[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-119040-en":3,"doc-seo-119040-105":30,"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":27,"seo_description":14,"update_tm":28,"read_time":29},119040,137441390410,"Hazel","https://ap-avatar.wpscdn.com/avatar/2000252f4ab5702993?_k=1776741390130283984",8,"Research & Report","Machine Learning for Prediction of Unitarity and Bounded from Below Constraints - Conference Proceedings Slide","Machine learning techniques are used to predict unitarity (UNI) and bounded from below (BFB) constraints in multi-scalar high energy physics models. The approach is tested on the two- and three-Higgs doublet models and a left-right model, leveraging neural network architectures and carefully curated training datasets to achieve high predictive power. Compared with traditional numerical methods like scalar-potential minimization, the method aims for faster constraint evaluation while improving feasibility as an alternative workflow.","arXiv :2401 .09130v1 [hep-ph] 17 Jan 2024  \nMachine 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)  \nThe machine learning (ML) techniques to predict unitarity (UNI) and bounded from below (BFB) constraints in multi-scalar models is 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 machine learning 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/)  \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 computation of 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 (LRM) model 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","cbCaioPMbrTGu9WU","https://ap.wps.com/l/cbCaioPMbrTGu9WU","pdf",786788,1,4,"English","en",105,"# Details of the computations\n## Theoretical role of UNI and BFB constraints\n## Analytical versus numerical computation\n## ML training strategies\n## Network architecture and training setup\n# Results","[{\"question\":\"Why are unitarity (UNI) and bounded from below (BFB) constraints important in multi-scalar models?\",\"answer\":\"UNI constrains scattering amplitudes to remain finite and well-behaved, while BFB conditions ensure vacuum stability by preventing the scalar potential from going to minus infinity in any field direction.\"},{\"question\":\"How does the paper justify using machine learning instead of traditional numerical methods?\",\"answer\":\"It highlights that analytical UNI and BFB computations are limited to simple models, whereas complex models often require slow and imprecise minimization of the scalar potential. ML is investigated as a faster alternative for predicting these constraints.\"},{\"question\":\"Which neural network strategy is emphasized for predicting UNI and BFB constraints?\",\"answer\":\"The paper focuses on training networks to predict both UNI and BFB simultaneously, using four linear networks of increasing size with a staged data preparation and filtering workflow.\"}]","Machine Learning for Prediction of Unitarity and Bounded from Below Constraints - Conference Proceedings Slide | PDF",1785722039,10,{"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":85,"head_meta":87,"extra_data":89,"updated_unix":28},"machine-learning-for-prediction-of-unitarity-and-bounded-from-below-constraints-conference-proceedings-slide","",{"@graph":36,"@context":84},[37,53,67],{"@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":21},"https://docshare.wps.com/document/machine-learning-for-prediction-of-unitarity-and-bounded-from-below-constraints-conference-proceedings-slide/119040/",{"url":52,"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":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-08-03",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},"Why are unitarity (UNI) and bounded from below (BFB) constraints important in multi-scalar models?","Question",{"text":74,"@type":75},"UNI constrains scattering amplitudes to remain finite and well-behaved, while BFB conditions ensure vacuum stability by preventing the scalar potential from going to minus infinity in any field direction.","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"How does the paper justify using machine learning instead of traditional numerical methods?",{"text":79,"@type":75},"It highlights that analytical UNI and BFB computations are limited to simple models, whereas complex models often require slow and imprecise minimization of the scalar potential. ML is investigated as a faster alternative for predicting these constraints.",{"name":81,"@type":72,"acceptedAnswer":82},"Which neural network strategy is emphasized for predicting UNI and BFB constraints?",{"text":83,"@type":75},"The paper focuses on training networks to predict both UNI and BFB simultaneously, using four linear networks of increasing size with a staged data preparation and filtering workflow.","https://schema.org",{"og:url":52,"og:type":86,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":88,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":91},[92,96,100,104,109,114,119,122,127,130,133],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":93,"show_sort_weight":94,"slug":95},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":97,"show_sort_weight":98,"slug":99},"Literature",80,"literature",{"id":21,"doc_module":4,"doc_module_name":46,"category_name":101,"show_sort_weight":102,"slug":103},"Exam",70,"exam",{"id":105,"doc_module":4,"doc_module_name":46,"category_name":106,"show_sort_weight":107,"slug":108},5,"Comic",60,"comic",{"id":110,"doc_module":4,"doc_module_name":46,"category_name":111,"show_sort_weight":112,"slug":113},6,"Technology",50,"technology",{"id":115,"doc_module":4,"doc_module_name":46,"category_name":116,"show_sort_weight":117,"slug":118},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":120,"slug":121},30,"research-report",{"id":123,"doc_module":4,"doc_module_name":46,"category_name":124,"show_sort_weight":125,"slug":126},9,"Religion & Spirituality",20,"religion-spirituality",{"id":125,"doc_module":4,"doc_module_name":46,"category_name":128,"show_sort_weight":125,"slug":129},"World Cup","world-cup",{"id":29,"doc_module":4,"doc_module_name":46,"category_name":131,"show_sort_weight":29,"slug":132},"Lifestyle","lifestyle",{"id":134,"doc_module":4,"doc_module_name":46,"category_name":135,"show_sort_weight":105,"slug":136},19,"General","general"]