[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-125406-en":3,"doc-seo-125406-105":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},125406,1374391974564,"Clementine","https://ap-avatar.wpscdn.com/avatar/14000253aa45c000a9e?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779874745381141002",8,"Research & Report","Machine learning approach for vibronically renormalized electronic band structures","Machine learning enables efficient computation of vibrational thermal expectation values for electronic properties using first-principles input. The method combines a nonperturbative frozen-phonon formulation with stochastic Monte Carlo sampling of finite-temperature nuclear configurations in a supercell. A deep neural network is trained to predict physical properties of sampled phonon configurations, avoiding repeated ab initio calculations. Point-group symmetry is enforced through a symmetry-invariant descriptor. The approach computes the temperature-dependent electronic energy gap of silicon from DFT, achieving order-of-magnitude sampling gains with fewer than 100 DFT training calculations.","arXiv :2409 .01523v1 [ cond-mat .mtrl-sci ] 3 Sep 2024  \nMachine learning approach for vibronically renormalized electronic band structures  \nNiraj Aryal, 1, ∗ Sheng Zhang,2,† Weiguo Yin, 1 and Gia-Wei Chern2,‡  \n1 Condensed Matter Physics and Materials Science Division,  \nBrookhaven National Laboratory, Upton, New York 11973, USA  \n2 Department of Physics, University of Virginia, Charlottesville, VA 22904, USA  \n(Dated: September 4, 2024)  \nWe present a machine learning (ML) method for efficient computation of vibrational thermal expectation values of physical properties from first principles. Our approach is based on the nonperturbative frozen phonon formulation in which stochastic Monte Carlo algorithm is employed to sample configurations of nuclei in a supercell at finite temperatures based on a first-principles phonon model. A deep-learning neural network is trained to accurately predict physical properties associated with sampled phonon configurations, thus bypassing the time-consuming ab initio calculations. To incorporate the point-group symmetry of the electronic system into the ML model, group-theoretical methods are used to develop a symmetry-invariant descriptor for phonon configurations in the supercell. We apply our ML approach to compute the temperature dependent electronic energy gap of silicon based on density functional theory (DFT) . We show that, with less than a hundred DFT calculations for training the neural network model, an order of magnitude larger number of sampling can be achieved for the computation of the vibrational thermal expectation values. Our work highlights the promising potential of ML techniques for finite temperature first-principles electronic structure methods.  \nI. INTRODUCTION  \nRecent advances in electronic structure methods and rapid progress in computational capabilities and artificial intelligence techniques have enabled accurate and fast computation of materials’ properties. This new paradigm of materials research is further assisted by the creation of large freely available databases containing many years worth of human knowledge [1, 2] . For example, several machine learning (ML) models have been developed for accurate and efficient structure-property mapping from large databases of Kohn-Sham density functional theory (DFT) calculations [3–6] . Another prominent application is the ML based force-field or interatomic potential models trained by dataset from DFT calculations [7–17] . Such ML models, which are essentially classical force-field models, yet with a desired quantum accuracy, allows for larger scale and longer time ab initio molecular dynamics simulations. More fundamentally, ML models are also shown to provide accurate approximations of the density functionals or the Hohenberg-Kohn mapping from external potential to electron density functionals [18–23] .  \nThe integration of ML and data science techniques with ab initio electronic structure methods have provided a tantalizing prospect of inverse materials design where a novel material of a given functionality can be predicted from available experimental measurements and theoretical calculations [24–27] . Yet, despite tremendous progress, efficient calculation of materials’ properties beyond the idealized zero temperature remains a challenge for a successful data-driven design and discovery pipeline.  \n∗  \n†  \n‡  \n[naryal@bnl.gov](naryal@bnl.gov)  \nThe first two authors contributed equally to this work.  \n[gchern@virginia.edu](gchern@virginia.edu)  \nIn particular, one important thermal effect is the phononinduced renormalization of electronic structures [28, 29] . This renormalization is the main mechanism for the temperature dependence of band gap energy.  \nA well-developed first-principles approach to incorporate electron-phonon coupling is based on the density functional perturbation theory (DFPT) [30–32] . For example, both phonon dispersion relations and electronphonon matrix elements can be obtained from DFPT. T","cbCaiviIHAJtuQLE","https://ap.wps.com/l/cbCaiviIHAJtuQLE","pdf",8253521,1,17,"English","en",105,"# Introduction\n## Machine learning for structure–property mapping\n## Phonon-induced electronic renormalization and band gap temperature dependence\n## Electron–phonon coupling methods: DFPT and Allen–Heine–Cardona theory\n## Frozen phonon and Monte Carlo sampling approaches","[{\"question\":\"What computational bottleneck does the method address?\",\"answer\":\"It targets the time-consuming ab initio calculations needed to obtain vibrational thermal expectation values at finite temperature.\"},{\"question\":\"How are finite-temperature nuclear configurations generated?\",\"answer\":\"Using a nonperturbative frozen-phonon formulation together with stochastic Monte Carlo sampling of nuclei in a supercell.\"},{\"question\":\"How does the approach incorporate electronic point-group symmetry?\",\"answer\":\"Group-theoretical techniques are used to construct a symmetry-invariant descriptor for phonon configurations used by the ML model.\"}]","Machine learning approach for vibronically renormalized electronic band structures | 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computational bottleneck does the method address?","Question",{"text":75,"@type":76},"It targets the time-consuming ab initio calculations needed to obtain vibrational thermal expectation values at finite temperature.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How are finite-temperature nuclear configurations generated?",{"text":80,"@type":76},"Using a nonperturbative frozen-phonon formulation together with stochastic Monte Carlo sampling of nuclei in a supercell.",{"name":82,"@type":73,"acceptedAnswer":83},"How does the approach incorporate electronic point-group symmetry?",{"text":84,"@type":76},"Group-theoretical techniques are used to construct a symmetry-invariant descriptor for phonon configurations used by the ML 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