[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-125977-en":3,"doc-seo-125977-105":31,"detail-sidebar-cat-0-en-105":97},{"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":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":28,"seo_description":14,"update_tm":29,"read_time":30},125977,687207024478,"Liam","https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd",8,"Research & Report","Machine learning for structure-property relationships - Scalability and limitations","A scalable machine learning framework is presented for predicting intensive properties and classifying phases of many-body systems. Scalability and transferability are linked to linear-scaling divide-and-conquer strategies that exploit the locality of physical properties. The model is trained on finite-size blocks, then large-scale predictions are obtained by averaging over randomly sampled blocks. Applicability depends on whether the block size exceeds the system’s characteristic length scale, with phase identification accuracy limited by the diverging correlation length. The two-dimensional Ising model is used to establish a scaling relation between accuracy and the block-size-to-correlation-length ratio, and practical implications are discussed.","arXiv :2304 .05502v1 [ cond-mat .stat-mech] 11 Apr 2023  \nMachine learning for structure-property relationships: Scalability and limitations  \nZhongzheng Tian, Sheng Zhang, and Gia-Wei Chern  \nDepartment of Physics, University of Virginia, Charlottesville, VA 22904, USA  \n(Dated: April 13, 2023)  \nWe present a scalable machine learning (ML) framework for predicting intensive properties and particularly classifying phases of many-body systems. Scalability and transferability are central to the unprecedented computational e􀀎ciency of ML methods. In general, linear-scaling computation can be achieved through the divide and conquer approach, and the locality of physical properties is key to partitioning the system into sub-domains that can be solved separately. Based on the locality assumption, ML model is developed for the prediction of intensive properties of a 􀀌nite-size block. Predictions of large-scale systems can then be obtained by averaging results of the ML model from randomly sampled blocks of the system. We show that the applicability of this approach depends on whether the block-size of the ML model is greater than the characteristic length scale of the system. In particular, in the case of phase identi􀀌cation across a critical point, the accuracy of the ML prediction is limited by the diverging correlation length. The two-dimensional Ising model is used to demonstrate the proposed framework. We obtain an intriguing scaling relation between the prediction accuracy and the ratio of ML block size over the spin-spin correlation length. Implications for practical applications are also discussed.  \nI. INTRODUCTION  \nMachine learning (ML) is a fast advancing 􀀌eld that has reshaped many industries. ML has achieved surprising success in many real-world problems including machine vision, speech recognition, and natural language processing. In recent years, numerous successful ML applications in a wide range of disciplines have also led toa paradigmatic shift in scienti􀀌c research. The remarkable capability of modern ML methods to deduce complex patterns from large datasets has allowed scientists to derive connections between raw data and desired quantities, a task which previously would have been impossible. One of the most important application of ML in materials science is the fast and accurate prediction of material properties from the structural or con􀀌gurational data [1{ 9] . Indeed, ML-based modeling of structure-property relationships is expected to open a new avenue for accelerated materials discoveries [10{14] .  \nSimilar ML approaches to structure-property modeling also have enormous applications in condensed matter physics [15, 16] . A particularly interesting aspect of condensed matter systems is the emergence of complex symmetry-breaking phases or topological orders. The objectives of ML models are to provide proper characterizations of such emergent \\structures\", from which accurate predictions about the properties of the system can be made. Of particular interest is the classi􀀌cation of di􀀋erent phases and the identi􀀌cation of phase transitions of many-body systems [17{26] . For example, deep neural networks (NN) have been employed to distinguish the ordered or critical phases from the high-temperature disordered state in various classical spin systems [17, 27{ 32] . With proper feature engineering, ML models have also been developed to capture topologically nontrivial phases or many-body localized states [33{37] .  \nDespite the impressive success of ML models in classifying the various many-body phases, the crucial is-  \nsue of scalability, which is one of the main motivations for adopting ML approaches, has not been carefully addressed. In most studies mentioned above, the ML models, mostly implemented using deep-learning NNs, are designed for a speci􀀌c system size and take the processed con􀀌guration of the whole system as the input. As a result, a new ML model has to be rebuilt and retrained fordi􀀋erent system","cbCaiaNX42LvcUHf","https://ap.wps.com/l/cbCaiaNX42LvcUHf","pdf",3216094,5,1,13,"English","en",105,"# Introduction\n## Structure-property ML and materials discovery\n## ML in condensed matter and phase classification\n## Motivation: scalability and transferability\n## Locality-based scalable ML frameworks","[{\"question\":\"What does the proposed machine learning framework predict for many-body systems?\",\"answer\":\"It predicts intensive properties and performs phase classification for many-body systems, including identifying phase transitions under critical conditions.\"},{\"question\":\"How are large-system predictions obtained from the finite-size ML model?\",\"answer\":\"The framework evaluates the trained model on randomly sampled blocks of the system and averages the block-level predictions to obtain results for large-scale systems.\"},{\"question\":\"What factor limits accuracy when identifying phases across a critical point?\",\"answer\":\"Accuracy is limited by the diverging correlation length near the critical point, which affects how block-based locality remains valid.\"},{\"question\":\"How does the framework’s applicability depend on block size?\",\"answer\":\"It works when the ML block size is greater than the system’s characteristic length scale; when it is not, transferability and prediction accuracy degrade.\"}]","Machine learning for structure-property relationships - Scalability and limitations | PDF",1785902347,33,{"code":4,"msg":32,"data":33},"ok",{"site_id":25,"language":24,"slug":34,"title":13,"keywords":35,"description":14,"schema_data":36,"social_meta":92,"head_meta":94,"extra_data":96,"updated_unix":29},"machine-learning-for-structure-property-relationships-scalability-and-limitations","",{"@graph":37,"@context":91},[38,55,70],{"@type":39,"itemListElement":40},"BreadcrumbList",[41,45,49,52],{"item":42,"name":43,"@type":44,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":46,"name":47,"@type":44,"position":48},"https://docshare.wps.com/document/","Document",2,{"item":50,"name":12,"@type":44,"position":51},"https://docshare.wps.com/document/research-report/",3,{"item":53,"name":13,"@type":44,"position":54},"https://docshare.wps.com/document/machine-learning-for-structure-property-relationships-scalability-and-limitations/125977/",4,{"url":53,"name":13,"@type":56,"author":57,"headline":13,"publisher":59,"fileFormat":62,"inLanguage":24,"description":14,"dateModified":63,"datePublished":64,"encodingFormat":62,"isAccessibleForFree":65,"interactionStatistic":66},"DigitalDocument",{"name":9,"@type":58},"Person",{"url":42,"name":60,"@type":61},"DocShare","Organization","application/pdf","2026-08-23","2026-08-05",true,{"@type":67,"interactionType":68,"userInteractionCount":20},"InteractionCounter",{"@type":69},"ViewAction",{"@type":71,"mainEntity":72},"FAQPage",[73,79,83,87],{"name":74,"@type":75,"acceptedAnswer":76},"What does the proposed machine learning framework predict for many-body systems?","Question",{"text":77,"@type":78},"It predicts intensive properties and performs phase classification for many-body systems, including identifying phase transitions under critical conditions.","Answer",{"name":80,"@type":75,"acceptedAnswer":81},"How are large-system predictions obtained from the finite-size ML model?",{"text":82,"@type":78},"The framework evaluates the trained model on randomly sampled blocks of the system and averages the block-level predictions to obtain results for large-scale systems.",{"name":84,"@type":75,"acceptedAnswer":85},"What factor limits accuracy when identifying phases across a critical point?",{"text":86,"@type":78},"Accuracy is limited by the diverging correlation length near the critical point, which affects how block-based locality remains valid.",{"name":88,"@type":75,"acceptedAnswer":89},"How does the framework’s applicability depend on block size?",{"text":90,"@type":78},"It works when the ML block size is greater than the system’s characteristic length scale; 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