[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-122992-en":3,"doc-seo-122992-105":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},122992,2336464648322,"Aria","https://ap-avatar.wpscdn.com/avatar/2200025388227c56fec?_k=1778556882303663488",8,"Research & Report","Neural Oscillators for Generalization of Physics-Informed Machine Learning","A primary challenge of physics-informed machine learning (PIML) is generalization beyond the training domain, especially for complex physical problems governed by partial differential equations (PDEs). This work improves PIML generalization by leveraging the causality and temporal sequential structure of PDE solutions. The method fuses PIML with recurrent neural architectures derived from systems of ordinary differential equations, termed neural oscillators, to capture long-time dependencies and address exploding and vanishing gradients. Experiments on time-dependent nonlinear PDEs and biharmonic beam equations show state-of-the-art performance across metrics for extrapolation beyond training data.","Neural Oscillators for Generalization of Physics-Informed Machine Learning  \nCitation for published version (APA):  \nKapoor, T. , Chandra, A. , Tartakovsky, D. M. , Wang, H. , Nunez, A. , & Dollevoet, R. (2024) . Neural Oscillators for Generalization of Physics-Informed Machine Learning. In M. Woolridge, J. Dy, & S. Natarajan (Eds.), Proceedings of the AAAI Conference on Artificial Intelligence (pp. 13059-13067) . Association for the Advancement of Artificial Intelligence (AAAI) . [https://doi.org/10.1609/aaai.v38i12.29204](https://doi.org/10.1609/aaai.v38i12.29204)  \nDocument license:  \nTAVERNE  \nDOI:  \n10.1609/aaai.v38i12.29204  \nDocument status and date:  \nPublished: 24/03/2024  \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. 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Feb. 2025  \nNeural Oscillators for Generalization of Physics-Informed Machine Learning  \nTaniya Kapoor 1 * , Abhishek Chandra2 * , Daniel M. Tartakovsky3 , Hongrui Wang 1 , Alfredo Nunez 1 , Rolf Dollevoet 1  \n1Department of Engineering Structures, Delft University of Technology, The Netherlands  \n2Department of Electrical Engineering, Eindhoven University of Technology, The Netherlands  \n3Department of Energy Science and Engineering, Stanford University, USA  \n[t.kapoor@tudelft.nl](t.kapoor@tudelft.nl)  \nAbstract  \nA primary challenge of physics-informed machine learning (PIML) is its generalization beyond the training domain, especially when dealing with complex physical problems represented by partial differential equations (PDEs) . This paper aims to enhance the generalization capabilities of PIML, facilitating practical, real-world applications where accurate predictions in unexplored regions are crucial. We leverage the inherent causality and temporal sequential characteristics of PDE solutions to fuse PIML models with recurrent neural architectures based on systems of ordinary differential equations, referred to as neural oscillators. Through effectively capturing long-time dependencies and mitigating the exploding and vanishing gradient problem, neural oscillators foster improved generalization in PIML tasks. Extensive experimentation involving time-dependent nonlinear PDEsand biharmonic beam equations demonstrates the efficacy ","cbCainIWuRdi72Nq","https://ap.wps.com/l/cbCainIWuRdi72Nq","pdf",656842,1,10,"English","en",105,"# Abstract\n# Introduction","[{\"question\":\"What problem does the paper address in physics-informed machine learning?\",\"answer\":\"It targets the difficulty of generalizing PIML models beyond the training domain, particularly for complex PDE-based physical scenarios.\"},{\"question\":\"How do neural oscillators help improve generalization?\",\"answer\":\"They combine PIML with recurrent neural architectures based on systems of ordinary differential equations, enabling the model to capture long-time dependencies and mitigate exploding/vanishing gradients.\"},{\"question\":\"What evidence is provided to validate the proposed approach?\",\"answer\":\"Extensive experiments on time-dependent nonlinear PDEs and biharmonic beam equations demonstrate improved performance over existing state-of-the-art methods across benchmark metrics.\"}]","Neural Oscillators for Generalization of Physics-Informed Machine Learning | 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problem does the paper address in physics-informed machine learning?","Question",{"text":75,"@type":76},"It targets the difficulty of generalizing PIML models beyond the training domain, particularly for complex PDE-based physical scenarios.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How do neural oscillators help improve generalization?",{"text":80,"@type":76},"They combine PIML with recurrent neural architectures based on systems of ordinary differential equations, enabling the model to capture long-time dependencies and mitigate exploding/vanishing gradients.",{"name":82,"@type":73,"acceptedAnswer":83},"What evidence is provided to validate the proposed approach?",{"text":84,"@type":76},"Extensive experiments on time-dependent nonlinear PDEs and biharmonic beam equations demonstrate improved performance over existing state-of-the-art methods across benchmark 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