[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-123368-en":3,"doc-seo-123368-105":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":20,"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},123368,962075114765,"Quinn","https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd",8,"Research & Report","Machine Learning static RPA response properties for accelerating GW calculations","This thesis investigates constructing machine-learning models for the interacting density-density response function (DDRF) and derived quantities. Accurate DDRF models are essential for enabling GW quasiparticle calculations for more complex systems, while avoiding the expensive dielectric-matrix inversion that causes poor scaling with atom number. The work reviews physically motivated descriptors with invariance and equivariance, develops models for scalar polarizability from RPA DDRF, and introduces localized and atom-decomposed DDRF approximations, culminating in GW-accurate quasiparticle energy corrections.","Imperial College London  \nDepartment of Materials  \nMachine Learning static RPA response properties for accelerating GW calculations  \nMario Gernot Zauchner  \nSubmitted in part fulfilment of the requirements for the degree of Doctor of Philosophy at Imperial College London, 2023  \nI hereby declare that all material presented in this thesis is my own work, except where other  \nwise noted.  \nMario Gernot Zauchner, 2023  \nThe copyright of this thesis rests with the author and is made available under a Creative Commons Attribution-Non Commercial 4.0 International Licence (CC BY-NC) . Researchers are free to copy, distribute or transmit the thesis on the condition that they attribute it, that they do not use it for commercial purposes and that they do not alter, transform or build upon it. For any reuse or redistribution, researchers must make clear to others the licence terms of this work. Please seek permission from the copyright holder for uses of this work that are not included in this licence or permitted under UK Copyright Law.  \nAbstract  \nIn this thesis, I explore the possibility of constructing machine-learning models of the interacting density-density response function (DDRF) and quantities derived from it. Accurate models of the DDRF are a crucial ingredient to enabling GW quasiparticle calculations of more complex systems. Model DDRFs bypass the expensive calculation and inversion of the dielectric matrix, which is the origin of the poor scaling of the GW method with the number of atoms.  \nThe thesis is organized as follows:  \n• Chapter 2 systematically reviews common descriptors used for machine-learning physical quantities. The key ideas behind the construction of such descriptors are discussed. First, I introduce several descriptors that systematically incorporate symmetry transformations that leave the target quantity invariant. These descriptors can be used for learning quantities such as the ground-state energy, atomization energies and scalar polarizabilities. Next, I discuss several descriptors and models that are equivariant under transformations of the molecular structure. These descriptors are ideal for learning quantities which transform in a defined way under the action of a transformation, such as vectors, tensorsand functions, including the DDRF.  \n• In Chapter 3, I introduce the key electronic structure methods employed throughout the thesis. I start by introducing density functional theory, followed by a detailed introduction to the GW method and the DDRF.  \n• In Chapter 4, I develop a machine-learning model of an invariant quantity derived from the random phase approximation (RPA) DDRF: the scalar polarizability. In this chapter, I calculate the DDRF of 110 hydrogenated silicon clusters. The results of these calculations are then used to train a model of the scalar polarizability based on the SOAP descriptor [16] . The resulting model is then used to predict the scalar polarizability of clusters with up to 3000 silicon atoms while converging to the correct silicon scalar polarizability bulk limit. The findings of this chapter indicate that the scalar polarizability-even though derived from the non-local DDRF-can be accurately predicted from structural descriptors that only encode the local environment of each atom. These results indicate that the response of a non-metallic system to an external potential described by the DDRF may also be  \napproximated as a sum of localized atomic contributions, which forms the motivation for the following two chapters.  \n• In Chapter 5, I develop an approximation to the DDRF of the silicon clusters based on a projection onto atom-centred auxiliary density-fitting basis sets. The results of this chapter indicate that the plane-wave DDRF can be efficiently represented by a small localized basis, thus significantly reducing the size of the DDRF. At the end of this section, I develop a simple neural-network model of the DDRF in this localized basis, highlighting the neces","cbCaivUsWbmh0dkA","https://ap.wps.com/l/cbCaivUsWbmh0dkA","pdf",4743418,1,183,"English","en",105,"# Abstract\n## Thesis organization and research scope\n## Descriptor design: invariance and equivariance\n## Electronic structure methods: DFT, GW, DDRF\n## ML model for scalar polarizability from RPA DDRF\n## Localized basis approximation for DDRF and neural network modeling\n## Atom-decomposed DDRF via neighbourhood density matrix (NDM)\n## Applications to GW quasiparticle energy corrections","[{\"question\":\"Why are accurate DDRF models important for GW quasiparticle calculations?\",\"answer\":\"Accurate density-density response function models are a crucial input for GW calculations, and better DDRF modeling enables treating more complex systems with improved computational efficiency.\"},{\"question\":\"What approach does the thesis use to reduce the computational cost of GW scaling?\",\"answer\":\"It constructs machine-learning models that bypass costly dielectric-matrix calculations and inversion, which are responsible for poor scaling with the number of atoms.\"},{\"question\":\"How does the thesis ultimately connect model DDRFs to GW results?\",\"answer\":\"Predicted DDRFs are transformed into a plane-wave basis and used directly in GW calculations, reproducing quasiparticle energy corrections obtained from an atomic decomposition of the DDRF.\"}]","Machine Learning static RPA response properties for accelerating GW calculations | 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are accurate DDRF models important for GW quasiparticle calculations?","Question",{"text":75,"@type":76},"Accurate density-density response function models are a crucial input for GW calculations, and better DDRF modeling enables treating more complex systems with improved computational efficiency.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What approach does the thesis use to reduce the computational cost of GW scaling?",{"text":80,"@type":76},"It constructs machine-learning models that bypass costly dielectric-matrix calculations and inversion, which are responsible for poor scaling with the number of atoms.",{"name":82,"@type":73,"acceptedAnswer":83},"How does the thesis ultimately connect model DDRFs to GW results?",{"text":84,"@type":76},"Predicted DDRFs are transformed into a plane-wave basis and used directly in GW calculations, reproducing quasiparticle energy corrections obtained from an atomic decomposition of the 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