[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-117262-en":3,"doc-seo-117262-105":29,"detail-sidebar-cat-0-en-105":90},{"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":13,"seo_description":14,"update_tm":27,"read_time":28},117262,8796095462418,"Noah","https://ap-avatar.wpscdn.com/avatar/80000253c1241d02b47?x-image-process=image/resize,m_fixed,w_180,h_180&k=1778826106357471780",8,"Research & Report","Machine learning supergravity vacua - Thesis","The thesis studies maximally symmetric vacua in four-dimensional maximal supergravity and shows how the vacua structure is determined by the gauging procedure. Consistency of the gauging combined with extremization of the scalar potential yields a parametrized system of equations describing the vacuum structure. It surveys literature strategies that apply machine learning to solve these equations and introduces an improved neural-network-based method. Finally, it presents an efficient symbolic algorithm for solving polynomial equation systems and reports its implementation in the Python library PyXLTensor to support tensor-expression manipulation and solution.","Universit`a degli Studi di Padova  \nDepartment of Physics and Astronomy “Galileo Galilei”Master’s Degree course in Theoretical Physics of Fundamental  \nInteractions  \nMachine learning supergravity vacua  \nThesis supervisor:  \nProf. Dall’Agata Gianguido  \nCandidate:  \nCostantini Riccardo  \nAcademic Year 2023-2024  \nAbstract  \nIn this thesis we study maximally symmetric vacua for maximal supergravity in 4D. We will begin by showing that the structure of those vacua is determined by the gauging procedure. The consistency of the gauging, together with the extremization of the scalar potential, allows us to parameterize a system of equations that describes the vacua structure.  \nWe also examine various approaches from the literature that utilize machine learning techniques to solve these equations. In particular, we present a novel approach based on a neural network architecture that improves the efficiency of those machine learning methods.  \nFinally, we will present an efficient algorithm for analytically solving systems of polynomial equations. This algorithm has been improved and implemented in a Python library, PyXLTensor. This library facilitates the writing, manipulation and solving of tensor expressions. Given its versatility it offers wide applicability in other fields where tensor equations need to be solved.  \nContents  \n1 Introduction 5  \n2 Maximal supergravity and its vacua 6  \n2.1 Maximal supergravity in 4D ......................... 6  \n2.2 Gaugings and the scalar potential ...................... 9  \n2.3 “Going to the origin” and vacua ....................... 12  \n2.4 Known solutions ............................... 13  \n3 Machine learning supergravity vacua 14  \n3.1 Learning machine learning .......................... 14  \n3.2 Old attempts ................................. 18  \n3.3 New attempts ................................. 20  \n3.3.1 Cluster algorithm ........................... 20  \n3.3.2 NS algorithm ............................. 22  \n4 Relinearization and new algorithms 26  \n4.1 Algebraic approaches ............................. 26  \n4.1.1 Relinearization algorithm ....................... 26  \n4.1.2 XL algorithm ............................. 27  \n4.2 Improvements on the XL algorithm ..................... 29  \n4.3 Examples ................................... 31  \n5 Summary and outlooks 33  \nA The group E7(7) 34  \nB How to deal with matrices with 0 positive(negative) eigenvalue 35  \nC How to use PyXLTensor 36  \nC.1 Initialization of the tensors .......................... 36  \nC.2 Basic operations ................................ 37  \nC.3 Block tensors ................................. 38  \nC.4 Symmetrization, anti-symmetrization, duality, δ and ϵ ........... 39  \nC.5 Managing the indices ............................. 40  \nC.6 Elements of the tensors ............................ 41  \nC.7 Reading the tensors .............................. 42  \nC.8 Initializing a system of equations ...................... 42  \nC.9 Obtaining and reading the solutions ..................... 43  \n1 Introduction  \nThe Standard Model of particle physics has been very successful in describing the electromagnetic, weak and strong interactions among particles. However, incorporating gravitational interactions in a consistent manner presents a significant challenge. One way to accommodate gravity in this picture can be achieved with supersymmetry. This providesan elegant solution, as supergravity naturally emerges when transitioning from global to local supersymmetry, analogous to how the other force-carrying fields in the Standard Model arise from localizing their respective symmetries.  \nSupergravity can be realized in various forms and each of them has its peculiarity. Of particular interest are the theories with the maximum possible amount of supersymmetry, known as maximal supergravity. These theories are particularly interesting because the stringent constraints imposed by maximal supersymmetry fully determine the structure of the theo","cbCaijFovCmrDMoO","https://ap.wps.com/l/cbCaijFovCmrDMoO","pdf",1502637,1,48,"English","en",105,"# Introduction\n## Standard Model challenge and supersymmetry\n## Vacuum classification problem\n# Maximal supergravity and its vacua\n## Maximal supergravity in 4D\n## Gaugings and the scalar potential\n## Going to the origin and vacua\n## Known solutions\n# Machine learning supergravity vacua\n## Learning machine learning\n## Old attempts\n## New attempts\n## Cluster algorithm\n## NS algorithm\n# Relinearization and new algorithms\n## Algebraic approaches\n## Relinearization algorithm\n## XL algorithm\n## Improvements on the XL algorithm\n## Examples\n# Summary and outlooks\n# Appendices\n## The group E7(7)\n## Handling matrices with zero-sign eigenvalues\n## Using PyXLTensor","[{\"question\":\"How does the thesis determine the structure of maximally symmetric vacua in 4D maximal supergravity?\",\"answer\":\"It shows the vacua structure is fixed by the gauging procedure. Gauging consistency together with extremization of the scalar potential produces a parameterized system of equations describing the vacua.\"},{\"question\":\"What role do machine learning methods play in solving the vacua equations?\",\"answer\":\"The thesis reviews prior literature approaches using machine learning and introduces a novel neural-network architecture that improves the efficiency of these methods for solving the resulting equations.\"},{\"question\":\"What is PyXLTensor and what problem does it solve?\",\"answer\":\"PyXLTensor is a Python library implementing an improved efficient algorithm for analytically solving systems of polynomial equations. It supports writing, manipulating, and solving tensor expressions to obtain solutions more conveniently.\"}]",1785674809,121,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":85,"head_meta":87,"extra_data":89,"updated_unix":27},"machine-learning-supergravity-vacua-thesis","",{"@graph":35,"@context":84},[36,53,67],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/machine-learning-supergravity-vacua-thesis/117262/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":61,"encodingFormat":60,"isAccessibleForFree":62,"interactionStatistic":63},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-08-02",true,{"@type":64,"interactionType":65,"userInteractionCount":4},"InteractionCounter",{"@type":66},"ViewAction",{"@type":68,"mainEntity":69},"FAQPage",[70,76,80],{"name":71,"@type":72,"acceptedAnswer":73},"How does the thesis determine the structure of maximally symmetric vacua in 4D maximal supergravity?","Question",{"text":74,"@type":75},"It shows the vacua structure is fixed by the gauging procedure. Gauging consistency together with extremization of the scalar potential produces a parameterized system of equations describing the vacua.","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"What role do machine learning methods play in solving the vacua equations?",{"text":79,"@type":75},"The thesis reviews prior literature approaches using machine learning and introduces a novel neural-network architecture that improves the efficiency of these methods for solving the resulting equations.",{"name":81,"@type":72,"acceptedAnswer":82},"What is PyXLTensor and what problem does it solve?",{"text":83,"@type":75},"PyXLTensor is a Python library implementing an improved efficient algorithm for analytically solving systems of polynomial equations. 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