[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-126298-en":3,"doc-seo-126298-105":31,"detail-sidebar-cat-0-en-105":97},{"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":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":28,"seo_description":14,"update_tm":29,"read_time":30},126298,2336475104957,"Seraphina","https://ap-avatar.wpscdn.com/avatar/22000c4c6bd8a5076e1?x-image-process=image/resize,m_fixed,w_180,h_180&k=1787554080175789136",8,"Research & Report","Machine Learning Chemically Accurate Orbital-Free Density Functional Theory - Doctoral Dissertation","Orbital-free density functional theory (OF-DFT) provides a cost-effective approach for electronic structure calculations. The work demonstrates machine-learning density functionals that remain accurate and generalizable, focusing especially on the kinetic energy required for OF-DFT. KineticNet, a deep neural network for kinetic energy density, is trained on varied data generated via sampling-based perturbations of the external potential. The method is extended from grid representations to linear combinations of atomic basis functions, enabling convergent density optimization with chemical accuracy. Surrogate functionals further allow efficient, scalable energy functional development by optimizing electron densities without direct replication of physical energy functionals, using surrogate loss functions and a novel training-time density optimization scheme.","Dissertation  \nsubmitted to the  \nCombined Faculty of Mathematics, Engineering and Natural Sciences of Heidelberg University, Germany for the degree of  \nDoctor of Natural Sciences  \nPut forward by  \nM.Sc. Roman Remme  \nborn in: Wiesbaden  \nOral examination: 21-01-2025  \nMachine Learning Chemically Accurate Orbital-Free Density Functional Theory  \nReferees: Prof. Dr. Fred A. Hamprecht  \nProf. Dr. Maurits W. Haverkort  \nAbstract  \nOrbital-free density functional theory (OF-DFT) is a cost-effective framework for electronic structure calculations. We demonstrate the feasibility of machine learning accurate and generalizable density functionals, particularly comprising the kinetic energy required for OF-DFT.  \nWe introduce KineticNet, a deep neural network tailored to predict the kinetic energy density. Trained on varied data generated with a novel scheme based on sampling the external potential, KineticNet achieves chemical accuracy on small molecules andreproduces chemical bonding in orbital-free density optimization.  \nExpanding this success, we transition from grid-based density representations to the more efficient linear combination of atomic basis functions Ansatz. Adapting and improving our external potential sampling strategy, we achieve state-of-the-art results for OF-DFT on the QM9 dataset of organic molecules, in both energy and density prediction. Crucially, we address a key limitation of previous approaches by enabling convergent density optimization with chemical accuracy.  \nFinally, we propose surrogate functionals, enabling optimization of electron densities without directly replicating physical energy functionals. By integrating surrogate loss functions and a novel train-time density optimization scheme, we further boost the accuracy of density predictions while reducing training data requirements. This innovative approach opens new avenues for efficient and scalable energy functional development.  \nZusammenfassung  \nOrbitalfreie Dichtefunktionaltheorie (OF-DFT) ist ein kostengünstiger Ansatz zur Berechnung elektronischer Strukturen. Wir zeigen, dass mittels maschinellen Lernens präzise und generalisierbare Dichtefunktionale entwickelt werden können, welcheinsbesondere die für OF-DFT benötigte kinetische Energie enthalten.  \nWir stellen KineticNet vor, ein tiefes neuronales Netzwerk zur Vorhersage der kinetischen Energiedichte. Trainiert mit neuartigen variierten Daten welche mithilfe von Störungen des externen Potentials generiert wurden, erreicht KineticNet chemische Genauigkeit auf kleinen Molekülen und reproduziert chemische Bindung in orbitalfreier Dichteoptimierung.  \nDarüber hinaus wechseln wir von gitterbasierten Dichte-Repräsentationen hin zureffizienteren Linearkombination atomarer Basisfunktionen. Mit einer für diesen Ansatz angepassten und verbesserten Strategie zur Störung des externen Potentials erzielen wir erstklassige Ergebnisse für OF-DFT auf dem QM9-Datensatz organischer Molekülefür Energie-und Dichtevorhersagen. Ein entscheidender Fortschritt ist die stabil konvergente Dichteoptimierung mit chemischer Genauigkeit.  \nAbschließend führen wir Surrogat-Funktionale ein, welche die Optimierung von Elektronendichten ohne direkte Nachbildung physikalischer Energiefunktionale erlauben. Durch die Integration von Surrogat-Kostenfunktionen und einem neuartigen Optimierungsschema für Dichten während des Trainings steigern wir die Genauigkeit der Dichtevorhersagen weiter und verringern den Datenbedarf für das Training. Dieser innovative Ansatz eröffnet neue Möglichkeiten für die effiziente Entwicklung von skalierbaren Energie-Funktionalen.  \nAcknowledgements  \nFirst, I want to thank my advisor Fred Hamprecht, who first sparked my interest in machine learning through one of his lectures. He gave me the opportunity to join his group, explore my interests and develop my scientific career. Thank you for creating a friendly atmosphere and mentoring me throughout the years, always encouraging me when I doubted myself","cbCaitJbvsxQjZUj","https://ap.wps.com/l/cbCaitJbvsxQjZUj","pdf",10157660,10,1,140,"English","en",105,"# Abstract\n## KineticNet and external potential sampling\n## Linear combination of atomic basis functions\n## Convergent density optimization with chemical accuracy\n## Surrogate functionals and training-time density optimization","[{\"question\":\"What is the main goal of this dissertation?\",\"answer\":\"Develop machine-learning density functionals for orbital-free DFT that are accurate, generalizable, and efficient—especially for the kinetic energy component.\"},{\"question\":\"How does KineticNet contribute to OF-DFT?\",\"answer\":\"KineticNet predicts the kinetic energy density and is trained on varied data produced by a sampling-based scheme using perturbations of the external potential.\"},{\"question\":\"What advances enable chemically accurate density optimization?\",\"answer\":\"The approach transitions to a linear combination of atomic basis functions and improves the external potential sampling strategy, enabling convergent density optimization with chemical accuracy.\"},{\"question\":\"What are surrogate functionals in this work?\",\"answer\":\"Surrogate functionals optimize electron densities without directly replicating physical energy functionals, using surrogate losses and a novel training-time density optimization scheme to improve accuracy and reduce data needs.\"}]","Machine Learning Chemically Accurate Orbital-Free Density Functional Theory - Doctoral Dissertation | PDF",1785904327,353,{"code":4,"msg":32,"data":33},"ok",{"site_id":25,"language":24,"slug":34,"title":13,"keywords":35,"description":14,"schema_data":36,"social_meta":92,"head_meta":94,"extra_data":96,"updated_unix":29},"machine-learning-chemically-accurate-orbital-free-density-functional-theory-doctoral-dissertation","",{"@graph":37,"@context":91},[38,55,70],{"@type":39,"itemListElement":40},"BreadcrumbList",[41,45,49,52],{"item":42,"name":43,"@type":44,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":46,"name":47,"@type":44,"position":48},"https://docshare.wps.com/document/","Document",2,{"item":50,"name":12,"@type":44,"position":51},"https://docshare.wps.com/document/research-report/",3,{"item":53,"name":13,"@type":44,"position":54},"https://docshare.wps.com/document/machine-learning-chemically-accurate-orbital-free-density-functional-theory-doctoral-dissertation/126298/",4,{"url":53,"name":13,"@type":56,"author":57,"headline":13,"publisher":59,"fileFormat":62,"inLanguage":24,"description":14,"dateModified":63,"datePublished":64,"encodingFormat":62,"isAccessibleForFree":65,"interactionStatistic":66},"DigitalDocument",{"name":9,"@type":58},"Person",{"url":42,"name":60,"@type":61},"DocShare","Organization","application/pdf","2026-08-22","2026-08-05",true,{"@type":67,"interactionType":68,"userInteractionCount":20},"InteractionCounter",{"@type":69},"ViewAction",{"@type":71,"mainEntity":72},"FAQPage",[73,79,83,87],{"name":74,"@type":75,"acceptedAnswer":76},"What is the main goal of this dissertation?","Question",{"text":77,"@type":78},"Develop machine-learning density functionals for orbital-free DFT that are accurate, generalizable, and efficient—especially for the kinetic energy component.","Answer",{"name":80,"@type":75,"acceptedAnswer":81},"How does KineticNet contribute to OF-DFT?",{"text":82,"@type":78},"KineticNet predicts the kinetic energy density and is trained on varied data produced by a sampling-based scheme using perturbations of the external potential.",{"name":84,"@type":75,"acceptedAnswer":85},"What advances enable chemically accurate density optimization?",{"text":86,"@type":78},"The approach transitions to a linear combination of atomic basis functions and improves the external potential sampling strategy, enabling convergent density optimization with chemical accuracy.",{"name":88,"@type":75,"acceptedAnswer":89},"What are surrogate functionals in this work?",{"text":90,"@type":78},"Surrogate functionals optimize electron densities without directly replicating physical energy functionals, using surrogate losses and a novel training-time density optimization scheme to improve accuracy and reduce data needs.","https://schema.org",{"og:url":53,"og:type":93,"og:title":13,"og:site_name":60,"og:description":14},"article",{"robots":95,"canonical":53},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":98},[99,103,107,111,116,121,126,129,134,137,140],{"id":21,"doc_module":4,"doc_module_name":47,"category_name":100,"show_sort_weight":101,"slug":102},"Story & Novel",90,"story-novel",{"id":48,"doc_module":4,"doc_module_name":47,"category_name":104,"show_sort_weight":105,"slug":106},"Literature",80,"literature",{"id":54,"doc_module":4,"doc_module_name":47,"category_name":108,"show_sort_weight":109,"slug":110},"Exam",70,"exam",{"id":112,"doc_module":4,"doc_module_name":47,"category_name":113,"show_sort_weight":114,"slug":115},5,"Comic",60,"comic",{"id":117,"doc_module":4,"doc_module_name":47,"category_name":118,"show_sort_weight":119,"slug":120},6,"Technology",50,"technology",{"id":122,"doc_module":4,"doc_module_name":47,"category_name":123,"show_sort_weight":124,"slug":125},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":47,"category_name":12,"show_sort_weight":127,"slug":128},30,"research-report",{"id":130,"doc_module":4,"doc_module_name":47,"category_name":131,"show_sort_weight":132,"slug":133},9,"Religion & Spirituality",20,"religion-spirituality",{"id":132,"doc_module":4,"doc_module_name":47,"category_name":135,"show_sort_weight":132,"slug":136},"World Cup","world-cup",{"id":20,"doc_module":4,"doc_module_name":47,"category_name":138,"show_sort_weight":20,"slug":139},"Lifestyle","lifestyle",{"id":141,"doc_module":4,"doc_module_name":47,"category_name":142,"show_sort_weight":112,"slug":143},19,"General","general"]