[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-116951-en":3,"doc-seo-116951-105":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},116951,34359740700684,"Finn","https://ap-avatar.wpscdn.com/avatar/1f400023980c374ae676?_k=1777273430885731487",8,"Research & Report","Machine Learning for PAC1D and SESE - Technical Memo","Machine learning methods are applied to PAC1D and SESE through physics-informed and operator-learning neural network frameworks. The report reviews key foundations in fully connected neural networks and surveys architectures including PINNs, DeepONET, and Fourier Neural Operators. Emphasis is placed on differentiable physics, exploring network and boundary-condition variations, and improving physics-informed neural networks. Results are benchmarked via L2 error comparisons across multiple problem dimensions, supported by figures and tables, culminating in conclusions and references.","AFRL-RH-FS-TM-2023-0003 Machine Learning for PAC1D and SESE  \nJason A. Kurz  \nNational Security Innovation Network  \nMatthew G. Seman  \nTaufiquar Khan  \nUniversity of North Carolina Charlotte  \nBrett A. Bowman  \nSAIC, Inc.  \nChad A. Oian  \n711th Human Performance Wing Airman Systems Directorate  \nBioeffects Division Optical Radiation Bioeffects Branch  \n3 April 2023  \nTechnical Memo-April 2021-February 2023  \nDISTRIBUTION STATEMENT A. Approved for public release; distribution is unlimited.  \nCleared: AFRL PA Case Number:  \nAFRL-2023-3436. The views expressed are those of the author and do not necessarily reflect the official policy or position of the Department of the Air Force, the Department of Defense, or the United States Government.  \nAir Force Research Laboratory 711th Human Performance Wing Airman Systems Directorate Bioeffects Division  \nOptical Radiation Bioeffects Branch JBSA Fort Sam Houston, Texas 78234  \nTABLE OF CONTENTS  \nSection Page  \nList of Figures ......................................... ii  \nList of Tables ......................................... ii  \nACKNOWLEDGEMENTS .................................. iii  \n1.0 SUMMARY ...................................... 1  \n2.0 INTRODUCTION TO MACHINE LEARNING ................... 1  \n2.1 Literature Review ................................... 1  \n2.2 Fully Connected Neural Networks .......................... 2  \n3.0 PAC1D AND SESE .................................. 6  \n4.0 PHYSICS-INFORMED NEURAL NETWORKS .................. 7  \n4.1 PINN for PAC1D ................................... 8  \n4.1.1 Overview of DGM .................................. 8  \n4.1.2 Differentiable Physics in Deep Learning: ....................... 10  \n4.1.3 Various Architecture and Boundary Condition Exploration ............. 16  \n4.1.4 Improving Physics-Informed Neural Network (PINN) and Hardcoding Boundary Conditions ....................................... 19  \n5.0 ONET ......................................... 25  \n5.1 DeepONET ...................................... 26  \n6.0 FOURIER NEURAL OPERATOR .......................... 27  \n6.1 PINO ......................................... 29  \n7.0 COMPARISON OF METHODS ........................... 31  \n7.1 Table with L2 Errors .................................. 31  \n8.0 CONCLUSION .................................... 32  \n9.0 REFERENCES .................................... 33  \nLIST OF SYMBOLS, ABBREVIATIONS, AND ACRONYMS .............. 38  \ni  \nDISTRIBUTION STATEMENT A. Approved for public release; distribution is unlimited. Cleared: AFRL PA Case Number: AFRL-2023-3436 . The views expressed are those of the author and do not necessarily reflect the official policy or position of the Department of the Air Force, the  \nDepartment of Defense, or the United States Government.  \nLIST OF FIGURES  \nPage  \nFigure 1 Fully-Connected Neural Network ....................... 4  \nFigure 2 PINN Results .................................. 12  \nFigure 3 PINN Error ................................... 13  \nFigure 4 PINN vs. DP .................................. 14  \nFigure 5 PINN vs. DP Error ............................... 14  \nFigure 6 Resnet ..................................... 16  \nFigure 7 DNN vs. LSTM Comparison ......................... 18  \nFigure 8 3-Layer Skin Temperature Rise Example. Temperature vs. depth in three  \nlayer (epidermis, dermis, fat) skin model. Each plot trace represents a snapshot in time................................. 20  \nFigure 9 3-Layer Skin Dose Example. Sharp changes in dose deposition occur near skin layer boundary due to layer-specific absorption differences. Dose does not change with time.............................. 21  \nFigure 10 ResNet Block .................................. 22  \nFigure 11 MIM 1 Network Structure ........................... 22  \nFigure 12 MIM 2 Network Structure ........................... 23  \nFigure 13 Sequence-to-sequence ............................. 25  \nFigure 14 DeepONET Visualization ........................... 26","cbCaisOQUctZfk4j","https://ap.wps.com/l/cbCaisOQUctZfk4j","pdf",1134168,1,43,"English","en",105,"# Summary\n# Introduction to Machine Learning\n## Literature Review\n## Fully Connected Neural Networks\n# PAC1D and SESE\n# Physics-Informed Neural Networks\n## PINN for PAC1D\n# DeepONET\n# Fourier Neural Operator\n## PINO\n# Comparison of Methods\n## Table with L2 Errors\n# Conclusion\n# References","[{\"question\":\"What machine learning approaches are used for PAC1D and SESE?\",\"answer\":\"The document uses physics-informed neural networks (PINNs), including PINNs tailored for PAC1D, and also explores operator-learning methods such as DeepONET and Fourier Neural Operators (FNO), including PINO. These approaches are compared using error metrics.\"},{\"question\":\"How does the report improve physics-informed neural networks for PAC1D?\",\"answer\":\"It focuses on differentiable physics within deep learning, architecture and boundary-condition exploration, and techniques for improving PINNs and hardcoding boundary conditions. The goal is to strengthen physical consistency and accuracy.\"},{\"question\":\"How are different methods evaluated and compared?\",\"answer\":\"Methods are benchmarked using L2 error tables for problems spanning different dimensionalities, including comparisons across mesh resolution. Visual results and quantitative summaries (figures and tables) support the assessment.\"}]","Machine Learning for PAC1D and SESE - Technical Memo | PDF",1785672791,108,{"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},"machine-learning-for-pac1d-and-sese-technical-memo","",{"@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/machine-learning-for-pac1d-and-sese-technical-memo/116951/",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","2026-08-05","2026-08-02",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 machine learning approaches are used for PAC1D and SESE?","Question",{"text":76,"@type":77},"The document uses physics-informed neural networks (PINNs), including PINNs tailored for PAC1D, and also explores operator-learning methods such as DeepONET and Fourier Neural Operators (FNO), including PINO. These approaches are compared using error metrics.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"How does the report improve physics-informed neural networks for PAC1D?",{"text":81,"@type":77},"It focuses on differentiable physics within deep learning, architecture and boundary-condition exploration, and techniques for improving PINNs and hardcoding boundary conditions. The goal is to strengthen physical consistency and accuracy.",{"name":83,"@type":74,"acceptedAnswer":84},"How are different methods evaluated and compared?",{"text":85,"@type":77},"Methods are benchmarked using L2 error tables for problems spanning different dimensionalities, including comparisons across mesh resolution. 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