{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,31]],"date-time":"2026-01-31T08:39:20Z","timestamp":1769848760982,"version":"3.49.0"},"reference-count":33,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2024,11,8]],"date-time":"2024-11-08T00:00:00Z","timestamp":1731024000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key Laboratory of Particle Transport and Separation Technology"},{"name":"Liao Yuan Project of China Nuclear Energy Industry Corporation"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Data-driven machine learning approaches with precise predictive capabilities are proposed to address the long-standing challenges in the calculation of complex many-electron atomic systems, including high computational costs and limited accuracy. In this work, we develop a general workflow for machine learning-assisted atomic structure calculations based on the Cowan code\u2019s Hartree\u2013Fock with relativistic corrections (HFR) theory. The workflow incorporates enhanced ElasticNet and XGBoost algorithms, refined using entropy weight methodology to optimize performance. This semi-empirical framework is applied to calculate and analyze the excited state energy levels of the 4f closed-shell Yb I atom, providing insights into the applicability of different algorithms under various conditions. The reliability and advantages of this innovative approach are demonstrated through comprehensive comparisons with ab initio calculations, experimental data, and other theoretical results.<\/jats:p>","DOI":"10.3390\/e26110962","type":"journal-article","created":{"date-parts":[[2024,11,8]],"date-time":"2024-11-08T06:05:41Z","timestamp":1731045941000},"page":"962","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Machine Learning-Assisted Hartree\u2013Fock Approach for Energy Level Calculations in the Neutral Ytterbium Atom"],"prefix":"10.3390","volume":"26","author":[{"given":"Kaichen","family":"Ma","sequence":"first","affiliation":[{"name":"National Key Laboratory of Particle Transport and Separation Technology, Tianjin 300180, China"},{"name":"Research Institute of Physical and Chemical Engineering of Nuclear Industry, Tianjin 300180, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4925-738X","authenticated-orcid":false,"given":"Chen","family":"Yang","sequence":"additional","affiliation":[{"name":"Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Junyao","family":"Zhang","sequence":"additional","affiliation":[{"name":"National Key Laboratory of Particle Transport and Separation Technology, Tianjin 300180, China"},{"name":"Research Institute of Physical and Chemical Engineering of Nuclear Industry, Tianjin 300180, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yunfei","family":"Li","sequence":"additional","affiliation":[{"name":"National Key Laboratory of Particle Transport and Separation Technology, Tianjin 300180, China"},{"name":"Research Institute of Physical and Chemical Engineering of Nuclear Industry, Tianjin 300180, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gang","family":"Jiang","sequence":"additional","affiliation":[{"name":"Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, China"},{"name":"Key Laboratory of High Energy Density Physics and Technology, Ministry of Education, Chengdu 610065, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Junjie","family":"Chai","sequence":"additional","affiliation":[{"name":"National Key Laboratory of Particle Transport and Separation Technology, Tianjin 300180, China"},{"name":"Research Institute of Physical and Chemical Engineering of Nuclear Industry, Tianjin 300180, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,11,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"5644","DOI":"10.1103\/PhysRevE.49.5644","article-title":"Plasma Diagnostics with Spectral Profile Calculations","volume":"49","author":"Godbert","year":"1994","journal-title":"Phys. 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