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Extensive numerical experiments in two- and multi-dimensional spaces with point sources, line sources, or their combinations are presented to illustrate the efficiency of the proposed approach, and a comparative study with several existing approaches based on neural networks is also given, which shows clearly its competitiveness for the specific class of problems. In addition, we briefly discuss the error analysis of the approach.<\/jats:p>","DOI":"10.1137\/22m1520840","type":"journal-article","created":{"date-parts":[[2023,8,8]],"date-time":"2023-08-08T05:17:48Z","timestamp":1691471868000},"page":"A2043-A2074","source":"Crossref","is-referenced-by-count":12,"title":["Solving Elliptic Problems with Singular Sources Using Singularity Splitting Deep Ritz Method"],"prefix":"10.1137","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3312-7492","authenticated-orcid":true,"given":"Tianhao","family":"Hu","sequence":"first","affiliation":[{"name":"School of Mathematics, Jilin University, Changchun 130012, People\u2019s Republic of China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bangti","family":"Jin","sequence":"additional","affiliation":[{"name":"Department of Mathematics, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong, People\u2019s Republic of China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3439-0313","authenticated-orcid":true,"given":"Zhi","family":"Zhou","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong, People\u2019s Republic of China."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2023,8,8]]},"reference":[{"key":"ref1","volume-title":"Sobolev Spaces","author":"Adams R. 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