[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-118767-en":3,"doc-seo-118767-105":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},118767,687197100911,"Himbo","https://ap-avatar.wpscdn.com/avatar/a000239b6f1da00475?x-image-process=image/resize,m_fixed,w_180,h_180&k=1785132997149421697",8,"Research & Report","Intelligent modeling with physics-informed machine learning for petroleum engineering problems - Perspective","The advancement in big data and artificial intelligence enables a novel exploration mode for petroleum engineering. Data-driven intelligent approaches offer flexibility, computational efficiency, and accuracy for complex multi-scale, multi-physics problems, yet they often ignore governing physical laws, creating uncertainty. Physics-informed machine learning addresses this by introducing physical guidance into learning. This work summarizes four embedding mechanisms to incorporate physical information into models, enabling “data + physics” dual-driven prediction with higher accuracy and faster convergence for improved computational efficiency.","Advances in  \nGeo-Energy Research Vol. 8, No. 2, p. 71-75, 2023 Perspective  \nIntelligent modeling with physics-informed machine learning for petroleum engineering problems  \nChiyu Xie 1 ,2 , Shuyi Du 1 ,2 , Jiulong Wang2 ,3 , Junming Lao 1 ,2 , Hongqing Song 1 ,2 *  \n1 School of Civil and Resource Engineering, University of Science and Technology Beijing, Beijing 100083, P. R. China  \n2 National & Local Joint Engineering Lab for Big Data Analysis and Computer Technology, Beijing 100190, P. R. China  \n3 Computer Network Information Center, Chinese Academy of Sciences, Beijing 065007, P. R. China  \n\n| Keywords:\u003Cbr>Physics-informed machine learning\u003Cbr>petroleum engineering data-driven embedding mechanism\u003Cbr>Cited as:\u003Cbr>Xie, C., Du, S., Wang, J., Lao, J., Song, H. Intelligent modeling with\u003Cbr>physics-informed machine learning for petroleum engineering problems. Advances in Geo-Energy Research, 2023, 8(2): 71-75 .\u003Cbr>[https://doi.org/10.46690/ager.2023.05.01](https://doi.org/10.46690/ager.2023.05.01) | Abstract:\u003Cbr>The advancement in big data and artificial intelligence has enabled a novel exploration mode for the study of petroleum engineering. Unlike theory-based solution methods, the data-driven intelligent approaches demonstrate superior flexibility, computational efficiency and accuracy for dealing with complex multi-scale, and multi-physics problems. However, these intelligent models often disregard physical laws in pursuit of error minimization, which leads to certain uncertainties. Therefore, physics-informed machine learning approaches have been developed based on data, guided by physics, and supported by machine learning models. This study summarizes four embedding mechanisms for introducing physical information into machine learning models, including input databased embedding, model architecture-based embedding, loss function-based embedding, and model optimization-based embedding mechanism. These “data + physics” dualdriven intelligent models not only exhibit higher prediction accuracy while adhering to physic laws, but also accelerate the convergence to improve computational efficiency. This paradigm will facilitate the guide developments in solving petroleum engineering problems toward a more comprehensive and efficient direction. |\n| --- | --- |\n\n1. Introduction  \nPetroleum engineering is an important field of engineering considering problems such as seismic exploration, well logging, production development, etc., which is essential for providing energy resources. Petroleum engineering problems are usually across multiple scales, with multi-physics coupling and multiple fluids. Researchers have developed many techniques to tackle the complex flow problems in petroleum engineering, such as molecular dynamics at the microscopic scale (Karplus and Petsko, 1990; Karplus and McCammon, 2002), Monte Carlo simulations (Metropolis and Ulam, 1949; Rubinstein et al., 2016) and lattice Boltzmann methods (Chen and Doolen, 1998) at the mesoscopic scale, computational fluid dynamics (Versteeg and Malalasekera, 2007; Hughes, 2012) at the continuous scale, and reservoir simulations atthe reservoir scale (Peaceman, 2000) . In recent years, break-  \nthroughs in artificial intelligence and big data technologies (Liu et al., 2023) are providing a new mode to further enhance the study of petroleum engineering problems.  \nWith the deep integration of big data, artificial intelligence, and petroleum engineering, the research methods are expanded into 4 models (Fig. 1): experimental investigation, theoretical analysis, numerical simulation, and digital intelligent modeling. Experimental investigations use all kinds of measurement approaches to obtain real and reliable data, then deduce and explain the flow phenomena and laws. Theoretical analysis is the process of analytically solving the mass conservation equations, energy equations, and state equations constructed by classical fluid mechanics theory under certain initial and boundary con","cbCaitaHSfXWRBby","https://ap.wps.com/l/cbCaitaHSfXWRBby","pdf",383120,1,5,"English","en",105,"# Introduction\n## Petroleum engineering challenges and multi-scale multi-physics\n## Digital intelligent modeling and research paradigms\n## Physics-informed machine learning concept and need\n# Embedding mechanisms for physics-informed learning\n## Input-data based embedding\n## Model architecture based embedding\n## Loss function based embedding\n## Model optimization based embedding","[{\"question\":\"Why are data-driven intelligent models not fully reliable for petroleum engineering?\",\"answer\":\"They often minimize prediction error without explicitly respecting physical laws, which can introduce uncertainties for complex multi-physics systems.\"},{\"question\":\"What is the core idea of physics-informed machine learning in this context?\",\"answer\":\"Learning is guided by physical information while still leveraging data and machine learning models, improving both accuracy and physical consistency.\"},{\"question\":\"How does the paper introduce physical information into machine learning models?\",\"answer\":\"It summarizes four embedding mechanisms: input-data based embedding, model architecture based embedding, loss function based embedding, and model optimization based embedding.\"}]","Intelligent modeling with physics-informed machine learning for petroleum engineering problems - Perspective | PDF",1785720126,13,{"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},"intelligent-modeling-with-physics-informed-machine-learning-for-petroleum-engineering-problems-perspective","",{"@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/intelligent-modeling-with-physics-informed-machine-learning-for-petroleum-engineering-problems-perspective/118767/",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","2026-08-03",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 are data-driven intelligent models not fully reliable for petroleum engineering?","Question",{"text":75,"@type":76},"They often minimize prediction error without explicitly respecting physical laws, which can introduce uncertainties for complex multi-physics systems.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What is the core idea of physics-informed machine learning in this context?",{"text":80,"@type":76},"Learning is guided by physical information while still leveraging data and machine learning models, improving both accuracy and physical consistency.",{"name":82,"@type":73,"acceptedAnswer":83},"How does the paper introduce physical information into machine learning models?",{"text":84,"@type":76},"It summarizes four embedding mechanisms: input-data based embedding, model architecture based embedding, loss function based embedding, and model optimization based embedding.","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},[93,97,101,105,109,114,119,122,127,130,134],{"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":21,"doc_module":4,"doc_module_name":46,"category_name":106,"show_sort_weight":107,"slug":108},"Comic",60,"comic",{"id":110,"doc_module":4,"doc_module_name":46,"category_name":111,"show_sort_weight":112,"slug":113},6,"Technology",50,"technology",{"id":115,"doc_module":4,"doc_module_name":46,"category_name":116,"show_sort_weight":117,"slug":118},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":120,"slug":121},30,"research-report",{"id":123,"doc_module":4,"doc_module_name":46,"category_name":124,"show_sort_weight":125,"slug":126},9,"Religion & Spirituality",20,"religion-spirituality",{"id":125,"doc_module":4,"doc_module_name":46,"category_name":128,"show_sort_weight":125,"slug":129},"World Cup","world-cup",{"id":131,"doc_module":4,"doc_module_name":46,"category_name":132,"show_sort_weight":131,"slug":133},10,"Lifestyle","lifestyle",{"id":135,"doc_module":4,"doc_module_name":46,"category_name":136,"show_sort_weight":21,"slug":137},19,"General","general"]