{"id":"https://openalex.org/W7225644228","doi":"https://doi.org/10.21203/rs.3.rs-11292477/v1","title":"Adaptive Neural Subspaces with Geometry-Aware Quadrature for Interface Problems","display_name":"Adaptive Neural Subspaces with Geometry-Aware Quadrature for Interface Problems","publication_year":2026,"publication_date":"2026-11-10","ids":{"openalex":"https://openalex.org/W7225644228","doi":"https://doi.org/10.21203/rs.3.rs-11292477/v1"},"language":"en","primary_location":{"id":"doi:10.21203/rs.3.rs-11292477/v1","doi":"https://doi.org/10.21203/rs.3.rs-11292477/v1","is_oa":true,"landing_page_url":"https://doi.org/10.21203/rs.3.rs-11292477/v1","pdf_url":"https://www.researchsquare.com/article/rs-11292477/latest.pdf","source":{"id":"https://openalex.org/S4306525896","display_name":"Research Square","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Research Square","raw_type":"posted-content"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://www.researchsquare.com/article/rs-11292477/latest.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5161340935","display_name":"Feiyi Liao","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Feiyi Liao","raw_affiliation_strings":["Academy of Mathematics and Systems Science,  Chinese Academy of Sciences"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Academy of Mathematics and Systems Science,  Chinese Academy of Sciences","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5125976807","display_name":"Zhongshuo Lin","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhongshuo Lin","raw_affiliation_strings":["Peking University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Peking University","institution_ids":["https://openalex.org/I20231570"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101880991","display_name":"Haochen Liu","orcid":"https://orcid.org/0000-0002-1801-4879","observed_orcids":["https://orcid.org/0000-0002-1801-4879","https://orcid.org/0009-0000-0389-4984","https://orcid.org/0009-0001-1079-2940"]},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Haochen Liu","raw_affiliation_strings":["Academy of Mathematics and Systems Science,  Chinese Academy of Sciences"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Academy of Mathematics and Systems Science,  Chinese Academy of Sciences","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5121305745","display_name":"Yifan Wang","orcid":"https://orcid.org/0009-0005-8862-6925","observed_orcids":["https://orcid.org/0009-0005-8862-6925"]},"institutions":[{"id":"https://openalex.org/I137867983","display_name":"Central University of Finance and Economics","ror":"https://ror.org/008e3hf02","country_code":"CN","type":"education","lineage":["https://openalex.org/I137867983"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yifan Wang","raw_affiliation_strings":["Central University of Finance and Economics"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Central University of Finance and Economics","institution_ids":["https://openalex.org/I137867983"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5150018090","display_name":"Hehu Xie","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hehu Xie","raw_affiliation_strings":["Academy of Mathematics and Systems Science,  Chinese Academy of Sciences"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Academy of Mathematics and Systems Science,  Chinese Academy of Sciences","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5025832907","display_name":"M. Zhang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Mingzhu Zhang","raw_affiliation_strings":["Academy of Mathematics and Systems Science,  Chinese Academy of Sciences"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Academy of Mathematics and Systems Science,  Chinese Academy of Sciences","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9106000065803528,"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":0.9106000065803528,"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/T10320","display_name":"Neural Networks and Applications","score":0.04390000179409981,"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"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.033399999141693115,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/interface-problems","display_name":"interface problems","score":0.890999972820282},{"id":"https://openalex.org/keywords/a-posteriori-error-estimates","display_name":"a posteriori error estimation","score":0.8360000252723694},{"id":"https://openalex.org/keywords/loss-function-design","display_name":"loss function design","score":0.7369999885559082},{"id":"https://openalex.org/keywords/singularities","display_name":"singularities","score":0.6930000185966492},{"id":"https://openalex.org/keywords/high-precision-numerical-integration","display_name":"high-precision numerical integration","score":0.7260000109672546}],"concepts":[{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.7210000157356262},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.7006999850273132},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6940000057220459},{"id":"https://openalex.org/C127349201","wikidata":"https://www.wikidata.org/wiki/Q753445","display_name":"Numerical integration","level":2,"score":0.6481999754905701},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.6254000067710876},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.5311999917030334},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5131000280380249},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4993000030517578},{"id":"https://openalex.org/C113843644","wikidata":"https://www.wikidata.org/wiki/Q901882","display_name":"Interface (matter)","level":4,"score":0.4722999930381775},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.45320001244544983},{"id":"https://openalex.org/C98856871","wikidata":"https://www.wikidata.org/wiki/Q1588488","display_name":"Radial basis function","level":3,"score":0.4512999951839447},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.44909998774528503},{"id":"https://openalex.org/C167196314","wikidata":"https://www.wikidata.org/wiki/Q767680","display_name":"Gaussian quadrature","level":4,"score":0.37470000982284546},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.3700000047683716},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.33469998836517334},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.33000001311302185},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.3116999864578247},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.30140000581741333},{"id":"https://openalex.org/C91873725","wikidata":"https://www.wikidata.org/wiki/Q3445816","display_name":"Function approximation","level":3,"score":0.2793000042438507},{"id":"https://openalex.org/C2776003309","wikidata":"https://www.wikidata.org/wiki/Q1988072","display_name":"Adaptive algorithm","level":2,"score":0.26910001039505005},{"id":"https://openalex.org/C102248274","wikidata":"https://www.wikidata.org/wiki/Q168388","display_name":"Adaptive filter","level":2,"score":0.2614000141620636},{"id":"https://openalex.org/C500300565","wikidata":"https://www.wikidata.org/wiki/Q925667","display_name":"Computer simulation","level":2,"score":0.2542000114917755},{"id":"https://openalex.org/C184599523","wikidata":"https://www.wikidata.org/wiki/Q4680758","display_name":"Adaptive quadrature","level":4,"score":0.25209999084472656}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.21203/rs.3.rs-11292477/v1","doi":"https://doi.org/10.21203/rs.3.rs-11292477/v1","is_oa":true,"landing_page_url":"https://doi.org/10.21203/rs.3.rs-11292477/v1","pdf_url":"https://www.researchsquare.com/article/rs-11292477/latest.pdf","source":{"id":"https://openalex.org/S4306525896","display_name":"Research Square","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Research Square","raw_type":"posted-content"}],"best_oa_location":{"id":"doi:10.21203/rs.3.rs-11292477/v1","doi":"https://doi.org/10.21203/rs.3.rs-11292477/v1","is_oa":true,"landing_page_url":"https://doi.org/10.21203/rs.3.rs-11292477/v1","pdf_url":"https://www.researchsquare.com/article/rs-11292477/latest.pdf","source":{"id":"https://openalex.org/S4306525896","display_name":"Research Square","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Research Square","raw_type":"posted-content"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321133","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7225644228.pdf","grobid_xml":"https://content.openalex.org/works/W7225644228.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W2772097715","https://openalex.org/W2964121744","https://openalex.org/W3022977644","https://openalex.org/W4295854546","https://openalex.org/W4297433807","https://openalex.org/W4365453697","https://openalex.org/W4377864577","https://openalex.org/W4389301323","https://openalex.org/W4396690897","https://openalex.org/W4403977411","https://openalex.org/W4406658697","https://openalex.org/W4407492516","https://openalex.org/W4411462597","https://openalex.org/W4412449870","https://openalex.org/W4414674947","https://openalex.org/W4415981289"],"related_works":["https://openalex.org/W4295854546","https://openalex.org/W4405056673","https://openalex.org/W3022977644","https://openalex.org/W7214239776","https://openalex.org/W7221769779","https://openalex.org/W4404504277","https://openalex.org/W4412449870","https://openalex.org/W7136075159","https://openalex.org/W4372353293","https://openalex.org/W4412450059"],"abstract_inverted_index":{"Abstract":[0],"Based":[1],"on":[2],"the":[3,33,42,61,76,82,91,119],"combination":[4],"of":[5,36,107],"neural":[6,27,83],"networks,":[7],"numerical":[8,135],"quadrature":[9],"schemes":[10],"and":[11],"adaptive":[12],"subspace":[13,48,66],"approximation,":[14],"we":[15],"propose":[16],"a":[17,37,53,132],"new":[18],"machine":[19,97],"learning":[20,98],"method":[21,93,121],"for":[22,125,138],"solving":[23],"interface":[24,113,126],"problems.":[25,114],"The":[26,86],"network":[28,84],"is":[29,45],"employed":[30],"to":[31,79],"construct":[32],"basis":[34],"functions":[35],"finite-dimensional":[38],"subspace,":[39],"upon":[40],"which":[41],"discrete":[43],"solution":[44],"obtained":[46],"via":[47],"approximation.":[49],"In":[50],"particular,":[51],"an":[52],"posteriori":[54],"error":[55],"estimator":[56,70],"can":[57,71],"be":[58,73],"derived":[59],"from":[60],"hypercircle":[62],"technique":[63],"within":[64],"this":[65],"approximation":[67],"framework.":[68],"This":[69],"further":[72],"used":[74],"as":[75],"loss":[77,140],"function":[78],"adaptively":[80],"refine":[81],"parameters.":[85],"high":[87,102,123,133],"accuracy":[88,124],"achieved":[89],"by":[90],"proposed":[92,120],"also":[94],"demonstrates":[95],"that":[96,118],"approaches":[99],"equipped":[100,130],"with":[101,131],"precision":[103,134],"integration":[104,136],"are":[105],"capable":[106],"automatically":[108],"handling":[109],"singularities":[110],"arising":[111],"in":[112],"Numerical":[115],"results":[116],"illustrate":[117],"attains":[122],"problem":[127],"simulations":[128],"when":[129],"scheme":[137],"designing":[139],"functions.":[141]},"counts_by_year":[],"updated_date":"2026-11-11T12:16:26.678958","created_date":"2026-11-10T00:00:00"}
