{"id":"https://openalex.org/W4404389485","doi":"https://doi.org/10.1016/j.neunet.2026.109067","title":"Solver-in-the-loop joint operator learning: Fractional Laplace-Beltrami features for interface reconstruction","display_name":"Solver-in-the-loop joint operator learning: Fractional Laplace-Beltrami features for interface reconstruction","publication_year":2026,"publication_date":"2026-05-17","ids":{"openalex":"https://openalex.org/W4404389485","doi":"https://doi.org/10.1016/j.neunet.2026.109067","pmid":"https://pubmed.ncbi.nlm.nih.gov/42214933"},"language":"en","primary_location":{"id":"doi:10.1016/j.neunet.2026.109067","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.neunet.2026.109067","pdf_url":null,"source":{"id":"https://openalex.org/S123019304","display_name":"Neural Networks","issn_l":"0893-6080","issn":["0893-6080","1879-2782"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Networks","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite","pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2411.05341","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5029787011","display_name":"Yangyang Zheng","orcid":"https://orcid.org/0000-0002-8249-0554"},"institutions":[{"id":"https://openalex.org/I4610292","display_name":"Xiangtan University","ror":"https://ror.org/00xsfaz62","country_code":"CN","type":"education","lineage":["https://openalex.org/I4610292"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yangyang Zheng","raw_affiliation_strings":["School of Mathematics and Computational Science, Xiangtan University, Xiangtan, Hunan, China"],"raw_orcid":"https://orcid.org/0009-0004-8495-2208","affiliations":[{"raw_affiliation_string":"School of Mathematics and Computational Science, Xiangtan University, Xiangtan, Hunan, China","institution_ids":["https://openalex.org/I4610292"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042394216","display_name":"Huayi Wei","orcid":"https://orcid.org/0000-0003-0380-9617"},"institutions":[{"id":"https://openalex.org/I121296143","display_name":"Hunan University of Science and Technology","ror":"https://ror.org/02m9vrb24","country_code":"CN","type":"education","lineage":["https://openalex.org/I121296143"]},{"id":"https://openalex.org/I4610292","display_name":"Xiangtan University","ror":"https://ror.org/00xsfaz62","country_code":"CN","type":"education","lineage":["https://openalex.org/I4610292"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Huayi Wei","raw_affiliation_strings":["School of Mathematics and Computational Science, Xiangtan University, National Center for Applied Mathematics in Hunan, Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan, 411105, China. Electronic address: weihuayi@xtu.edu.cn"],"raw_orcid":"https://orcid.org/0000-0003-0380-9617","affiliations":[{"raw_affiliation_string":"School of Mathematics and Computational Science, Xiangtan University, National Center for Applied Mathematics in Hunan, Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan, 411105, China. Electronic address: weihuayi@xtu.edu.cn","institution_ids":["https://openalex.org/I4610292","https://openalex.org/I121296143"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066985452","display_name":"Shuhao Cao","orcid":"https://orcid.org/0000-0001-6555-706X"},"institutions":[{"id":"https://openalex.org/I75421653","display_name":"University of Missouri\u2013Kansas City","ror":"https://ror.org/01w0d5g70","country_code":"US","type":"education","lineage":["https://openalex.org/I75421653"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Shuhao Cao","raw_affiliation_strings":["School of Science and Engineering, University of Missouri-Kansas City, Kansas City, Missouri, United States. Electronic address: scao@umkc.edu"],"raw_orcid":"https://orcid.org/0000-0001-6555-706X","affiliations":[{"raw_affiliation_string":"School of Science and Engineering, University of Missouri-Kansas City, Kansas City, Missouri, United States. Electronic address: scao@umkc.edu","institution_ids":["https://openalex.org/I75421653"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003060391","display_name":"Ruchi Guo","orcid":"https://orcid.org/0000-0002-8558-1574"},"institutions":[{"id":"https://openalex.org/I24185976","display_name":"Sichuan University","ror":"https://ror.org/011ashp19","country_code":"CN","type":"education","lineage":["https://openalex.org/I24185976"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ruchi Guo","raw_affiliation_strings":["School of Mathematics, Sichuan University, Chengdu, Sichuan, China. Electronic address: ruchiguo@scu.edu.cn"],"raw_orcid":"https://orcid.org/0000-0002-8558-1574","affiliations":[{"raw_affiliation_string":"School of Mathematics, Sichuan University, Chengdu, Sichuan, China. Electronic address: ruchiguo@scu.edu.cn","institution_ids":["https://openalex.org/I24185976"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":3350,"currency":"USD","value_usd":3350},"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00042477,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"203","issue":null,"first_page":"109067","last_page":"109067"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11948","display_name":"Machine Learning in Materials Science","score":0.9394999742507935,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11948","display_name":"Machine Learning in Materials Science","score":0.9394999742507935,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/interface","display_name":"Interface (matter)","score":0.668616771697998},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6315711736679077},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.6024643182754517},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5429875254631042},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.397722065448761},{"id":"https://openalex.org/keywords/engineering-drawing","display_name":"Engineering drawing","score":0.35583239793777466},{"id":"https://openalex.org/keywords/computational-science","display_name":"Computational science","score":0.32312726974487305},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.24371469020843506},{"id":"https://openalex.org/keywords/structural-engineering","display_name":"Structural engineering","score":0.20419076085090637},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.15595918893814087},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.057792216539382935}],"concepts":[{"id":"https://openalex.org/C113843644","wikidata":"https://www.wikidata.org/wiki/Q901882","display_name":"Interface (matter)","level":4,"score":0.668616771697998},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6315711736679077},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.6024643182754517},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5429875254631042},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.397722065448761},{"id":"https://openalex.org/C199639397","wikidata":"https://www.wikidata.org/wiki/Q1788588","display_name":"Engineering drawing","level":1,"score":0.35583239793777466},{"id":"https://openalex.org/C459310","wikidata":"https://www.wikidata.org/wiki/Q117801","display_name":"Computational science","level":1,"score":0.32312726974487305},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.24371469020843506},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.20419076085090637},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.15595918893814087},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.057792216539382935},{"id":"https://openalex.org/C129307140","wikidata":"https://www.wikidata.org/wiki/Q6795880","display_name":"Maximum bubble pressure method","level":3,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C157915830","wikidata":"https://www.wikidata.org/wiki/Q2928001","display_name":"Bubble","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1016/j.neunet.2026.109067","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.neunet.2026.109067","pdf_url":null,"source":{"id":"https://openalex.org/S123019304","display_name":"Neural Networks","issn_l":"0893-6080","issn":["0893-6080","1879-2782"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Networks","raw_type":"journal-article"},{"id":"pmid:42214933","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/42214933","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural networks : the official journal of the International Neural Network Society","raw_type":null},{"id":"pmh:oai:arXiv.org:2411.05341","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2411.05341","pdf_url":"https://arxiv.org/pdf/2411.05341","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"pmh:oai:arXiv.org:2411.05341","is_oa":true,"landing_page_url":"https://arxiv.org/abs/2411.05341","pdf_url":"https://arxiv.org/pdf/2411.05341","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2411.05341","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2411.05341","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2411.05341","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2411.05341","pdf_url":"https://arxiv.org/pdf/2411.05341","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1832942644","display_name":null,"funder_award_id":"12261131501","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3650193559","display_name":null,"funder_award_id":"DMS-2309778","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6376118933","display_name":null,"funder_award_id":"12371410","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7055750589","display_name":null,"funder_award_id":"2309777","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7736401583","display_name":null,"funder_award_id":"2309777","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8431781965","display_name":"Collaborative Research: Theory and Applications of Structure-Conforming Deep Operator Learning","funder_award_id":"2309778","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322990","display_name":"Sichuan University","ror":"https://ror.org/011ashp19"},{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4404389485.pdf"},"referenced_works_count":54,"referenced_works":["https://openalex.org/W1981696101","https://openalex.org/W2095463076","https://openalex.org/W3007906701","https://openalex.org/W4362470054","https://openalex.org/W2552701315","https://openalex.org/W1979646278","https://openalex.org/W2131742412","https://openalex.org/W3165847773","https://openalex.org/W2888785267","https://openalex.org/W2022920697","https://openalex.org/W4283460575","https://openalex.org/W2896618593","https://openalex.org/W2948801778","https://openalex.org/W2057235791","https://openalex.org/W2905450017","https://openalex.org/W3183994952","https://openalex.org/W2782053562","https://openalex.org/W4296060623","https://openalex.org/W2801227107","https://openalex.org/W2963231761","https://openalex.org/W4410361090","https://openalex.org/W2010099677","https://openalex.org/W1983053523","https://openalex.org/W3007480459","https://openalex.org/W2936869293","https://openalex.org/W3165950543","https://openalex.org/W3136599486","https://openalex.org/W3161200675","https://openalex.org/W3099709074","https://openalex.org/W4405615986","https://openalex.org/W4387573065","https://openalex.org/W4376868980","https://openalex.org/W2982546823","https://openalex.org/W2759764994","https://openalex.org/W3128157635","https://openalex.org/W2057137545","https://openalex.org/W4388750071","https://openalex.org/W2128648870","https://openalex.org/W3000220657","https://openalex.org/W2969381807","https://openalex.org/W2016196567","https://openalex.org/W2899283552","https://openalex.org/W2160137631","https://openalex.org/W3152007055","https://openalex.org/W2767248316","https://openalex.org/W4403929679","https://openalex.org/W4408761525","https://openalex.org/W2007008305","https://openalex.org/W2807879753","https://openalex.org/W4409107913","https://openalex.org/W4403409840","https://openalex.org/W4401262836","https://openalex.org/W3010849941","https://openalex.org/W4401707330"],"related_works":["https://openalex.org/W2055836843","https://openalex.org/W2755775996","https://openalex.org/W3131818128","https://openalex.org/W2095941963","https://openalex.org/W2366062865","https://openalex.org/W2069701013","https://openalex.org/W2378005410","https://openalex.org/W2170435352","https://openalex.org/W2169158840","https://openalex.org/W1997375727"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2024-11-15T00:00:00"}