[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-290601-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-290601-en":130},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","machine-learning-for-prediction-of-unitarity-and-bounded-from-below-constraints-eps-hep2023-poster","Machine Learning for Prediction of Unitarity and Bounded from Below Constraints - EPS-HEP2023 Poster","","Machine learning methods are developed to predict unitarity (UNI) and bounded-from-below (BFB) constraints in multi-scalar high-energy physics models. The approach is validated on the two- and three-Higgs doublet models and a left-right model using neural network architectures, curated training datasets, and targeted strategies for learning. Results are framed against traditional calculations, highlighting faster inference relative to scalar-potential minimization. Computational details include multiple deep linear networks and GPU/CPU workflows.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/research-report/","Research & Report",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/machine-learning-for-prediction-of-unitarity-and-bounded-from-below-constraints-eps-hep2023-poster/290601/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/machine-learning-for-prediction-of-unitarity-and-bounded-from-below-constraints-eps-hep2023-poster/290601.png","ImageObject",300,407,{"name":42,"@type":43},"Ezra","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-11-04","2026-09-17",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",6,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What are UNI and BFB constraints in multi-scalar models?","Question",{"text":63,"@type":64},"UNI constraints restrict the behavior of scattering amplitudes so they remain finite and well-behaved. BFB conditions ensure vacuum stability by preventing directions where the scalar potential can go to minus infinity.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"Which models are used to demonstrate the machine learning approach?",{"text":68,"@type":64},"The method is applied to the two- and three-Higgs doublet models and the left-right model (LRM).",{"name":70,"@type":61,"acceptedAnswer":71},"How are the neural networks trained and used for predictions?",{"text":72,"@type":64},"The study focuses on training networks to predict UNI and BFB simultaneously, using four linear networks (net-1 to net-4). net-2 is trained with raw data prepared from net-1, and net-3/net-4 use progressively larger matrix sizes to filter net-2 predictions.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},290601,1789642171,{"code":4,"msg":82,"data":83},"success",[84,88,92,96,101,105,110,114,119,122,126],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":93,"show_sort_weight":94,"slug":95},"Exam",70,"exam",{"id":97,"doc_module":4,"doc_module_name":25,"category_name":98,"show_sort_weight":99,"slug":100},5,"Comic",60,"comic",{"id":55,"doc_module":4,"doc_module_name":25,"category_name":102,"show_sort_weight":103,"slug":104},"Technology",50,"technology",{"id":106,"doc_module":4,"doc_module_name":25,"category_name":107,"show_sort_weight":108,"slug":109},7,"Healthcare",40,"healthcare",{"id":111,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":112,"slug":113},8,30,"research-report",{"id":115,"doc_module":4,"doc_module_name":25,"category_name":116,"show_sort_weight":117,"slug":118},9,"Religion & Spirituality",20,"religion-spirituality",{"id":117,"doc_module":4,"doc_module_name":25,"category_name":120,"show_sort_weight":117,"slug":121},"World Cup","world-cup",{"id":123,"doc_module":4,"doc_module_name":25,"category_name":124,"show_sort_weight":123,"slug":125},10,"Lifestyle","lifestyle",{"id":127,"doc_module":4,"doc_module_name":25,"category_name":128,"show_sort_weight":97,"slug":129},19,"General","general",{"code":4,"msg":82,"data":131},{"doc_id":79,"user_id":132,"nickname":42,"user_avatar":133,"doc_module":4,"category_id":111,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":33,"language":139,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":12,"update_tm":80,"read_time":123,"preview_page_count":4},1099514068035,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","Machine Learning for Prediction of Unitarity and Bounded from Below Constraints  \nD. Juriukonis*  \n(1) Vilnius University, Institute of Theoretical Physics and Astronomy E-mail: [darius.jurciukonis@tfai.vu.lt](darius.jurciukonis@tfai.vu.lt)  \nMachine learning (ML) techniques to predict unitarity (UNI) and bounded from below (BFB) constraints in multi-scalar models are employed. The effectiveness of this approach is demonstrated by applying it to the two and three Higgs doublet models, as well as the left-right model. By employing suitable neural network architectures, learning algorithms, and carefully curated training datasets, a significantly high level of predictivity is achieved. Machine learning offers a distinct advantage by enabling faster calculations compared to alternative numerical methods, such as scalar potential minimization. This research investigates the feasibility of utilizing ML techniques as an alternative for predicting these constraints, offering potential improvements over traditional numerical calculations.  \nThe European Physical Society Conference on High Energy Physics (EPS-HEP2023) 21-25 August 2023  \nHamburg, Germany  \n* Speaker.  \n© Copyright owned by the author(s) under the terms of the Creative Commons  \nAttribution-NonCommercial-NoDerivatives 4 .0 International License (CC BY-NC-ND 4 .0) . [https://pos.sissa.it/](https://pos.sissa.it/)  \nPoS ( EPS-HEP2023)494  \n Machine Learning for Prediction of Unitarity and Bounded from Below Constraints D. Juriukonis  \n1. Details of the computations  \nTheoretical constraints such as unitarity and bounded from below conditions play important roles in model building within the realm of high energy physics, ensuring both the physical consistency and stability of the theoretical models. In high energy physics, UNI constrains the behavior of scattering amplitudes, ensuring that they remain finite and well-behaved. The BFB conditions is essential for the stability of the vacuum. In the context of scalar field theories, the BFB condition helps in ensuring that the scalar potential is phenomenologically consistent and that there is no direction in field space along which the potential tends to minus infinity.  \nThe unitarity conditions can be computed analytically. Typically, the computation necessitates determining the eigenvalues of the scattering matrices. These computations are precise and fast. The analytical computation of BFB conditions is feasible only for simple models. For complex models, minimization of the scalar potential is required. The computations involved in minimization are often slow and imprecise.  \nIn this paper, three models with precise analytical procedures for BFB computations were investigated to verify the reliability of machine learning. Necessary and sufficient conditions for the scalar potential of the general two Higgs doublet model (G2HDM) to be BFB were derived by several groups in ref. [1, 2] through computations of a simple and precise algorithm [3] . The aligned three Higgs doublet model (A3HDM) has a quite large number of free parameters in the quartic scalar potential, but due to additional constraints, the BFB conditions for the model can be expressed analytically [4, 5], while the CP-conserved left-right model (LRM) requires a quite complicated algorithm for the estimation of BFB conditions [6, 7] .  \nTypically, the parameters of quartic potential, lambdas, are generated within certain limits and later they are sampled according to UNI or BFB conditions 1. Depending on the model, there maybe a very small percentage of samples that satisfy UNI, BFB, or both UNI and BFB conditions, as shown in Table 1.  \n\n| Model (λ’s) | UNI | BFB-I | BFB-II | UNI+BFB |\n| --- | --- | --- | --- | --- |\n\n\n| G2HDM (10)\u003Cbr>LRM (13)\u003Cbr>A3HDM (14) | 1.02\u003Cbr>0.41\u003Cbr>0.18 | 23.3\u003Cbr>18.4\u003Cbr>1.73 | 3.25\u003Cbr>0.7\u003Cbr>0.05 | 0.033\u003Cbr>0.0028\u003Cbr>0.00009 |\n| --- | --- | --- | --- | --- |\n\nTable 1: Percentage of true samples for models when lambdas are generated","cbCailGOSbkbgUDY","https://ap.wps.com/l/cbCailGOSbkbgUDY","pdf",782777,"English","# Details of the computations\n## Results","[{\"question\":\"What are UNI and BFB constraints in multi-scalar models?\",\"answer\":\"UNI constraints restrict the behavior of scattering amplitudes so they remain finite and well-behaved. BFB conditions ensure vacuum stability by preventing directions where the scalar potential can go to minus infinity.\"},{\"question\":\"Which models are used to demonstrate the machine learning approach?\",\"answer\":\"The method is applied to the two- and three-Higgs doublet models and the left-right model (LRM).\"},{\"question\":\"How are the neural networks trained and used for predictions?\",\"answer\":\"The study focuses on training networks to predict UNI and BFB simultaneously, using four linear networks (net-1 to net-4). net-2 is trained with raw data prepared from net-1, and net-3/net-4 use progressively larger matrix sizes to filter net-2 predictions.\"}]","Machine Learning for Prediction of Unitarity and Bounded from Below Constraints - EPS-HEP2023 Poster | PDF"]