[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-122263-en":3,"doc-seo-122263-105":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":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},122263,1099514067415,"Rowan","https://ap-avatar.wpscdn.com/avatar/100002539d78ffe74a7?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779092875211072502",8,"Research & Report","Role of Physics in Physics-Informed Machine Learning","Physics-informed machine learning benefits from embedding physical structure rather than relying only on limited experimental or numerical data. This work argues that symmetries encoded in units and parameter/state relationships can be leveraged through dimensional analysis. The study shows that applying dimensional analysis to data used for learning constitutive or secondary laws improves interpretability and generalizability. Numerical experiments on creeping fluid flow past solid ellipsoids demonstrate recovery of known results and discovery of new ones, highlighting the need to incorporate broader physics-based invariances.","Role of physics in physics-informed machine learning  \nCitation for published version (APA):  \nChandra, A. , Bakarji, J. , & Tartakovsky, D. M. (2024) . Role of physics in physics-informed machine learning. Journal of Machine Learning for Modeling and Computing, 5(1), 85-97.  \n[https://doi.org/10.1615/JMachLearnModelComput.2024053170](https://doi.org/10.1615/JMachLearnModelComput.2024053170)  \nDocument license:  \nTAVERNE  \nDOI:  \n10.1615/JMachLearnModelComput.2024053170  \nDocument status and date:  \nPublished: 01/01/2024  \nDocument Version:  \nPublisher’s PDF, also known as Version of Record (includes final page, issue and volume numbers)  \nPlease check the document version of this publication:  \n• A submitted manuscript is the version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website.  \n• The final author version and the galley proof are versions of the publication after peer review.  \n• The final published version features the final layout of the paper including the volume, issue and page numbers.  \nLink to publication  \nGeneral rights  \nCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.  \n• Users may download and print one copy of any publication from the public portal for the purpose of private study or research.  \n• You may not further distribute the material or use it for any profit-making activity or commercial gain  \n• You may freely distribute the URL identifying the publication in the public portal.  \nIf the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license above, please follow below link for the End User Agreement:  \n[www.tue.nl/taverne](www.tue.nl/taverne)  \nTake down policy  \nIf you believe that this document breaches copyright please contact us at:  \n[openaccess@tue.nl](openaccess@tue.nl)  \nproviding details and we will investigate your claim.  \nDownload date: 11. Jun. 2025  \nJournal of Machine Learning for Modeling and Computing, 5(1):85–97 (2024)  \nROLE OF PHYSICS IN PHYSICS-INFORMED MACHINE LEARNING  \nAbhishek Chandra,1,2 Joseph Bakarji,3,4 & Daniel M. Tartakovsky5,􀀃  \n1Department of Electrical Engineering, Eindhoven University of Technology, The Netherlands  \n2Eindhoven Arti􀀂cial Intelligence Systems Institute, Eindhoven University of Technology, The Netherlands  \n3Department of Mechanical Engineering, American University of Beirut, Beirut, Lebanon  \n4Arti􀀂cial Intelligence, Computing and Data Science Hub, American University of Beirut, Beirut, Lebanon  \n5Department of Energy Science and Engineering, Stanford University, Stanford, California, USA  \n*Address all correspondence to: Daniel M. Tartakovsky, Department of Energy Science and Engineering, Stanford University, USA, E-mail: [tartakovsky@stanford.edu](tartakovsky@stanford.edu)  \nOriginal Manuscript Submitted: 3/11/2024; Final Draft Received: 5/2/2024  \nPhysical systems are characterized by inherent symmetries, one of which is encapsulated in the units of their parameters and system states. These symmetries enable a lossless order-reduction, e.g., via dimensional analysis based on the Buckingham theorem. Despite the latter’s bene􀀂ts, machine learning (ML) strategies for the discovery of constitutive laws seldom subject experimental and/or numerical data to dimensional analysis. We demonstrate the potential of dimensional analysis to signi􀀂cantly enhance the interpretability and generalizability of ML-discovered secondary laws. Our numerical experiments with creeping 􀀃uid 􀀃ow past solid ellipsoids ","cbCailsCuX8L1wGe","https://ap.wps.com/l/cbCailsCuX8L1wGe","pdf",1036094,1,14,"English","en",105,"# Introduction\n## Physics-based knowledge in ML\n## Dimensional analysis and symmetry in equation discovery\n## Numerical experiments on creeping flow past ellipsoids\n## Findings and implications for future ML methods","[{\"question\":\"Why is physics important for physics-informed machine learning?\",\"answer\":\"Physics informs how mathematical models are formulated, such as using conservation laws and symmetry/invariance considerations that constrain differential equations.\"},{\"question\":\"How does dimensional analysis improve ML-based equation discovery?\",\"answer\":\"Dimensional analysis uses unit-based symmetries to enhance interpretability and generalizability of laws discovered from experimental or numerical data.\"},{\"question\":\"What do the numerical experiments on ellipsoids demonstrate?\",\"answer\":\"They show that both deep neural networks and sparse regression can reproduce established results (e.g., Stokes’ law) and generate new expressions for ellipsoids with misaligned flow direction.\"}]","Role of Physics in Physics-Informed Machine Learning | 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is physics important for physics-informed machine learning?","Question",{"text":75,"@type":76},"Physics informs how mathematical models are formulated, such as using conservation laws and symmetry/invariance considerations that constrain differential equations.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does dimensional analysis improve ML-based equation discovery?",{"text":80,"@type":76},"Dimensional analysis uses unit-based symmetries to enhance interpretability and generalizability of laws discovered from experimental or numerical data.",{"name":82,"@type":73,"acceptedAnswer":83},"What do the numerical experiments on ellipsoids demonstrate?",{"text":84,"@type":76},"They show that both deep neural networks and sparse regression can reproduce established results (e.g., Stokes’ law) and generate new expressions for ellipsoids with misaligned flow 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