[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-119162-en":3,"doc-seo-119162-105":30,"detail-sidebar-cat-0-en-105":92},{"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":20,"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},119162,8796095461564,"Liam","https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d",8,"Research & Report","Discussing the Spectrum of Physics-Enhanced Machine Learning - a Survey on Structural Mechanics Applications","Physics-enhanced machine learning (PEML) merges physical knowledge with machine learning to strengthen capabilities and mitigate weaknesses of purely data-driven or physics-only approaches. The paper surveys the PEML “spectrum” by organizing methods along core axes of physics and data, detailing characteristics, motivations, and usage. It highlights recent applications in structural mechanics and illustrates distinct PEML genres using a single-degree-of-freedom Duffing oscillator example. Supplementary code supports transparency and reproducibility, reinforcing PEML’s value for advancing scientific and engineering research.","Data-Centric Engineering (2023), 1–36 doi:XX.XXXX/dce.XXXX.X  \nSURVEY PAPER  \narXiv :2310 .20425v3 [ cs .LG] 22 Apr 2024  \nDiscussing the Spectrum of Physics-Enhanced Machine Learning; a Survey on Structural Mechanics Applications  \nMarcus Haywood-Alexander 1 * , Wei Liu2,3, Kiran Bacsa 1,3, Zhilu Lai4,5 and Eleni Chatzi 1,3  \n1Department of Civil, Environmental and Geomatic Engineering, ETH Zürich, Zürich, 8049, Switzerland  \n2Department of Industrial Systems Engineering and Management, National University of Singapore, Singapore  \n3Future Resilient Systems, Singapore-ETH Centre, Singapore  \n4Internet of Things Thrust, HKUST(GZ), Guangzhou, People’s Republic of China  \n5Department of Civil and Environmental Engineering, HKUST, Hong Kong, People’s Republic of China  \n*[Corresponding author. E-mail: mhaywood@ethz.ch](Corresponding author. E-mail: mhaywood@ethz.ch)[ ](Corresponding author. E-mail: mhaywood@ethz.ch)Received xx xxx xxxx  \nKeywords: physics enhanced, physics-based, physics-guided, physics-encoded, data driven, hybrid learning, structural mechanics  \nAbstract  \nThe intersection of physics and machine learning has given rise to the physics-enhanced machine learning (PEML) paradigm, aiming to improve the capabilities and reduce the individual shortcomings of data- or physics-only methods. In this paper, the spectrum of physics-enhanced machine learning methods, expressed across the defining axes of physics and data, is discussed by engaging in a comprehensive exploration of its characteristics, usage, and motivations. In doing so, we present a survey of recent applications and developments of PEML techniques, revealing the potency of PEML in addressing complex challenges. We further demonstrate application of select such schemes on the simple working example of a single degree-of-freedom Duffing oscillator, which allows to highlight the individual characteristics and motivations of different ‘genres’ of PEML approaches. To promote collaboration and transparency, and to provide practical examples for the reader, the code generating these working examples is provided alongside this paper. As a foundational contribution, this paper underscores the significance of PEML in pushing the boundaries of scientific and engineering research, underpinned by the synergy of physical insights and machine learning capabilities.  \nImpact Statement  \nThis paper discusses methods born from fusion of physics and machine learning, known as physics-enhanced machine learning (PEML) schemes. By considering their characteristics, this work clarifies and categorizes PEML techniques, aiding researchers and users to targetedly select methods on the basis of specific problem characteristics and requirements. The discussion of PEML techniques is framed around a survey of recent applications/developments of PEML in the field of structural mechanics. A running example of a Duffing oscillator is used to highlight the traits and potential of diverse PEML approaches. Additionally, code is provided to foster transparency and collaboration. The work advocates the pivotal role of PEML in advancing computing for engineering through the merger of physics based knowledge and machine learning capabilities.  \n© The Authors(s), 2020. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence ([http://](http://)[ ](http://)[creativecommons.org/licenses/by/4.0/](creativecommons.org/licenses/by/4.0/)), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.  \n2 M. Haywood-Alexander et al.  \n1. Introduction  \nWith the increase in both computing power and data availability, machine learning (ML) and deep learning (DL) are in scientific and engineering applications (Reich, 1997 ; Hey et al., 2020 ; Zhong et al., 2021 ; Cuomo et al., 2022) . Such methods have shown enormous potential in yielding efficient and accurate estimates over highly complex domains","cbCailkcI1yvsmbf","https://ap.wps.com/l/cbCailkcI1yvsmbf","pdf",4448688,1,36,"English","en",105,"# Introduction\n## Motivation and challenges of data-driven learning\n## Physics-enhanced machine learning paradigm\n# Survey focus and spectrum of PEML approaches\n## Axes of physics and data\n## Structural mechanics applications\n# Running example: Duffing oscillator\n## Comparing PEML genres\n# Reproducibility and code availability\n## Transparency and collaboration\n# Impact statement\n## Targeted method selection for engineering problems","[{\"question\":\"What problem does physics-enhanced machine learning (PEML) address?\",\"answer\":\"PEML addresses limitations of data-driven models, such as weak generalisability beyond the collected data domain, by injecting physics-oriented structure to improve robustness in engineering tasks.\"},{\"question\":\"How does the paper organize the different PEML methods?\",\"answer\":\"The paper discusses PEML methods across defining axes of physics and data, categorizing their characteristics, motivations, and typical usage patterns.\"},{\"question\":\"Why is the Duffing oscillator used as a running example?\",\"answer\":\"The single degree-of-freedom Duffing oscillator provides a simple working testbed to highlight and compare the distinct traits and motivations of different PEML “genres”.\"}]","Discussing the Spectrum of Physics-Enhanced Machine Learning - a Survey on Structural Mechanics Applications | PDF",1785722853,91,{"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":87,"head_meta":89,"extra_data":91,"updated_unix":28},"discussing-the-spectrum-of-physics-enhanced-machine-learning-a-survey-on-structural-mechanics-applications","",{"@graph":36,"@context":86},[37,54,69],{"@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/discussing-the-spectrum-of-physics-enhanced-machine-learning-a-survey-on-structural-mechanics-applications/119162/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":63,"encodingFormat":61,"isAccessibleForFree":64,"interactionStatistic":65},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-04","2026-08-03",true,{"@type":66,"interactionType":67,"userInteractionCount":20},"InteractionCounter",{"@type":68},"ViewAction",{"@type":70,"mainEntity":71},"FAQPage",[72,78,82],{"name":73,"@type":74,"acceptedAnswer":75},"What problem does physics-enhanced machine learning (PEML) address?","Question",{"text":76,"@type":77},"PEML addresses limitations of data-driven models, such as weak generalisability beyond the collected data domain, by injecting physics-oriented structure to improve robustness in engineering tasks.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"How does the paper organize the different PEML methods?",{"text":81,"@type":77},"The paper discusses PEML methods across defining axes of physics and data, categorizing their characteristics, motivations, and typical usage patterns.",{"name":83,"@type":74,"acceptedAnswer":84},"Why is the Duffing oscillator used as a running example?",{"text":85,"@type":77},"The single degree-of-freedom Duffing oscillator provides a simple working testbed to highlight and compare the distinct traits and motivations of different PEML “genres”.","https://schema.org",{"og:url":52,"og:type":88,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":90,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":93},[94,98,102,106,111,116,121,124,129,132,136],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":95,"show_sort_weight":96,"slug":97},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":99,"show_sort_weight":100,"slug":101},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":103,"show_sort_weight":104,"slug":105},"Exam",70,"exam",{"id":107,"doc_module":4,"doc_module_name":46,"category_name":108,"show_sort_weight":109,"slug":110},5,"Comic",60,"comic",{"id":112,"doc_module":4,"doc_module_name":46,"category_name":113,"show_sort_weight":114,"slug":115},6,"Technology",50,"technology",{"id":117,"doc_module":4,"doc_module_name":46,"category_name":118,"show_sort_weight":119,"slug":120},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":122,"slug":123},30,"research-report",{"id":125,"doc_module":4,"doc_module_name":46,"category_name":126,"show_sort_weight":127,"slug":128},9,"Religion & Spirituality",20,"religion-spirituality",{"id":127,"doc_module":4,"doc_module_name":46,"category_name":130,"show_sort_weight":127,"slug":131},"World Cup","world-cup",{"id":133,"doc_module":4,"doc_module_name":46,"category_name":134,"show_sort_weight":133,"slug":135},10,"Lifestyle","lifestyle",{"id":137,"doc_module":4,"doc_module_name":46,"category_name":138,"show_sort_weight":107,"slug":139},19,"General","general"]