{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,20]],"date-time":"2026-03-20T06:33:23Z","timestamp":1773988403732,"version":"3.50.1"},"reference-count":48,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2023,5,8]],"date-time":"2023-05-08T00:00:00Z","timestamp":1683504000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["11925502"],"award-info":[{"award-number":["11925502"]}]},{"name":"National Natural Science Foundation of China","award":["11935001"],"award-info":[{"award-number":["11935001"]}]},{"name":"National Natural Science Foundation of China","award":["11961141003"],"award-info":[{"award-number":["11961141003"]}]},{"name":"National Natural Science Foundation of China","award":["11421505"],"award-info":[{"award-number":["11421505"]}]},{"name":"National Natural Science Foundation of China","award":["11475244"],"award-info":[{"award-number":["11475244"]}]},{"name":"National Natural Science Foundation of China","award":["11927901"],"award-info":[{"award-number":["11927901"]}]},{"name":"National Natural Science Foundation of China","award":["11835002"],"award-info":[{"award-number":["11835002"]}]},{"name":"National Natural Science Foundation of China","award":["XDB34030000"],"award-info":[{"award-number":["XDB34030000"]}]},{"name":"National Natural Science Foundation of China","award":["2018YFA0404404"],"award-info":[{"award-number":["2018YFA0404404"]}]},{"name":"Strategic Priority Research Program of the CAS","award":["11925502"],"award-info":[{"award-number":["11925502"]}]},{"name":"Strategic Priority Research Program of the CAS","award":["11935001"],"award-info":[{"award-number":["11935001"]}]},{"name":"Strategic Priority Research Program of the CAS","award":["11961141003"],"award-info":[{"award-number":["11961141003"]}]},{"name":"Strategic Priority Research Program of the CAS","award":["11421505"],"award-info":[{"award-number":["11421505"]}]},{"name":"Strategic Priority Research Program of the CAS","award":["11475244"],"award-info":[{"award-number":["11475244"]}]},{"name":"Strategic Priority Research Program of the CAS","award":["11927901"],"award-info":[{"award-number":["11927901"]}]},{"name":"Strategic Priority Research Program of the CAS","award":["11835002"],"award-info":[{"award-number":["11835002"]}]},{"name":"Strategic Priority Research Program of the CAS","award":["XDB34030000"],"award-info":[{"award-number":["XDB34030000"]}]},{"name":"Strategic Priority Research Program of the CAS","award":["2018YFA0404404"],"award-info":[{"award-number":["2018YFA0404404"]}]},{"name":"National Key R&amp;D Program of China","award":["11925502"],"award-info":[{"award-number":["11925502"]}]},{"name":"National Key R&amp;D Program of China","award":["11935001"],"award-info":[{"award-number":["11935001"]}]},{"name":"National Key R&amp;D Program of China","award":["11961141003"],"award-info":[{"award-number":["11961141003"]}]},{"name":"National Key R&amp;D Program of China","award":["11421505"],"award-info":[{"award-number":["11421505"]}]},{"name":"National Key R&amp;D Program of China","award":["11475244"],"award-info":[{"award-number":["11475244"]}]},{"name":"National Key R&amp;D Program of China","award":["11927901"],"award-info":[{"award-number":["11927901"]}]},{"name":"National Key R&amp;D Program of China","award":["11835002"],"award-info":[{"award-number":["11835002"]}]},{"name":"National Key R&amp;D Program of China","award":["XDB34030000"],"award-info":[{"award-number":["XDB34030000"]}]},{"name":"National Key R&amp;D Program of China","award":["2018YFA0404404"],"award-info":[{"award-number":["2018YFA0404404"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The charge radius is a fundamental physical quantity that describes the size of one nucleus, but contains rich information about the nuclear structure. There are already many machine learning (ML) studies on charge radii. After reviewing the relevant works in detail, the convolutional neural networks (CNNs) are established to reproduce the latest experimental values of charge radii. The extrapolating and interpolating abilities in terms of two CNN structures partnering two inputting matrix forms are discussed, and a testing root-mean-square (RMS) error 0.015 fm is achieved. The shell effect on charge radii of both isotones and isotopes are predicted successfully, and the CNN method works well when predicting the charge radii of a whole isotopic chain.<\/jats:p>","DOI":"10.3390\/sym15051040","type":"journal-article","created":{"date-parts":[[2023,5,9]],"date-time":"2023-05-09T01:06:28Z","timestamp":1683594388000},"page":"1040","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Progress of Machine Learning Studies on the Nuclear Charge Radii"],"prefix":"10.3390","volume":"15","author":[{"given":"Ping","family":"Su","sequence":"first","affiliation":[{"name":"Key Laboratory of Nuclear Physics and Ion-Beam Application (MOE), Institute of Modern Physics, Fudan University, Shanghai 200433, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3854-4965","authenticated-orcid":false,"given":"Wan-Bing","family":"He","sequence":"additional","affiliation":[{"name":"Key Laboratory of Nuclear Physics and Ion-Beam Application (MOE), Institute of Modern Physics, Fudan University, Shanghai 200433, China"},{"name":"Shanghai Research Center for Theoretical Nuclear Physics, NSFC and Fudan University, Shanghai 200438, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6123-3014","authenticated-orcid":false,"given":"De-Qing","family":"Fang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Nuclear Physics and Ion-Beam Application (MOE), Institute of Modern Physics, Fudan University, Shanghai 200433, China"},{"name":"Shanghai Research Center for Theoretical Nuclear Physics, NSFC and Fudan University, Shanghai 200438, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,5,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"471","DOI":"10.1134\/1.1358471","article-title":"Coulomb Energy of Nuclei","volume":"64","author":"Shaginyan","year":"2001","journal-title":"Phys. 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