal entropy features. For complex multimodal understanding tasks requiring nuanced cross-modal interactions, multi-head self-attention fusion is implemented that dynamically weights feature importance based on contextual relevance. A dual-branch deep learning model is constructed that processes both raw sequences (via LSTM) and extracted entropy features (via MLP) in parallel. Extensive experiments on a carefully designed simulated multimodal dataset demonstrate the framework\u2019s robustness in recognizing diverse dynamic patterns, achieving MSE of 0.0125, MAE of 0.0794, and R2 of 0.9932. Validation on the real-world ETDataset for power load forecasting confirms that the proposed method significantly outperforms baseline models (LSTM, TCN, transformer, and informer) and traditional entropy methods across standard evaluation metrics (MSE, MAE, RMSE, MAPE, and R2). Ablation studies further verify the critical roles of both the entropy features and the fusion mechanism.<\/jats:p>","DOI":"10.3390\/e28020158","type":"journal-article","created":{"date-parts":[[2026,2,2]],"date-time":"2026-02-02T09:48:08Z","timestamp":1770025688000},"page":"158","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Ensemble Entropy with Adaptive Deep Fusion for Short-Term Power Load Forecasting"],"prefix":"10.3390","volume":"28","author":[{"given":"Yiling","family":"Wang","sequence":"first","affiliation":[{"name":"College of Computer Science and Technology, Taiyuan University of Technology, Taiyuan 030024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8136-6631","authenticated-orcid":false,"given":"Yan","family":"Niu","sequence":"additional","affiliation":[{"name":"College of Computer Science and Technology, Taiyuan University of Technology, Taiyuan 030024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xuejun","family":"Li","sequence":"additional","affiliation":[{"name":"Jiangsu Haohan Information Technology Co., Ltd., Nantong 226300, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xianglong","family":"Dai","sequence":"additional","affiliation":[{"name":"Jiangsu Haohan Information Technology Co., Ltd., Nantong 226300, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaopeng","family":"Wang","sequence":"additional","affiliation":[{"name":"Jiangsu Haohan Information Technology Co., Ltd., Nantong 226300, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yong","family":"Jiang","sequence":"additional","affiliation":[{"name":"Jiangsu Haohan Information Technology Co., Ltd., Nantong 226300, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chenghu","family":"He","sequence":"additional","affiliation":[{"name":"Jiangsu Haohan Information Technology Co., Ltd., Nantong 226300, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Li","family":"Zhou","sequence":"additional","affiliation":[{"name":"College of Computer Science and Technology, Taiyuan University of Technology, Taiyuan 030024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,1,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"100165","DOI":"10.1016\/j.adapen.2024.100165","article-title":"Probabilistic load forecasting for integrated energy systems using attentive quantile regression temporal convolutional network","volume":"14","author":"Guo","year":"2024","journal-title":"Adv. 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