{"id":"https://openalex.org/W7127081766","doi":"https://doi.org/10.3390/computation14020037","title":"LocRes\u2013PINN: A Physics\u2013Informed Neural Network with Local Awareness and Residual Learning","display_name":"LocRes\u2013PINN: A Physics\u2013Informed Neural Network with Local Awareness and Residual Learning","publication_year":2026,"publication_date":"2026-02-02","ids":{"openalex":"https://openalex.org/W7127081766","doi":"https://doi.org/10.3390/computation14020037"},"language":"en","primary_location":{"id":"doi:10.3390/computation14020037","is_oa":true,"landing_page_url":"https://doi.org/10.3390/computation14020037","pdf_url":null,"source":{"id":"https://openalex.org/S2738402919","display_name":"Computation","issn_l":"2079-3197","issn":["2079-3197"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.3390/computation14020037","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5103210486","display_name":"T. Lv","orcid":"https://orcid.org/0000-0002-8356-7349"},"institutions":[{"id":"https://openalex.org/I143413998","display_name":"Qingdao University of Science and Technology","ror":"https://ror.org/041j8js14","country_code":"CN","type":"education","lineage":["https://openalex.org/I143413998"]},{"id":"https://openalex.org/I4210112270","display_name":"Qingdao Academy of Intelligent Industries","ror":"https://ror.org/02a0rnh86","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210112270"]},{"id":"https://openalex.org/I4210164862","display_name":"Artificial Intelligence in Medicine (Canada)","ror":"https://ror.org/05p590m36","country_code":"CA","type":"company","lineage":["https://openalex.org/I4210164862"]}],"countries":["CA","CN"],"is_corresponding":false,"raw_author_name":"Tangying Lv","raw_affiliation_strings":["Qingdao Innovation Center of Artificial Intelligence Ocean Technology, Qingdao 266061, China","School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao 266061, China","Shandong Engineering Research Center for Marine Scenarized Application of Artificial Intelligence Technology, Qingdao 266061, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Qingdao Innovation Center of Artificial Intelligence Ocean Technology, Qingdao 266061, China","institution_ids":["https://openalex.org/I4210112270"]},{"raw_affiliation_string":"School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao 266061, China","institution_ids":["https://openalex.org/I143413998"]},{"raw_affiliation_string":"Shandong Engineering Research Center for Marine Scenarized Application of Artificial Intelligence Technology, Qingdao 266061, China","institution_ids":["https://openalex.org/I4210164862"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088368030","display_name":"Wenming Yin","orcid":null},"institutions":[{"id":"https://openalex.org/I143413998","display_name":"Qingdao University of Science and Technology","ror":"https://ror.org/041j8js14","country_code":"CN","type":"education","lineage":["https://openalex.org/I143413998"]},{"id":"https://openalex.org/I4210112270","display_name":"Qingdao Academy of Intelligent Industries","ror":"https://ror.org/02a0rnh86","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210112270"]},{"id":"https://openalex.org/I4210164862","display_name":"Artificial Intelligence in Medicine (Canada)","ror":"https://ror.org/05p590m36","country_code":"CA","type":"company","lineage":["https://openalex.org/I4210164862"]},{"id":"https://openalex.org/I59028903","display_name":"Ocean University of China","ror":"https://ror.org/04rdtx186","country_code":"CN","type":"education","lineage":["https://openalex.org/I59028903"]},{"id":"https://openalex.org/I80432865","display_name":"Hainan Tropical Ocean University","ror":"https://ror.org/01y5fjx51","country_code":"CN","type":"education","lineage":["https://openalex.org/I80432865"]}],"countries":["CA","CN"],"is_corresponding":true,"raw_author_name":"Wenming Yin","raw_affiliation_strings":["Key Laboratory of Ocean Observation and Information of Hainan Province, Sanya Oceanographic Institution, Ocean University of China, Sanya 572025, China","Qingdao Innovation Center of Artificial Intelligence Ocean Technology, Qingdao 266061, China","School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao 266061, China","Shandong Engineering Research Center for Marine Scenarized Application of Artificial Intelligence Technology, Qingdao 266061, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Key Laboratory of Ocean Observation and Information of Hainan Province, Sanya Oceanographic Institution, Ocean University of China, Sanya 572025, China","institution_ids":["https://openalex.org/I80432865","https://openalex.org/I59028903"]},{"raw_affiliation_string":"Qingdao Innovation Center of Artificial Intelligence Ocean Technology, Qingdao 266061, China","institution_ids":["https://openalex.org/I4210112270"]},{"raw_affiliation_string":"School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao 266061, China","institution_ids":["https://openalex.org/I143413998"]},{"raw_affiliation_string":"Shandong Engineering Research Center for Marine Scenarized Application of Artificial Intelligence Technology, Qingdao 266061, China","institution_ids":["https://openalex.org/I4210164862"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055209182","display_name":"Hengkai Yao","orcid":"https://orcid.org/0009-0002-6277-0775"},"institutions":[{"id":"https://openalex.org/I143413998","display_name":"Qingdao University of Science and Technology","ror":"https://ror.org/041j8js14","country_code":"CN","type":"education","lineage":["https://openalex.org/I143413998"]},{"id":"https://openalex.org/I4210112270","display_name":"Qingdao Academy of Intelligent Industries","ror":"https://ror.org/02a0rnh86","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210112270"]},{"id":"https://openalex.org/I4210164862","display_name":"Artificial Intelligence in Medicine (Canada)","ror":"https://ror.org/05p590m36","country_code":"CA","type":"company","lineage":["https://openalex.org/I4210164862"]}],"countries":["CA","CN"],"is_corresponding":false,"raw_author_name":"Hengkai Yao","raw_affiliation_strings":["Qingdao Innovation Center of Artificial Intelligence Ocean Technology, Qingdao 266061, China","School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao 266061, China","Shandong Engineering Research Center for Marine Scenarized Application of Artificial Intelligence Technology, Qingdao 266061, China"],"raw_orcid":"https://orcid.org/0009-0002-6277-0775","affiliations":[{"raw_affiliation_string":"Qingdao Innovation Center of Artificial Intelligence Ocean Technology, Qingdao 266061, China","institution_ids":["https://openalex.org/I4210112270"]},{"raw_affiliation_string":"School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao 266061, China","institution_ids":["https://openalex.org/I143413998"]},{"raw_affiliation_string":"Shandong Engineering Research Center for Marine Scenarized Application of Artificial Intelligence Technology, Qingdao 266061, China","institution_ids":["https://openalex.org/I4210164862"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5124761732","display_name":"Qingliang Liu","orcid":null},"institutions":[{"id":"https://openalex.org/I143413998","display_name":"Qingdao University of Science and Technology","ror":"https://ror.org/041j8js14","country_code":"CN","type":"education","lineage":["https://openalex.org/I143413998"]},{"id":"https://openalex.org/I4210112270","display_name":"Qingdao Academy of Intelligent Industries","ror":"https://ror.org/02a0rnh86","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210112270"]},{"id":"https://openalex.org/I4210164862","display_name":"Artificial Intelligence in Medicine (Canada)","ror":"https://ror.org/05p590m36","country_code":"CA","type":"company","lineage":["https://openalex.org/I4210164862"]}],"countries":["CA","CN"],"is_corresponding":false,"raw_author_name":"Qingliang Liu","raw_affiliation_strings":["Qingdao Innovation Center of Artificial Intelligence Ocean Technology, Qingdao 266061, China","School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao 266061, China","Shandong Engineering Research Center for Marine Scenarized Application of Artificial Intelligence Technology, Qingdao 266061, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Qingdao Innovation Center of Artificial Intelligence Ocean Technology, Qingdao 266061, China","institution_ids":["https://openalex.org/I4210112270"]},{"raw_affiliation_string":"School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao 266061, China","institution_ids":["https://openalex.org/I143413998"]},{"raw_affiliation_string":"Shandong Engineering Research Center for Marine Scenarized Application of Artificial Intelligence Technology, Qingdao 266061, China","institution_ids":["https://openalex.org/I4210164862"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100629962","display_name":"Yitong Sun","orcid":"https://orcid.org/0009-0006-5294-2093"},"institutions":[{"id":"https://openalex.org/I143413998","display_name":"Qingdao University of Science and Technology","ror":"https://ror.org/041j8js14","country_code":"CN","type":"education","lineage":["https://openalex.org/I143413998"]},{"id":"https://openalex.org/I4210112270","display_name":"Qingdao Academy of Intelligent Industries","ror":"https://ror.org/02a0rnh86","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210112270"]},{"id":"https://openalex.org/I4210164862","display_name":"Artificial Intelligence in Medicine (Canada)","ror":"https://ror.org/05p590m36","country_code":"CA","type":"company","lineage":["https://openalex.org/I4210164862"]}],"countries":["CA","CN"],"is_corresponding":false,"raw_author_name":"Yitong Sun","raw_affiliation_strings":["Qingdao Innovation Center of Artificial Intelligence Ocean Technology, Qingdao 266061, China","School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao 266061, China","Shandong Engineering Research Center for Marine Scenarized Application of Artificial Intelligence Technology, Qingdao 266061, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Qingdao Innovation Center of Artificial Intelligence Ocean Technology, Qingdao 266061, China","institution_ids":["https://openalex.org/I4210112270"]},{"raw_affiliation_string":"School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao 266061, China","institution_ids":["https://openalex.org/I143413998"]},{"raw_affiliation_string":"Shandong Engineering Research Center for Marine Scenarized Application of Artificial Intelligence Technology, Qingdao 266061, China","institution_ids":["https://openalex.org/I4210164862"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110370618","display_name":"Kuan Zhao","orcid":null},"institutions":[{"id":"https://openalex.org/I59028903","display_name":"Ocean University of China","ror":"https://ror.org/04rdtx186","country_code":"CN","type":"education","lineage":["https://openalex.org/I59028903"]},{"id":"https://openalex.org/I80432865","display_name":"Hainan Tropical Ocean University","ror":"https://ror.org/01y5fjx51","country_code":"CN","type":"education","lineage":["https://openalex.org/I80432865"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Kuan Zhao","raw_affiliation_strings":["Key Laboratory of Ocean Observation and Information of Hainan Province, Sanya Oceanographic Institution, Ocean University of China, Sanya 572025, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Key Laboratory of Ocean Observation and Information of Hainan Province, Sanya Oceanographic Institution, Ocean University of China, Sanya 572025, China","institution_ids":["https://openalex.org/I80432865","https://openalex.org/I59028903"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080452156","display_name":"Shanliang Zhu","orcid":null},"institutions":[{"id":"https://openalex.org/I143413998","display_name":"Qingdao University of Science and Technology","ror":"https://ror.org/041j8js14","country_code":"CN","type":"education","lineage":["https://openalex.org/I143413998"]},{"id":"https://openalex.org/I4210112270","display_name":"Qingdao Academy of Intelligent Industries","ror":"https://ror.org/02a0rnh86","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210112270"]},{"id":"https://openalex.org/I4210164862","display_name":"Artificial Intelligence in Medicine (Canada)","ror":"https://ror.org/05p590m36","country_code":"CA","type":"company","lineage":["https://openalex.org/I4210164862"]}],"countries":["CA","CN"],"is_corresponding":false,"raw_author_name":"Shanliang Zhu","raw_affiliation_strings":["Qingdao Innovation Center of Artificial Intelligence Ocean Technology, Qingdao 266061, China","School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao 266061, China","Shandong Engineering Research Center for Marine Scenarized Application of Artificial Intelligence Technology, Qingdao 266061, China"],"raw_orcid":"https://orcid.org/0000-0002-6194-3614","affiliations":[{"raw_affiliation_string":"Qingdao Innovation Center of Artificial Intelligence Ocean Technology, Qingdao 266061, China","institution_ids":["https://openalex.org/I4210112270"]},{"raw_affiliation_string":"School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao 266061, China","institution_ids":["https://openalex.org/I143413998"]},{"raw_affiliation_string":"Shandong Engineering Research Center for Marine Scenarized Application of Artificial Intelligence Technology, Qingdao 266061, China","institution_ids":["https://openalex.org/I4210164862"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5088368030"],"corresponding_institution_ids":["https://openalex.org/I143413998","https://openalex.org/I4210112270","https://openalex.org/I4210164862","https://openalex.org/I59028903","https://openalex.org/I80432865"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.1460298,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"2","first_page":"37","last_page":"37"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9976000189781189,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9976000189781189,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.7027999758720398},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.669700026512146},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.5866000056266785},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5615000128746033},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.4163999855518341},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.3571000099182129},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.33340001106262207},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.32670000195503235}],"concepts":[{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.7027999758720398},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.669700026512146},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.5866000056266785},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5649999976158142},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5615000128746033},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5097000002861023},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.4163999855518341},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3813999891281128},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.3571000099182129},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.3553999960422516},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.33340001106262207},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.32670000195503235},{"id":"https://openalex.org/C118505674","wikidata":"https://www.wikidata.org/wiki/Q42586063","display_name":"Encoder","level":2,"score":0.31610000133514404},{"id":"https://openalex.org/C98856871","wikidata":"https://www.wikidata.org/wiki/Q1588488","display_name":"Radial basis function","level":3,"score":0.30959999561309814},{"id":"https://openalex.org/C136389625","wikidata":"https://www.wikidata.org/wiki/Q334384","display_name":"Supervised learning","level":3,"score":0.2809000015258789},{"id":"https://openalex.org/C155032097","wikidata":"https://www.wikidata.org/wiki/Q798503","display_name":"Backpropagation","level":3,"score":0.2705000042915344},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.2689000070095062},{"id":"https://openalex.org/C116834253","wikidata":"https://www.wikidata.org/wiki/Q2039217","display_name":"Identification (biology)","level":2,"score":0.2685000002384186},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2615000009536743},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.257999986410141},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.2547999918460846},{"id":"https://openalex.org/C89109886","wikidata":"https://www.wikidata.org/wiki/Q1535924","display_name":"Trust region","level":3,"score":0.2508000135421753}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/computation14020037","is_oa":true,"landing_page_url":"https://doi.org/10.3390/computation14020037","pdf_url":null,"source":{"id":"https://openalex.org/S2738402919","display_name":"Computation","issn_l":"2079-3197","issn":["2079-3197"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computation","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:6d00e011481d4e25a719248a0bf5787e","is_oa":false,"landing_page_url":"https://doaj.org/article/6d00e011481d4e25a719248a0bf5787e","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"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":"Computation, Vol 14, Iss 2, p 37 (2026)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/computation14020037","is_oa":true,"landing_page_url":"https://doi.org/10.3390/computation14020037","pdf_url":null,"source":{"id":"https://openalex.org/S2738402919","display_name":"Computation","issn_l":"2079-3197","issn":["2079-3197"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2949797788","display_name":null,"funder_award_id":"42476018","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W2140809812","https://openalex.org/W2899283552","https://openalex.org/W3003922491","https://openalex.org/W3008419421","https://openalex.org/W3014009018","https://openalex.org/W3118861991","https://openalex.org/W3163993681","https://openalex.org/W3168693326","https://openalex.org/W3200673624","https://openalex.org/W3207471124","https://openalex.org/W4205205982","https://openalex.org/W4212954647","https://openalex.org/W4212988227","https://openalex.org/W4220717841","https://openalex.org/W4281672236","https://openalex.org/W4283157728","https://openalex.org/W4288039037","https://openalex.org/W4311051104","https://openalex.org/W4382893306","https://openalex.org/W4385561992","https://openalex.org/W4385855301","https://openalex.org/W4387504329","https://openalex.org/W4389681626","https://openalex.org/W4389727853","https://openalex.org/W4390512032","https://openalex.org/W4391069915","https://openalex.org/W4401640270","https://openalex.org/W4402621273","https://openalex.org/W4403004220","https://openalex.org/W4403069620","https://openalex.org/W4403967442","https://openalex.org/W4405106683","https://openalex.org/W4405123550","https://openalex.org/W4405280781","https://openalex.org/W4407430485","https://openalex.org/W4408489371","https://openalex.org/W4409273904","https://openalex.org/W4410960667"],"related_works":[],"abstract_inverted_index":{"Physics\u2013Informed":[0],"Neural":[1],"Networks":[2],"(PINNs)":[3],"have":[4],"demonstrated":[5],"efficacy":[6],"in":[7,31,49,160],"solving":[8],"both":[9],"forward":[10],"and":[11,41,43,89,109,122,134,163],"inverse":[12],"problems":[13],"for":[14],"nonlinear":[15],"partial":[16],"differential":[17],"equations":[18,136],"(PDEs).":[19],"However,":[20],"they":[21],"frequently":[22],"struggle":[23],"to":[24,82,96,115,147,150],"accurately":[25],"capture":[26],"multiscale":[27],"physical":[28],"features,":[29],"particularly":[30],"regions":[32,121],"exhibiting":[33],"sharp":[34],"local":[35,67,87],"variations":[36,88],"such":[37],"as":[38],"shock":[39],"waves":[40],"discontinuities,":[42],"often":[44],"suffer":[45],"from":[46],"optimization":[47],"difficulties":[48],"complex":[50],"loss":[51,113],"landscapes.":[52],"To":[53],"address":[54],"these":[55],"issues,":[56],"we":[57,102],"propose":[58],"LocRes\u2013PINN,":[59],"a":[60,76,93,104],"physics\u2013informed":[61],"neural":[62],"network":[63],"framework":[64,74],"that":[65,138],"integrates":[66,75],"awareness":[68],"mechanisms":[69],"with":[70],"residual":[71,94],"learning.":[72],"This":[73],"radial":[77],"basis":[78],"function":[79],"(RBF)":[80],"encoder":[81],"enhance":[83],"the":[84,129,157],"perception":[85],"of":[86],"embeds":[90],"it":[91],"within":[92],"backbone":[95],"facilitate":[97],"stable":[98],"gradient":[99],"propagation.":[100],"Furthermore,":[101],"incorporate":[103],"residual\u2013based":[105],"adaptive":[106,111],"refinement":[107],"strategy":[108],"an":[110],"weighted":[112],"scheme":[114],"dynamically":[116],"focus":[117],"training":[118],"on":[119,128],"high\u2013error":[120],"balance":[123],"multi\u2013objective":[124],"constraints.":[125],"Numerical":[126],"experiments":[127],"Extended":[130],"Korteweg\u2013de":[131],"Vries,":[132],"Navier\u2013Stokes,":[133],"Burgers":[135],"demonstrate":[137],"LocRes\u2013PINN":[139],"reduces":[140],"relative":[141],"prediction":[142],"errors":[143],"by":[144],"approximately":[145],"12%":[146],"67%":[148],"compared":[149],"standard":[151],"benchmarks.":[152],"The":[153],"results":[154],"also":[155],"verify":[156],"model\u2019s":[158],"robustness":[159],"parameter":[161],"identification":[162],"noise":[164],"resilience.":[165]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2026-02-03T00:00:00"}