{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,16]],"date-time":"2026-06-16T17:11:47Z","timestamp":1781629907340,"version":"3.54.5"},"reference-count":25,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2026,1,19]],"date-time":"2026-01-19T00:00:00Z","timestamp":1768780800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2026,2,11]],"date-time":"2026-02-11T00:00:00Z","timestamp":1770768000000},"content-version":"vor","delay-in-days":23,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"Scientific and Technological Project of State Grid Qinghai Electric Power Company","award":["52281424000C"],"award-info":[{"award-number":["52281424000C"]}]},{"name":"Scientific and Technological Project of State Grid Qinghai Electric Power Company","award":["52281424000C"],"award-info":[{"award-number":["52281424000C"]}]},{"name":"Scientific and Technological Project of State Grid Qinghai Electric Power Company","award":["52281424000C"],"award-info":[{"award-number":["52281424000C"]}]},{"name":"Scientific and Technological Project of State Grid Qinghai Electric Power Company","award":["52281424000C"],"award-info":[{"award-number":["52281424000C"]}]},{"name":"Scientific and Technological Project of State Grid Qinghai Electric Power Company","award":["52281424000C"],"award-info":[{"award-number":["52281424000C"]}]},{"name":"Scientific and Technological Project of State Grid Qinghai Electric Power Company","award":["52281424000C"],"award-info":[{"award-number":["52281424000C"]}]},{"name":"Scientific and Technological Project of State Grid Qinghai Electric Power Company","award":["52281424000C"],"award-info":[{"award-number":["52281424000C"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Energy Inform"],"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    With the rapid development of renewable energy, photovoltaic power generation has become a key part of the global energy transition. Short-term photovoltaic prediction is critical for intra-day real-time power grid dispatching, and enhancing its accuracy is a key research focus. However, existing methods still have limitations in handling complex nonlinear relationships in photovoltaic temporal data. To tackle this, this paper proposes a new model combining Long Short-Term Memory (LSTM), Differential Transformer (DiffTransformer), and Multi-Objective Escape Algorithm (MOESC) for short-term photovoltaic power prediction optimization: Preprocessed data is input into the LSTM-Differential Transformer model, with the Differential Transformer encoder capturing fine-grained temporal changes via optimized multi-head attention and rotary positional encoding, and the LSTM decoder integrating local temporal information for power prediction. Subsequently, Pareto-improved MOESC performs multi-objective optimization on the model\u2019s key parameters (balancing\n                    <jats:italic>RMSE<\/jats:italic>\n                    ,\n                    <jats:italic>MAE<\/jats:italic>\n                    , and\n                    <jats:italic>R\u00b2<\/jats:italic>\n                    ), with the optimal parameters selected from the Pareto frontier. Experiments based on the Guoneng Rixin photovoltaic dataset show that, with user-defined weights (\n                    <jats:italic>RMSE<\/jats:italic>\n                    : 30%,\n                    <jats:italic>MAE<\/jats:italic>\n                    : 30%,\n                    <jats:italic>R\u00b2<\/jats:italic>\n                    : 40%), this method outperforms XGBoost, LightGBM, SVR, LSTM, GRU and the unoptimized LSTM-Differential Transformer model in photovoltaic power prediction. It not only can effectively improve prediction accuracy but also exhibits better stability compared with the unoptimized LSTM-Differential Transformer model.\n                  <\/jats:p>","DOI":"10.1186\/s42162-026-00621-0","type":"journal-article","created":{"date-parts":[[2026,1,19]],"date-time":"2026-01-19T14:05:14Z","timestamp":1768831514000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A method for short-term photovoltaic power prediction integrating long short-term memory network, differential transformer, and multi-objective escape algorithm"],"prefix":"10.1186","volume":"9","author":[{"given":"Yi","family":"Zhang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Guangde","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zengwei","family":"Li","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hongkai","family":"Zhao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuanming","family":"Ma","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Guodong","family":"Li","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rongfu","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,1,19]]},"reference":[{"key":"621_CR1","unstructured":"IEA(2025), Global EnergyReview 2025, Paris IEA https:\/\/www.iea.org\/reports\/global-energy-review-2025, Licence: CC BY 4.0"},{"issue":"24","key":"621_CR2","doi-asserted-by":"publisher","DOI":"10.3390\/su142417005","volume":"14","author":"KJ Iheanetu","year":"2022","unstructured":"Iheanetu KJ (2022) Solar photovoltaic power forecasting: a review. Sustainability 14(24):17005","journal-title":"Sustainability"},{"key":"621_CR3","doi-asserted-by":"publisher","first-page":"40820","DOI":"10.1109\/ACCESS.2023.3270041","volume":"11","author":"J Gaboitaolelwe","year":"2023","unstructured":"Gaboitaolelwe J, Zungeru AM, Yahya A et al (2023) Machine learning based solar photovoltaic power forecasting: a review and comparison. IEEE Access 11:40820\u201340845","journal-title":"IEEE Access"},{"key":"621_CR4","doi-asserted-by":"publisher","first-page":"60","DOI":"10.1016\/j.solener.2017.11.023","volume":"168","author":"D Yang","year":"2018","unstructured":"Yang D, Kleissl J, Gueymard CA et al (2018) History and trends in solar irradiance and PV power forecasting: a preliminary assessment and review using text mining. Solar Energy 168:60\u2013101","journal-title":"Solar Energy"},{"issue":"3","key":"621_CR5","doi-asserted-by":"publisher","first-page":"1255","DOI":"10.1109\/TSTE.2016.2535466","volume":"7","author":"HS Jang","year":"2016","unstructured":"Jang HS, Bae KY, Park HS et al (2016) Solar power prediction based on satellite images and support vector machine. IEEE Trans Sustain Energy 7(3):1255\u20131263","journal-title":"IEEE Trans Sustain Energy"},{"key":"621_CR6","doi-asserted-by":"publisher","DOI":"10.1016\/j.apenergy.2021.117514","volume":"302","author":"Z Si","year":"2021","unstructured":"Si Z, Yang M, Yu Y et al (2021) Photovoltaic power forecast based on satellite images considering effects of solar position. Appl Energy 302:117514","journal-title":"Appl Energy"},{"key":"621_CR7","doi-asserted-by":"publisher","first-page":"855","DOI":"10.1016\/j.renene.2018.03.070","volume":"126","author":"F Rodr\u00edguez","year":"2018","unstructured":"Rodr\u00edguez F, Fleetwood A, Galarza A et al (2018) Predicting solar energy generation through artificial neural networks using weather forecasts for microgrid control. Renew Energy 126:855\u2013864","journal-title":"Renew Energy"},{"key":"621_CR8","doi-asserted-by":"publisher","DOI":"10.1016\/j.enconman.2023.117186","volume":"288","author":"A Keddouda","year":"2023","unstructured":"Keddouda A, Ihaddadene R, Boukhari A et al (2023) Solar photovoltaic power prediction using artificial neural network and multiple regression considering ambient and operating conditions. Energy Convers Manag 288:117186","journal-title":"Energy Convers Manag"},{"issue":"3","key":"621_CR9","doi-asserted-by":"publisher","first-page":"1064","DOI":"10.1109\/TIA.2012.2190816","volume":"48","author":"J Shi","year":"2012","unstructured":"Shi J, Lee WJ, Liu Y et al (2012) Forecasting power output of photovoltaic systems based on weather classification and support vector machines[J]. IEEE Trans Ind Appl 48(3):1064\u20131069","journal-title":"IEEE Trans Ind Appl"},{"key":"621_CR10","doi-asserted-by":"publisher","first-page":"427","DOI":"10.1016\/j.enbuild.2014.10.002","volume":"86","author":"F Wang","year":"2015","unstructured":"Wang F, Zhen Z, Mi Z et al (2015) Solar irradiance feature extraction and support vector machines based weather status pattern recognition model for short-term photovoltaic power forecasting. Energy Build 86:427\u2013438","journal-title":"Energy Build"},{"key":"621_CR11","doi-asserted-by":"publisher","DOI":"10.1016\/j.jclepro.2020.119966","volume":"253","author":"G-Q Lin","year":"2020","unstructured":"Lin G-Q, Li L-L, Tseng M-L et al (2020) An improved moth-flame optimization algorithm for support vector machine prediction of photovoltaic power generation. J Clean Prod 253:119966","journal-title":"J Clean Prod"},{"key":"621_CR12","doi-asserted-by":"publisher","DOI":"10.1038\/s41598-024-65159-1","author":"R Zhu","year":"2024","unstructured":"Zhu R, Li T, Tang B (2024) Research on short-term photovoltaic power generation forecasting model based on multi-strategy improved squirrel search algorithm and support vector machine. Sci Rep. https:\/\/doi.org\/10.1038\/s41598-024-65159-1","journal-title":"Sci Rep"},{"key":"621_CR13","doi-asserted-by":"publisher","first-page":"357","DOI":"10.1016\/j.renene.2017.11.011","volume":"118","author":"AT Eseye","year":"2018","unstructured":"Eseye AT, Zhang J, Zheng D (2018) Short-term photovoltaic solar power forecasting using a hybrid wavelet-PSO-SVM model based on SCADA and meteorological information. Renew Energy 118:357\u2013367","journal-title":"Renew Energy"},{"issue":"1","key":"621_CR14","doi-asserted-by":"publisher","DOI":"10.3390\/atmos12010124","volume":"12","author":"M Konstantinou","year":"2021","unstructured":"Konstantinou M, Peratikou S, Charalambides AG (2021) Solar photovoltaic forecasting of power output using LSTM networks. Atmosphere 12(1):124","journal-title":"Atmosphere"},{"key":"621_CR15","doi-asserted-by":"publisher","first-page":"172524","DOI":"10.1109\/ACCESS.2020.3024901","volume":"8","author":"MS Hossain","year":"2020","unstructured":"Hossain MS, Mahmood H (2020) Short-term photovoltaic power forecasting using an LSTM neural network and synthetic weather forecast. IEEE Access 8:172524\u2013172533","journal-title":"IEEE Access"},{"key":"621_CR16","doi-asserted-by":"publisher","first-page":"122709","DOI":"10.1016\/j.apenergy.2024.122709","volume":"359","author":"Z Hu","year":"2024","unstructured":"Hu Z, Gao Y, Ji S et al (2024) Improved multistep ahead photovoltaic power prediction model based on LSTM and self-attention with weather forecast data[J]. Appl Energy 359:122709","journal-title":"Appl Energy"},{"key":"621_CR17","doi-asserted-by":"publisher","DOI":"10.1016\/j.energy.2019.116225","volume":"189","author":"K Wang","year":"2019","unstructured":"Wang K, Qi X, Liu H (2019) Photovoltaic power forecasting based LSTM-convolutional network. Energy 189:116225","journal-title":"Energy"},{"key":"621_CR18","doi-asserted-by":"publisher","DOI":"10.1016\/j.epsr.2022.107908","volume":"208","author":"A Agga","year":"2022","unstructured":"Agga A, Abbou A, Labbadi M et al (2022) CNN-LSTM: an efficient hybrid deep learning architecture for predicting short-term photovoltaic power production. Electr Power Syst Res 208:107908","journal-title":"Electr Power Syst Res"},{"issue":"7","key":"621_CR19","doi-asserted-by":"publisher","first-page":"2727","DOI":"10.1007\/s00521-017-3225-z","volume":"31","author":"M Abdel-Nasser","year":"2019","unstructured":"Abdel-Nasser M, Mahmoud K (2019) Accurate photovoltaic power forecasting models using deep LSTM-RNN. Neural Comput Appl 31(7):2727\u20132740","journal-title":"Neural Comput Appl"},{"key":"621_CR20","doi-asserted-by":"publisher","DOI":"10.1016\/j.rser.2024.114479","volume":"200","author":"J Kim","year":"2024","unstructured":"Kim J, Obregon J, Park H et al (2024) Multi-step photovoltaic power forecasting using transformer and recurrent neural networks. Renew Sustain Energy Rev 200:114479","journal-title":"Renew Sustain Energy Rev"},{"key":"621_CR21","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1016\/j.neucom.2023.01.083","volume":"531","author":"J Wang","year":"2023","unstructured":"Wang J, Xie H, Wang FL et al (2023) A transformer\u2013convolution model for enhanced session-based recommendation. Neurocomputing 531:21\u201333","journal-title":"Neurocomputing"},{"key":"621_CR22","unstructured":"Ye T, Dong L, Xia Y et al (2024) Differential transformer . arXiv preprint arXiv:2410.05258"},{"issue":"1","key":"621_CR23","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1007\/s10462-024-11008-6","volume":"58","author":"K Ouyang","year":"2024","unstructured":"Ouyang K, Fu S, Chen Y et al (2024) Escape: an optimization method based on crowd evacuation behaviors[J]. Artif Intell Rev 58(1):19","journal-title":"Artif Intell Rev"},{"issue":"1","key":"621_CR24","doi-asserted-by":"publisher","DOI":"10.1038\/s41598-025-23822-1","volume":"15","author":"PNL Mohamad Radzi","year":"2025","unstructured":"Mohamad Radzi PNL, Mekhilef S, Mohamed Shah N et al (2025) Optimizing solar power forecasting with metaheuristic algorithms and deep learning models for photovoltaic grid connected systems. Sci Rep 15(1):40045","journal-title":"Sci Rep"},{"issue":"19","key":"621_CR25","doi-asserted-by":"publisher","DOI":"10.3390\/s25195977","volume":"25","author":"J Pian","year":"2025","unstructured":"Pian J, Chen X (2025) A high-precision short-term photovoltaic power forecasting model based on multivariate variational mode decomposition and gated recurrent unit-attention with crested porcupine optimizer-enhanced vector weighted average algorithm. Sensors 25(19):5977","journal-title":"Sensors"}],"container-title":["Energy Informatics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/article\/10.1186\/s42162-026-00621-0","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s42162-026-00621-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s42162-026-00621-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,6,16]],"date-time":"2026-06-16T16:47:36Z","timestamp":1781628456000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1186\/s42162-026-00621-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,1,19]]},"references-count":25,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2026,12]]}},"alternative-id":["621"],"URL":"https:\/\/doi.org\/10.1186\/s42162-026-00621-0","relation":{},"ISSN":["2520-8942"],"issn-type":[{"value":"2520-8942","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,1,19]]},"assertion":[{"value":"21 October 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 January 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 January 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":"Not applicable.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethics approval and consent to participate"}},{"value":"Not applicable.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent for publication"}},{"value":"The authors declare no competing interests.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"18"}}