[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-126757-en":3,"doc-seo-126757-105":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":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},126757,962084928432,"Emma Wilson","https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d",8,"Research & Report","Machine learning analysis of dimensional reduction conjecture for nonequilibrium Berezinskii-Kosterlitz-Thouless transition in three dimensions","Machine learning is used to test the dimensional reduction conjecture in driven disordered systems. The conjecture claims that a static snapshot of a D-dimensional disordered system driven at constant velocity corresponds to a space-time trajectory of a (D−1)-dimensional pure counterpart. The study targets the three-dimensional random-field XY model and its predicted nonequilibrium Berezinskii–Kosterlitz–Thouless transition. Neural networks classify 3D driven random-field XY snapshots versus 2D pure XY space-time trajectories, yielding accuracy no better than random, confirming indistinguishability.","Machine learning analysis of dimensional reduction conjecture for nonequilibrium Berezinskii–Kosterlitz–Thouless transition in three dimensions  \narXiv :2311 .07828v2 [ cond-mat .dis-nn] 26 Jul 2024  \nTaiki Haga 1, ∗  \n1 Department of Physics and Electronics, Osaka Metropolitan University, Sakai-shi, Osaka 599-8531, Japan  \n(Dated: July 29, 2024)  \nWe investigate the recently proposed dimensional reduction conjecture in driven disordered systems using a machine learning technique. The conjecture states that a static snapshot of a disordered system driven at a constant velocity is equal to a space-time trajectory of its lower-dimensional pure counterpart. This suggests that the three-dimensional random field XY model exhibits the Berezinskii–Kosterlitz–Thouless transition when driven out of equilibrium. To verify the conjecture directly by observing configurations ofthe system, we utilize the capacity of neural networks to detect subtle features of images. Specifically, we train neural networks to differentiate snapshots of the three-dimensional driven random field XY model from space-time trajectories of the two-dimensional pure XY model. Our results demonstrate that the network cannot distinguish between the two, confirming the dimensional reduction conjecture.  \nI. INTRODUCTION  \nThe large-scale behavior of classical and quantum manybody systems in nonequilibrium steady states has been a central research topic in modern statistical physics. The absence of the detailed balance due to nonequilibrium driving results in unique behaviors that are not found in thermal equilibrium, such as long-range order in two-dimensional (2D) systems with continuous symmetry [1, 2], absorbing-state phase transitions [3–5], and motility-induced phase separation [6–9] . Recent advancements in experiments, from ultracold atomic gases to biological systems, have heightened interest in this expansive subject.  \nRecent studies suggest that when the three-dimensional (3D) XY model with a random field is driven at a constant velocity, it shows the Berezinskii–Kosterlitz–Thouless (BKT) transition [10, 11] . This finding is striking because, under thermal equilibrium, the 3D random field XY model remains disordered and does not exhibit any phase transition [12, 13] . The principle behind the 3D nonequilibrium BKT transition is the dimensional reduction conjecture [14, 15] . In simple terms, it proposes that a static snapshot of a D-dimensional disordered system driven at a constant velocity is equal to a space-time trajectory of its (D− 1)-dimensional pure counterpart (see Fig. 1 for a schematic illustration) . Using this idea, the 3D driven random field XY model equates to the 2D pure XY model, leading to the expectation of the BKT transition in the 3D model. However, it remains unclear when and under which circumstances this dimensional reduction holds true, as there are simple counterexamples (see Appendix E) .  \nThis study aims to test the dimensional reduction conjecture using machine learning. Neural networks excel at identifying subtle data patterns that humans cannot capture. In statistical physics, they have been employed to identify and categorize thermodynamic phases in classical spin systems [16– 21], glassy systems [22–26], and quantum many-body systems [27–33] . Our goal with the neural network is to compare the structures of a driven disordered system with its sim-  \n∗ [taiki.haga@omu.ac.jp](taiki.haga@omu.ac.jp)  \npler, lower-dimensional pure version. To do this, we train convolutional and fully-connected neural networks to distinguish between snapshots of the 3D driven random field XY model (DRFXYM) and space-time trajectories of the 2D pure XY model. This is a standard binary classification task (see Fig. 4) . We demonstrate that the classification accuracy of the trained network is no better than a random guess, suggesting that the two systems are indistinguishable.  \nThis paper is organized as follows: In Sec. II, we introduce a proto","cbCaihToMdP7vshP","https://ap.wps.com/l/cbCaihToMdP7vshP","pdf",11004566,1,14,"English","en",105,"# Introduction\n## Nonequilibrium steady states and dimensional reduction conjecture\n## Aim: machine-learning verification\n# Model and dimensional reduction","[{\"question\":\"What does the dimensional reduction conjecture predict in this study?\",\"answer\":\"A static snapshot of a D-dimensional disordered system driven at constant velocity should match a space-time trajectory of its (D−1)-dimensional pure counterpart.\"},{\"question\":\"How is machine learning used to test the conjecture?\",\"answer\":\"Neural networks are trained to distinguish 3D driven random-field XY snapshots from 2D pure XY space-time trajectories as a binary classification task.\"},{\"question\":\"What is the main outcome of the neural-network classification?\",\"answer\":\"The network cannot distinguish the two cases; classification accuracy is no better than a random guess, indicating confirmation of the conjecture.\"}]","Machine learning analysis of dimensional reduction conjecture for nonequilibrium Berezinskii-Kosterlitz-Thouless transition in three dimensions | PDF",1785934619,35,{"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":86,"head_meta":88,"extra_data":90,"updated_unix":28},"machine-learning-analysis-of-dimensional-reduction-conjecture-for-nonequilibrium-berezinskii-kosterlitz-thouless-transition-in-three-dimensions","",{"@graph":36,"@context":85},[37,54,68],{"@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-analysis-of-dimensional-reduction-conjecture-for-nonequilibrium-berezinskii-kosterlitz-thouless-transition-in-three-dimensions/126757/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-05",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What does the dimensional reduction conjecture predict in this study?","Question",{"text":75,"@type":76},"A static snapshot of a D-dimensional disordered system driven at constant velocity should match a space-time trajectory of its (D−1)-dimensional pure counterpart.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How is machine learning used to test the conjecture?",{"text":80,"@type":76},"Neural networks are trained to distinguish 3D driven random-field XY snapshots from 2D pure XY space-time trajectories as a binary classification task.",{"name":82,"@type":73,"acceptedAnswer":83},"What is the main outcome of the neural-network classification?",{"text":84,"@type":76},"The network cannot distinguish the two cases; 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