[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-120914-en":3,"doc-seo-120914-105":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},120914,4398048949847,"Eliana","https://ap-avatar.wpscdn.com/avatar/400002536579ef2da7f?_k=1778318612642679267",8,"Research & Report","SOME COMPARISONS OF NEURAL NETWORK ARCHITECTURES FOR SCIENTIFIC MACHINE LEARNING","The thesis compares multiple neural network architectures used to approximate solutions and solution operators for several elementary 1D partial differential equations. It evaluates whether residual layers provide advantages over fully connected layers within physics-informed machine learning, concluding similar performance for the studied problems. It also contrasts DeepONet and Fourier neural operator methods for operator learning, noting comparable accuracy on linear cases and improved modeling accuracy of Fourier neural operators when a simple nonlinearity is introduced.","Calhoun: The NPS Institutional Archive  \nDSpace Repository  \n\n| 2023-12\u003Cbr>SOME COMPARISONS OF NEURAL NETWORK\u003Cbr>ARCHITECTURES FOR SCIENTIFIC MACHINE LEARNING\u003Cbr>Sustaita, Javier J.\u003Cbr>Monterey, CA; Naval Postgraduate School |\n| --- |\n| [https://hdl.handle.net/10945/72612](https://hdl.handle.net/10945/72612) |\n\nNPS Scholarship Theses  \nThis publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.  \nDownloaded from NPS Archive: Calhoun  \nNAVAL POSTGRADUATE  \nSCHOOL MONTEREY, CALIFORNIA  \nTHESIS  \nSOME COMPARISONS OF NEURAL NETWORK ARCHITECTURES FOR SCIENTIFIC  \nMACHINE LEARNING  \nby  \nJavier J. Sustaita  \nDecember 2023  \nThesis Advisor: Anthony Austin  \nSecond Reader: Wei Kang  \nApproved for public release. Distribution is unlimited.  \nTHIS PAGE INTENTIONALLY LEFT BLANK  \n\n| REPORT DOCUMENTATION PAGE |  |  |  | Form Approved OMB No. 0704-0188 |  |\n| --- | --- | --- | --- | --- | --- |\n| Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instruction, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302, and to the Office of Management and Budget, Paperwork Reduction Project (0704-0188) Washington, DC 20503. |  |  |  |  |  |\n| 1. AGENCY USE ONLY (Leave blank) |  | 2. REPORT DATE\u003Cbr>December 2023 | 3. REPORT TYPE AND DATES COVERED\u003Cbr>Master's thesis |  |  |\n| 4. TITLE AND SUBTITLE\u003Cbr>SOME COMPARISONS OF NEURAL NETWORK ARCHITECTURES FOR SCIENTIFIC MACHINE LEARNING |  |  |  | 5. FUNDING NUMBERS |  |\n| 6. AUTHOR(S) Javier J. Sustaita |  |  |  |  |  |\n| 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)\u003Cbr>Naval Postgraduate School\u003Cbr>Monterey, CA 93943-5000 |  |  |  | 8. PERFORMING\u003Cbr>ORGANIZATION REPORT NUMBER |  |\n| 9. SPONSORING / MONITORING AGENCY NAME(S) AND\u003Cbr>ADDRESS(ES)\u003Cbr>N/A |  |  |  | 10. SPONSORING / MONITORING AGENCY REPORT NUMBER |  |\n| 11. SUPPLEMENTARY NOTES The views expressed in this thesis are those of the author and do not reflect the official policy or position of the Department of Defense or the U.S. Government. |  |  |  |  |  |\n| 12a. DISTRIBUTION / AVAILABILITY STATEMENT\u003Cbr>Approved for public release. Distribution is unlimited. |  |  |  | 12b. DISTRIBUTION CODE\u003Cbr>A |  |\n| 13. ABSTRACT (maximum 200 words)\u003Cbr>We compare several neural network architectures for approximating solutions to and solution operators for a handful of elementary 1D partial differential equations. Specifically, we examine whether residual layers offer any benefits over fully connected layers in the context of physics-informed machine learning, finding that the two perform similarly on the problems considered. We also compare the popular DeepONet and Fourier neural operator approaches to operator learning and observe that while the two attain comparable accuracies for linear problems, the latter yields more accurate models in the presence of a simple nonlinearity. |  |  |  |  |  |\n| 14. SUBJECT TERMS\u003Cbr>scientific machine learning, physics-informed neural networks, operator learning, residual neural networks, DeepONet, Fourier neural operator |  |  |  |  | 15. NUMBER OF PAGES\u003Cbr>63 |\n|  |  |  |  |  | 16. PRICE CODE |\n| 17. SECURITY\u003Cbr>CLASSIFICATION OF REPORT\u003Cbr>Unclassified | 18. SECURITY\u003Cbr>CLASSIFICATION OF THIS PAGE\u003Cbr>Unclassified |  | 19. SECURITY\u003Cbr>CLASSIFICATION OF ABSTRACT\u003Cbr>Unclassified |  | 20. LIMITATION OF ABSTRACT\u003Cbr>UU |\n\nNSN 7540-01-280-5500 Standard Form 298 (Rev. 2-89) Prescribed by ANSI Std. 239-18  \ni  \nTHIS PAGE INTENTIONALLY LEFT BLA","cbCaicalW500sHgM","https://ap.wps.com/l/cbCaicalW500sHgM","pdf",6381200,1,65,"English","en",105,"# Introduction\n# Background\n## Neural Networks\n## Training\n## Physics-Informed Neural Networks (PINNs)\n# Residual Layers in Physics-Informed Learning\n## Residual Learning\n## Experimental Setup\n## Experiments\n## Findings and Results\n## Conclusions\n# A Comparison of Two Neural Operators","[{\"question\":\"What is the main focus of the thesis?\",\"answer\":\"The thesis compares neural network architectures for scientific machine learning tasks involving 1D partial differential equations, both for approximating solutions and solution operators.\"},{\"question\":\"Do residual layers outperform fully connected layers in physics-informed learning?\",\"answer\":\"The study finds no clear advantage: residual layers and fully connected layers perform similarly on the problems considered.\"},{\"question\":\"How do DeepONet and Fourier neural operator approaches compare?\",\"answer\":\"They achieve comparable accuracies for linear problems, but Fourier neural operators perform better when a simple nonlinearity is present.\"}]","SOME COMPARISONS OF NEURAL NETWORK ARCHITECTURES FOR SCIENTIFIC MACHINE LEARNING | 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