[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-123250-en":3,"doc-seo-123250-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},123250,1099514067438,"River Wang","https://ap-avatar.wpscdn.com/avatar/100002539ee87300030?x-image-process=image/resize,m_fixed,w_180,h_180&k=1780474512215547542",8,"Research & Report","Efficient estimation of convective cooling of photovoltaic arrays - A physics-informed machine learning approach","Convective cooling by wind strongly influences the operating temperature and thus the power generation of large-scale photovoltaic (PV) systems, making accurate prediction of the convective heat transfer coefficient essential for array design across different geometric configurations. The study proposes a physics-informed machine learning framework that couples Physics-Informed Machine Learning with a deep convolutional neural network (PIML-DCNN). Trained and validated using 160 CFD simulations, the method introduces a Pocket Loss to improve robustness and interpretability, achieving 2.5% relative error on validation and 2.7% on test sets while outperforming empirical methods and running far faster than CFD.","Energy and AI 20 (2025) 100499  \n\n| \u003Cbr>\u003Cbr>Contents lists available at ScienceDirect\u003Cbr>Energy and AI\u003Cbr>journal [homepage: www.elsevier.com/locate/egyai](homepage: www.elsevier.com/locate/egyai) |  |\n| --- | --- |\n\n\n| Efficient estimation of convective cooling of photovoltaic arrays: A physics-informed machine learning approach\u003Cbr>Dapeng Wang, Zhaojian Liang, Ziqi Zhang, Mengying Li ∗\u003Cbr>Department of Mechanical Engineering & Research Institute for Smart Energy, The Hong Kong Polytechnic University, Hong Kong Special Administrative Region |  |  |  |\n| --- | --- | --- | --- |\n| H I G H L I G H T S\u003Cbr>• A Physics-Informed Machine Learning model estimates heat dissipation in PV arrays.\u003Cbr>• Data from 160 CFD simulations is used to train and validate the proposed model.\u003Cbr>• A novel Pocket Loss function improves interpretability and model robustness.\u003Cbr>• The model achieves 2.7% errors on testing datasets.\u003Cbr>• The model outperforms empirical methods and is faster than CFD simulations. |  | G RAP H I CA L A B ST RA CT\u003Cbr> |  |\n| A R T I C L E I N F O |  | A B S T R A C T |  |\n| Keywords:\u003Cbr>Geometric configuration of PV array Convective heat transfer\u003Cbr>Deep convolution neural network Physics informed machine learning Pocket loss |  | Convective cooling by wind is crucial for large-scale photovoltaic (PV) systems, as power generation inversely correlates with panel temperature. Therefore, accurately determining the convective heat transfer coefficient for PV arrays with various geometric configurations is essential to optimize array design. Traditional methods to quantify the effects of configuration utilize either Computational Fluid Dynamics (CFD) simulations or empirical methods. These approaches often face challenges due to high computational demands or limited accuracy, particularly with complex array configurations. Machine learning approaches, especially hybrid learning models, have emerged as effective tools to address challenges in heat transfer design optimization. This study introduces a method that combines Physics-Informed Machine Learning with a Deep Convolutional Neural Network (PIML-DCNN) to predict convective heat transfer rates with high accuracy and computational efficiency. Additionally, an innovative loss function, termed the \"Pocket Loss\", is developed to enhance the interpretability and robustness of the PIML-DCNN model. The proposed model achieves relative estimation errors of 2.5% and 2.7% on the validation and test datasets, respectively, when benchmarked against comprehensive CFD simulations. These results highlight the potential of the proposed model to efficiently guide the configuration design of PV arrays, thereby enhancing power generation in real-world operations. |  |\n\n∗ Corresponding author.  \nE-mail address: [mengying.li@polyu.edu.hk](mengying.li@polyu.edu.hk) (M. Li).  \n[https://doi.org/10.1016/j.egyai.2025.100499](https://doi.org/10.1016/j.egyai.2025.100499)  \nReceived 14 August 2024; Received in revised form 29 January 2025; Accepted 10 March 2025  \nAvailable online 22 March 2025  \n2666-5468/© 2025 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license ([http://creativecommons.org/licenses/by/4.0/](http://creativecommons.org/licenses/by/4.0/)).  \nD. Wang et al.  \nNomenclature  \nSymbols  \n􀀋 Coefficient of Pocket Loss  \n􀀌􀁰 Temperature coefficient of photovoltaic panels,[%/K]  \n􀀟 Parameters need physical interpretation  \n􀀢 Relative error  \n􀀀 Distinguish label in training,[m2/s]  \n􀀃 Lacunarity  \n􀀗 Kinematic viscosity of air,[N s/m2 ]  \n􀀈 Convolution Neural Network  \n􀀉 Geometric features  \n􀀒 Tilt angle of the panels, [rad], or Feed forward layers  \n􀀘 Pocket Loss  \n􀁃low Lower boundary in Pocket Loss  \n􀁃up Upper boundary in Pocket Loss  \n􀁄 Characteristic height of the array used to calculate Nu,[m]  \n􀁤 Panel length,[m]  \n􀁥 Maximum relative error  \n􀁈 Height of the computation domain,[m]  \nℎ Coefficient of convective heat transfer,  \n[W/m2 K]  \n􀁫 Thermal condu","cbCaiffXGtuPwCKs","https://ap.wps.com/l/cbCaiffXGtuPwCKs","pdf",5427253,1,13,"English","en",105,"# Highlights\n# Nomenclature and Abbreviations\n## Symbols and Subscripts\n## Abbreviations\n# Introduction\n# Methods and Model Design\n## Physics-Informed Machine Learning and DCNN\n## Pocket Loss Function","[{\"question\":\"Why is convective cooling important for photovoltaic arrays?\",\"answer\":\"Wind-driven convective cooling affects PV panel temperature, which directly influences power generation and conversion efficiency. Accurate prediction helps optimize array design and real-world performance.\"},{\"question\":\"How is the proposed model trained and validated?\",\"answer\":\"The PIML-DCNN model is trained and validated using 160 CFD simulations, covering PV arrays under various geometric configurations.\"},{\"question\":\"What is the Pocket Loss and what benefit does it provide?\",\"answer\":\"Pocket Loss is a customized loss function developed to enhance both interpretability and robustness of the PIML-DCNN model compared with standard training objectives.\"}]","Efficient estimation of convective cooling of photovoltaic arrays - A physics-informed machine learning approach | PDF",1785815474,33,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"efficient-estimation-of-convective-cooling-of-photovoltaic-arrays-a-physics-informed-machine-learning-approach","",{"@graph":36,"@context":85},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/efficient-estimation-of-convective-cooling-of-photovoltaic-arrays-a-physics-informed-machine-learning-approach/123250/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-04",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"Why is convective cooling important for photovoltaic arrays?","Question",{"text":75,"@type":76},"Wind-driven convective cooling affects PV panel temperature, which directly influences power generation and conversion efficiency. Accurate prediction helps optimize array design and real-world performance.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How is the proposed model trained and validated?",{"text":80,"@type":76},"The PIML-DCNN model is trained and validated using 160 CFD simulations, covering PV arrays under various geometric configurations.",{"name":82,"@type":73,"acceptedAnswer":83},"What is the Pocket Loss and what benefit does it provide?",{"text":84,"@type":76},"Pocket Loss is a customized loss function developed to enhance both interpretability and robustness of the PIML-DCNN model compared with standard training objectives.","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]