[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-125000-en":3,"doc-seo-125000-105":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},125000,8796095462418,"Noah","https://ap-avatar.wpscdn.com/avatar/80000253c1241d02b47?x-image-process=image/resize,m_fixed,w_180,h_180&k=1778826106357471780",8,"Research & Report","Machine learning Hubbard parameters withequivariant neural networks","Density-functional theory with extended Hubbard functionals (DFT+U+V) offers a reliable way to model transition-metal and rare-earth materials, but its accuracy depends on determining on-site U and inter-site V Hubbard parameters. These parameters are often obtained through semi-empirical tuning or costly predictive first-principles workflows. A machine learning approach using equivariant neural networks predicts Hubbard parameters from atomic occupation matrices as descriptors, targeting self-consistent iterative linear-response results from DFPT and structural relaxations. Trained on 11 materials, the model achieves mean absolute relative errors of 3% for U and 5% for V, largely reproducing DFPT accuracy with negligible overhead and enabling faster materials discovery.","arXiv :2406 .02457v1 [ cond-mat .mtrl-sci ] 4 Jun 2024  \nMachine learning Hubbard parameters withequivariant neural networks  \nMartin Uhrin 1,2,* , Austin Zadoks1 , Luca Binci 1,3,4 , Nicola Marzari 1,5 , and Iurii Timrov 1,5,+  \n1Theory and Simulation of Materials (THEOS), and National Centre for Computational Design and Discovery of Novel Materials (MARVEL), ´Ecole Polytechnique Fdrale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland 2 Universit Grenoble Alpes, 1130 Rue de la Piscine, BP 75, 38402 St Martin D’Heres, France  \n3 Department of Materials Science and Engineering, University of California at Berkeley, Berkeley, California 94720, United States  \n4 Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, 94720, USA  \n5 Laboratory for Materials Simulations (LMS), Paul Scherrer Institut (PSI), CH-5232 Villigen PSI, Switzerland  \n* [Email: martin.uhrin@grenoble-inp.fr](Email: martin.uhrin@grenoble-inp.fr)[ ](Email: martin.uhrin@grenoble-inp.fr)+ Email: [iurii.timrov@psi.ch](iurii.timrov@psi.ch)  \nABSTRACT  \nDensity-functional theory with extended Hubbard functionals (DFT+U+V) provides a robust framework to accurately describe complex materials containing transition-metal or rare-earth elements. It does so by mitigating self-interaction errors inherent to semi-local functionals which are particularly pronounced in systems with partially-filled d and f electronic states. However, achieving accuracy in this approach hinges upon the accurate determination of the on-site U and inter-site V Hubbard parameters. In practice, these are obtained either by semi-empirical tuning, requiring prior knowledge, or, more correctly, by using predictive but expensive first-principles calculations. Here, we present a machine learning model based on equivariant neural networks which uses atomic occupation matrices as descriptors, directly capturing the electronic structure, local chemical environment, and oxidation states of the system at hand. We target here the prediction of Hubbard parameters computed self-consistently with iterative linear-response calculations, as implemented in density-functional perturbation theory (DFPT), and structural relaxations. Remarkably, when trained on data from 11 materials spanning various crystal structures and compositions, our model achieves mean absolute relative errors of 3% and 5% for Hubbard U and V parameters, respectively. By circumventing computationally expensive DFT or DFPT self-consistent protocols, our model significantly expedites the prediction of Hubbard parameters with negligible computational overhead, while approaching the accuracy of DFPT. Moreover, owing to its robust transferability, the model facilitates accelerated materials discovery and design via high-throughput calculations, with relevance for various technological applications.  \nINTRODUCTION  \nA fundamental tool in investigating compounds involving transition-metal (TM) and rare-earth (RE) compounds is density-functional theory (DFT), 1, 2 a cornerstone for firstprinciples simulations in physics, chemistry, and materials science. In practical applications, DFT necessitates approximations to the exchange-correlation (xc) functional, with the local spin-density approximation (LSDA) and spin-polarized generalized-gradient approximation (σ-GGA) being the most prevalent choices. However, these approximations yield unsatisfactory outcomes for various properties of TM and RE compounds, primarily due to significant self-interaction errors (SIEs)3–5 that are particularly pronounced for localized d and f electrons. To address these challenges, more accurate approaches surpassing the limitations of “standard DFT” have been devised. Noteworthy among these are Hubbard-corrected DFT (so-called DFT+U6–8 and its extension DFT+U+V ,9–11 whose role in addressing SIEs, rather than correlation errors, was first pointed out in Ref. 4), meta-GGA functionals,12–14 and hybrid functionals.15–17 While these methods offer valu","cbCaib9h9cwfipSc","https://ap.wps.com/l/cbCaib9h9cwfipSc","pdf",2917313,1,24,"English","en",105,"# Abstract\n# Introduction\n## Background: limitations of standard DFT\n## Hubbard-corrected DFT and DFT+U+V\n## Extended Hubbard correction energy and parameters\n## Self-consistent DFPT protocol and convergence examples","[{\"question\":\"Why are Hubbard parameters important in DFT+U+V?\",\"answer\":\"DFT+U+V accuracy depends on correctly determining on-site U and inter-site V Hubbard parameters, which control the extended Hubbard correction.\"},{\"question\":\"How does the proposed machine learning model predict U and V?\",\"answer\":\"It uses equivariant neural networks with atomic occupation matrices as descriptors to capture electronic structure, local chemical environment, and oxidation states.\"},{\"question\":\"What computational bottleneck does the model avoid, and how accurate is it?\",\"answer\":\"It bypasses expensive self-consistent DFT/DFPT procedures while approaching DFPT-level accuracy, achieving mean absolute relative errors of 3% for U and 5% for V on 11 training materials.\"}]","Machine learning Hubbard parameters withequivariant neural networks | 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are Hubbard parameters important in DFT+U+V?","Question",{"text":75,"@type":76},"DFT+U+V accuracy depends on correctly determining on-site U and inter-site V Hubbard parameters, which control the extended Hubbard correction.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the proposed machine learning model predict U and V?",{"text":80,"@type":76},"It uses equivariant neural networks with atomic occupation matrices as descriptors to capture electronic structure, local chemical environment, and oxidation states.",{"name":82,"@type":73,"acceptedAnswer":83},"What computational bottleneck does the model avoid, and how accurate is it?",{"text":84,"@type":76},"It bypasses expensive self-consistent DFT/DFPT procedures while approaching DFPT-level accuracy, achieving mean absolute relative errors of 3% for U and 5% for V on 11 training 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