[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-116888-en":3,"doc-seo-116888-105":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},116888,687197100911,"Himbo","https://ap-avatar.wpscdn.com/avatar/a000239b6f1da00475?x-image-process=image/resize,m_fixed,w_180,h_180&k=1785132997149421697",8,"Research & Report","Delta Machine Learning for Predicting Dielectric Properties and Raman Spectra","A delta machine learning framework predicts dielectric polarizabilities to enable Raman spectra from molecular dynamics trajectories at reduced computational cost. The approach uses a linear-response model as a first step to capture key dielectric-response information, then applies symmetry-adapted machine learning for higher-order contributions. Tests on molecules and extended solids show improved accuracy and smaller training-set requirements versus single-step tensor-property learning. The method supports practical MD-Raman simulations while addressing limitations of purely harmonic Raman calculations.","arXiv :2307 . 10578v1 [ cond-mat .mtrl-sci ] 20 Jul 2023  \nDelta Machine Learning for Predicting Dielectric Properties and Raman Spectra  \nManuel Grumet, 1 Clara von Scarpatetti, 1 Tom􀀓a􀀔s Bu􀀔cko,2, 3, 􀀃 and David A. Egger 1, y  \n1 Physics Department, TUM School of Natural Sciences,  \nTechnical University of Munich, 85748 Garching, Germany  \n2 Department of Physical and Theoretical Chemistry, Faculty of Natural Sciences,  \nComenius University in Bratislava, SK-84215 Bratislava, Slovakia  \n3 Institute of Inorganic Chemistry, Slovak Academy of Sciences, SK-84236 Bratislava, Slovakia  \n(Dated: July 21, 2023)  \nWe propose a machine learning method for predicting polarizabilities with the goal of providing Raman spectra from molecular dynamics trajectories at reduced computational cost. A linearresponse model is used as a 􀀌rst step and symmetry-adapted machine learning is employed for the higher-order contributions as a second step. We investigate the performance of the approach for several systems including molecules and extended solids. The method can reduce training set sizes required for accurate dielectric properties and Raman spectra in comparison to a single-step machine learning approach.  \nAtomic motions are often key to physical and chemical phenomena occurring at 􀀌nite temperature, both in solid-state and molecular systems. Experimentally, the dynamical behavior of such systems can be probed by Raman spectroscopy. It is a table-top technique that is available in many laboratories because it is less complicated and expensive than, for example, neutron scattering [1] . Computational predictions of Raman spectra using 􀀌rst-principles calculations are an important counterpart to experimental measurements. They provide further insight into the behavior of materials, facilitate the interpretation of measured spectra via theory-experiment comparisons, and enable predictions of dynamical properties in new compounds.  \nThe central quantity for theoretical calculations of Raman spectra is the polarizability tensor, 􀀋 . It describes the 􀀌rst-order dielectric response of a system to external electric 􀀌elds. In practice, the dielectric tensor, 􀀏, can be used for periodic systems since it contains the same information [2]; in the following text, we shall use both quantities interchangeably. Raman spectra are commonly calculated within the harmonic approximation whereby the derivatives of 􀀋 with respect to atomic displacements, determining the intensity of peaks, are calculated along eigenvectors of harmonic modes [3{5] . But this method is limited since it cannot capture anharmonic e􀀋ects, higher-order Raman scattering, or the explicit temperature dependencies of Raman modes. These e􀀋ects are relevant in a variety of physical systems and scenarios. For example, a description of phase-transitions in solid materials requires temperature-dependent phonon modes [6], which cannot be captured in a strictly harmonic phonon picture.  \nMolecular dynamics (MD) simulations o􀀋er a way to include these e􀀋ects and overcome limitations of the harmonic approach. A Raman spectrum can be computed from an MD trajectory by calculating Fouriertransformed velocity autocorrelation functions of the  \ncomponents of 􀀋 [7{9] . However, this requires computing a time series of 􀀋 values from multiple MD snapshots. The number of data points needed in such an MD-Raman approach depends on the desired frequency resolution and the total range of frequencies that needs to be covered, but typically at least a few hundred points are needed. Such polarizability calculations can be done from 􀀌rst-principles using density functional perturbation theory (DFPT) [10], but this renders MD-based Raman calculations computationally demanding. The large computational e􀀋ort involved in MD-Raman calculations limit the range of physical scenarios and systems one can investigate with the method.  \nThe computational cost of 􀀌rst-principles calculations can be signi􀀌cantly reduced by mac","cbCairjbOajq8cvd","https://ap.wps.com/l/cbCairjbOajq8cvd","pdf",731717,1,6,"English","en",105,"# Abstract\n## Problem and motivation\n## Proposed Delta ML framework\n## Method components and evaluation\n## Results and implications","[{\"question\":\"What does the Delta Machine Learning approach aim to predict?\",\"answer\":\"It predicts dielectric polarizabilities so that Raman spectra can be generated from molecular dynamics trajectories with lower computational cost.\"},{\"question\":\"How is the method structured in two steps?\",\"answer\":\"A linear-response model provides an initial approximation, and symmetry-adapted machine learning learns higher-order differences from the first-step predictions.\"},{\"question\":\"What advantages does the delta ML method offer over direct ML?\",\"answer\":\"The method increases prediction accuracy and reduces the training-set size needed for accurate dielectric properties and Raman spectra.\"}]","Delta Machine Learning for Predicting Dielectric Properties and Raman Spectra | 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does the Delta Machine Learning approach aim to predict?","Question",{"text":75,"@type":76},"It predicts dielectric polarizabilities so that Raman spectra can be generated from molecular dynamics trajectories with lower computational cost.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How is the method structured in two steps?",{"text":80,"@type":76},"A linear-response model provides an initial approximation, and symmetry-adapted machine learning learns higher-order differences from the first-step predictions.",{"name":82,"@type":73,"acceptedAnswer":83},"What advantages does the delta ML method offer over direct ML?",{"text":84,"@type":76},"The method increases prediction accuracy and reduces the training-set size needed for accurate dielectric properties and Raman 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