[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-123643-en":3,"doc-seo-123643-105":30,"detail-sidebar-cat-0-en-105":92},{"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},123643,549758146520,"Patrick","https://ap-avatar.wpscdn.com/avatar/80002397d8c0411e94?_k=1775819394049821470",8,"Research & Report","Machine-learning Kohn-Sham Potential from Dynamics in Time-Dependent Kohn-Sham Systems","Construction of a more accurate exchange-correlation potential is central to improving time-dependent density functional theory (TDDFT) results and the predictive power for many-electron properties. This work proposes a machine-learning approach to develop the energy functional and the Kohn-Sham potential for time-dependent Kohn-Sham systems. The method leverages Kohn-Sham dynamics and avoids any training data for the exact Kohn-Sham potential. Benchmarks on 1D harmonic-oscillator and two-electron cases validate agreement without memory effects and successful dynamics capture when memory effects are present.","arXiv :2207 .00687v2 [ quant-ph] 21 Aug 2023  \nMachine-learning Kohn-Sham Potential from  \nDynamics in Time-Dependent Kohn-Sham Systems  \nJun Yang 1 & James Whit􀀌eld1,∗  \n1 Department of Physics and Astronomy, Dartmouth College. Hanover, NH 03755  \n􀀃 Corresponding author:  \nE-mail: [james.d.whitfield@dartmouth.edu](james.d.whitfield@dartmouth.edu)  \nAbstract. The construction of a better exchange-correlation potential in timedependent density functional theory (TDDFT) can improve the accuracy of TDDFT calculations and provide more accurate predictions of the properties of many-electron systems. Here, we propose a machine learning method to develop the energy functional and the Kohn-Sham potential of a time-dependent Kohn-Sham system is proposed. The method is based on the dynamics of the Kohn-Sham system and does not require any data on the exact Kohn-Sham potential for training the model. We demonstrate the results of our method with a 1D harmonic oscillator example and a 1D twoelectron example. We show that the machine-learned Kohn-Sham potential matches the exact Kohn-Sham potential in the absence of memory e􀀋ect. Our method can still capture the dynamics of the Kohn-Sham system in the presence of memory e􀀋ects. The machine learning method developed in this article provides insight into making better approximations of the energy functional and the Kohn-Sham potential in the time-dependent Kohn-Sham system.  \n2  \n1. Introduction  \nA major challenge in TDDFT is the development of high-accuracy approximations for the Kohn-Sham potential vKS (r, t) in the time-dependent Kohn-Sham (TDKS) system. The Kohn-Sham potential is an e􀀋ective potential that allows us to equivalently convert the interacting electron system to a 􀀌ctitious non-interacting system known as the KohnSham system. As a tradeo􀀋 of this conversion, it is extremely hard to derive the explicit expression of the Kohn-Sham potential, which, in principle, determines the property of the electron system. As a result, signi􀀌cant research e􀀋ort has been devoted to developing better approximations for the Kohn-Sham potential.  \nThe Runge-Gross theorem [1] guarantees that the Kohn-Sham potential is uniquely determined (up to a purely time-dependent function) by the time-dependent electronic density n (r, t) for a given initial many-body state 􀀉0 = 􀀉(r, t0 ) of the interacting system and initial Kohn-Sham state 􀀈 0 = 􀀈(r, t0 ) of the non-interacting Kohn-Sham system. The associated Kohn-Sham potential is often written as a sum of three terms vKS [n, 􀀉0 , 􀀈 0 ](r, t) = vext (r, t) + vH [n](r, t) + vxc [n, 􀀉0 , 􀀈 0](r, t), where the 􀀌rst term is the external potential, the second term is the Hartree potential describing the classical electron-electron interaction. The 􀀌rst two terms are numerically easy and can be calculated explicitly given the electronic density. The last term is the exchange-correlation (xc) potential. The xc potential includes all the complex and non-trivial e􀀋ects whose exact form is unknown. Hence, the primary challenge in determining an accurate approximation of the Kohn-Sham potential is 􀀌nding ane􀀋ective approximation for the exchange-correlation potential. This task is challenging due to the complexity of electron interactions in many-electron systems.  \nTo enhance the accuracy of TDDFT calculations and provide more precise predictions of the properties of many-electron systems, various approximation methods for the xc-potential have been developed. Commonly used methods include local density approximation (LDA), generalized gradient approximation (GGA), and metageneralized gradient approximation (meta-GGA) [2–4], etc. Besides these traditional explicit constructions, some semi-empirical approaches were developed as well [5] . Recent works have provided approximation methods via machine learning techniques [6 , 7] . In Ref. [7], the authors investigated a two-electron system, where the electron densities and the exact xc-potential at di􀀋erent times wer","cbCaivQVmH1TSd0U","https://ap.wps.com/l/cbCaivQVmH1TSd0U","pdf",3519646,1,20,"English","en",105,"# Abstract\n# Introduction\n## Kohn-Sham potential and exchange-correlation challenge\n## Existing approximations and motivation for machine learning\n## Classical learning of potentials and neural network categories\n# Proposed approach and scope","[{\"question\":\"What problem does the document address in TDDFT?\",\"answer\":\"The document targets the difficulty of developing high-accuracy approximations for the time-dependent Kohn-Sham potential, especially the exchange-correlation part whose exact form is unknown.\"},{\"question\":\"How does the proposed machine-learning method avoid using exact Kohn-Sham potential data?\",\"answer\":\"It bases training on the dynamics of the Kohn-Sham system rather than requiring any pre-calculated pairs containing the exact Kohn-Sham potential.\"},{\"question\":\"Does the method work when memory effects are present?\",\"answer\":\"Yes. It matches the exact Kohn-Sham potential without memory effects and can still capture the Kohn-Sham dynamics in the presence of memory effects.\"}]","Machine-learning Kohn-Sham Potential from Dynamics in Time-Dependent Kohn-Sham Systems | PDF",1785817800,50,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":87,"head_meta":89,"extra_data":91,"updated_unix":28},"machine-learning-kohn-sham-potential-from-dynamics-in-time-dependent-kohn-sham-systems","",{"@graph":36,"@context":86},[37,54,69],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/machine-learning-kohn-sham-potential-from-dynamics-in-time-dependent-kohn-sham-systems/123643/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":63,"encodingFormat":61,"isAccessibleForFree":64,"interactionStatistic":65},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-05","2026-08-04",true,{"@type":66,"interactionType":67,"userInteractionCount":20},"InteractionCounter",{"@type":68},"ViewAction",{"@type":70,"mainEntity":71},"FAQPage",[72,78,82],{"name":73,"@type":74,"acceptedAnswer":75},"What problem does the document address in TDDFT?","Question",{"text":76,"@type":77},"The document targets the difficulty of developing high-accuracy approximations for the time-dependent Kohn-Sham potential, especially the exchange-correlation part whose exact form is unknown.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"How does the proposed machine-learning method avoid using exact Kohn-Sham potential data?",{"text":81,"@type":77},"It bases training on the dynamics of the Kohn-Sham system rather than requiring any pre-calculated pairs containing the exact Kohn-Sham potential.",{"name":83,"@type":74,"acceptedAnswer":84},"Does the method work when memory effects are present?",{"text":85,"@type":77},"Yes. It matches the exact Kohn-Sham potential without memory effects and can still capture the Kohn-Sham dynamics in the presence of memory effects.","https://schema.org",{"og:url":52,"og:type":88,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":90,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":93},[94,98,102,106,111,115,120,123,127,130,134],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":95,"show_sort_weight":96,"slug":97},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":99,"show_sort_weight":100,"slug":101},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":103,"show_sort_weight":104,"slug":105},"Exam",70,"exam",{"id":107,"doc_module":4,"doc_module_name":46,"category_name":108,"show_sort_weight":109,"slug":110},5,"Comic",60,"comic",{"id":112,"doc_module":4,"doc_module_name":46,"category_name":113,"show_sort_weight":29,"slug":114},6,"Technology","technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":21,"slug":126},9,"Religion & Spirituality","religion-spirituality",{"id":21,"doc_module":4,"doc_module_name":46,"category_name":128,"show_sort_weight":21,"slug":129},"World Cup","world-cup",{"id":131,"doc_module":4,"doc_module_name":46,"category_name":132,"show_sort_weight":131,"slug":133},10,"Lifestyle","lifestyle",{"id":135,"doc_module":4,"doc_module_name":46,"category_name":136,"show_sort_weight":107,"slug":137},19,"General","general"]