[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-290318-105":59,"doc-detail-290318-en":131},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","self-consistent-validation-for-machine-learning-electronic-structure","Self-consistent Validation for Machine Learning Electronic Structure","","Machine learning is increasingly used to address electronic structure problems efficiently, but limited generalization to unseen systems restricts real-world deployment. The work proposes a physics-informed self-consistent surrogate framework that estimates prediction convergence accuracy with low validation cost and improved interpretability. By integrating a DIIS-inspired error vector into ML models to avoid expensive self-consistent calculations, the method enables differentiable uncertainty signals and uncertainty-driven active learning, building confidence for studies on novel materials.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/self-consistent-validation-for-machine-learning-electronic-structure/290318/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/self-consistent-validation-for-machine-learning-electronic-structure/290318.png","ImageObject",300,407,{"name":92,"@type":93},"Violet","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-28","2026-09-17",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",16,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"Why is generalization a problem for machine learning electronic-structure models?","Question",{"text":113,"@type":114},"Models can be reliable only within the distribution of their training data. When applied to target systems outside training, prediction accuracy may degrade, so reliable estimation of prediction quality becomes essential.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"What does the proposed method do to estimate prediction accuracy?",{"text":118,"@type":114},"It builds a full surrogate model to DFT that provides an estimation of convergence accuracy in a physics-informed manner. The criterion is derived from a DIIS error vector and generalized to predicted matrices without running expensive self-consistent calculations.",{"name":120,"@type":111,"acceptedAnswer":121},"How does the approach support active learning?",{"text":122,"@type":114},"The criterion is constructed in a fully differentiable way, enabling gradients with respect to atomic coordinates. This makes it suitable for uncertainty-driven active learning to select informative data points.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},290318,1789641320,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":29,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":130,"read_time":144,"preview_page_count":4},4398048950312,"https://ap-avatar.wpscdn.com/avatar/400002538284de19e3c?_k=1778320343897328908","Self-consistent Validation for Machine Learning Electronic Structure  \nGengyuan Hu,∗ Gengchen Wei, Zekun Lou, Philip H.S. Torr, Wanli Ouyang, Han-sen Zhong, and Chen Lin†  \nShanghai Artificial Intelligence Laboratory and  \nDepartment of Engineering, University of Oxford  \n(Dated: February 16, 2024)  \nMachine learning has emerged as a significant approach to efficiently tackle electronic structure problems. Despite its potential, there is less guarantee for the model to generalize to unseen data that hinders its application in real-world scenarios. To address this issue, a technique has been proposed to estimate the accuracy of the predictions. This method integrates machine learning with self-consistent field methods to achieve both low validation cost and interpret-ability. This, in turn, enables exploration of the model’s ability with active learning and instills confidence in its integration into real-world studies.  \narXiv :2402 . 10186v1 [ cs .LG] 15 Feb 2024  \nIntroduction: Determining the electronic structure of a system is a central challenge in computational modeling. Despite quantum mechanics, the governing theory, having been discovered over a century ago, the exact solution to many-body electronic structure is still limited to only a handful of systems, even with the vast computational power available today. Density functional theory(DFT)[1–3], is a successful tool in computational chemistry that provides insights into molecules and materials at a reduced cost. Despite significant improvements in time complexity, the size of systems that can be effectively modeled using DFT is still limited due to the exponentially growing cost as the system size increases[4– 6] . As a result, it remains a challenge to scale DFT to practical and important systems with more than 1000 atoms.  \nThe integration of machine learning models has led to significant advancements in the field of electronic structure calculations for very large systems[7–12] . The machine learning method builds surrogate models for traditional algorithms by directly learn from data [13] . A successful example, ML potentials, which predict the atomic forces learned from DFT, make it possible to simulate millions of atoms with DFT-level accuracy [14–16] .  \nHowever, those methods are restricted to application in molecular dynamics and fail to serve as a general surrogates for DFT. Recently, learning the full solution to the DFT equations, has been explored[12, 17–22] . Predictions can be made towards the charge density or the effective Hamiltonian for the Kohn-Sham auxiliary system. These approaches are generally versatile and can yield various physical properties without the need for a self-consistency loop. In contrast to conventional methods which is very transferable, ML models are reliant on the data on which they were trained and may exhibit suboptimal performance when applied to target systems outside of their training data. Consequently, the precise estimation of prediction accuracy plays a critical role when employing ML models, particularly when exploring uncharted systems.  \nUncertainty estimation [23–25] is an active research topic in the field of machine learning. Existing methods  \nestimate the distribution of the prediction with Bayesian Neural Networks or ensembles of model[26, 27] . However, these methods have no guarantee of prediction accuracy and are typically used to produce confidence. We suggest that more physical constraint, rather than only statistical information, should be considered within the design of machine learning DFT surrogates to make it more reliable in unknown systems.  \nIn this letter, we introduce a full surrogate model to DFT that by design provides an estimation of the convergence accuracy of its prediction in a physics-informed manner. This is archived by following the concept of error vector defined in the direct inversion of the iterative subspace(DIIS) optimization method [28, 29] that examines the commutability of t","cbCairxBCM9MHItd","https://ap.wps.com/l/cbCairxBCM9MHItd","pdf",1170669,"English","# Introduction\n## Uncertainty estimation and reliability limits\n# Theory\n## Kohn-Sham DFT and LCAO basis formulation","[{\"question\":\"Why is generalization a problem for machine learning electronic-structure models?\",\"answer\":\"Models can be reliable only within the distribution of their training data. When applied to target systems outside training, prediction accuracy may degrade, so reliable estimation of prediction quality becomes essential.\"},{\"question\":\"What does the proposed method do to estimate prediction accuracy?\",\"answer\":\"It builds a full surrogate model to DFT that provides an estimation of convergence accuracy in a physics-informed manner. The criterion is derived from a DIIS error vector and generalized to predicted matrices without running expensive self-consistent calculations.\"},{\"question\":\"How does the approach support active learning?\",\"answer\":\"The criterion is constructed in a fully differentiable way, enabling gradients with respect to atomic coordinates. This makes it suitable for uncertainty-driven active learning to select informative data points.\"}]","Self-consistent Validation for Machine Learning Electronic Structure | PDF",15]