{"id":"https://openalex.org/W7151580766","doi":"https://doi.org/10.48550/arxiv.2604.04061","title":"A Geometry-Aware Operator Learning Framework for Interface Problems on Varying Domains","display_name":"A Geometry-Aware Operator Learning Framework for Interface Problems on Varying Domains","publication_year":2026,"publication_date":"2026-04-05","ids":{"openalex":"https://openalex.org/W7151580766","doi":"https://doi.org/10.48550/arxiv.2604.04061"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.04061","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.04061","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":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2604.04061","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100565655","display_name":"Shanshan Xiao","orcid":"https://orcid.org/0009-0006-4738-6432"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Xiao, Shanshan","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5133082185","display_name":"Ye Li","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Ye","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5133071314","display_name":"Zhongyi Huang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Huang, Zhongyi","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5133077012","display_name":"Hao Wu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wu, Hao","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5100565655"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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":0.6848000288009644,"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":0.6848000288009644,"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/T11115","display_name":"Topology Optimization in Engineering","score":0.07180000096559525,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"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":0.06589999794960022,"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","display_name":"Interface (matter)","score":0.6751999855041504},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.6072999835014343},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.47110000252723694},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.4691999852657318},{"id":"https://openalex.org/keywords/task","display_name":"Task (project management)","score":0.4625999927520752},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.4187000095844269},{"id":"https://openalex.org/keywords/bridge","display_name":"Bridge (graph theory)","score":0.40450000762939453},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.3813999891281128},{"id":"https://openalex.org/keywords/base","display_name":"Base (topology)","score":0.3440999984741211}],"concepts":[{"id":"https://openalex.org/C113843644","wikidata":"https://www.wikidata.org/wiki/Q901882","display_name":"Interface (matter)","level":4,"score":0.6751999855041504},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.6072999835014343},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5202999711036682},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.47110000252723694},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4691999852657318},{"id":"https://openalex.org/C2780451532","wikidata":"https://www.wikidata.org/wiki/Q759676","display_name":"Task (project management)","level":2,"score":0.4625999927520752},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.4187000095844269},{"id":"https://openalex.org/C100776233","wikidata":"https://www.wikidata.org/wiki/Q2532492","display_name":"Bridge (graph theory)","level":2,"score":0.40450000762939453},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.39309999346733093},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.3813999891281128},{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.3440999984741211},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3312999904155731},{"id":"https://openalex.org/C27592594","wikidata":"https://www.wikidata.org/wiki/Q865821","display_name":"Helmholtz free energy","level":2,"score":0.31769999861717224},{"id":"https://openalex.org/C18591234","wikidata":"https://www.wikidata.org/wiki/Q860615","display_name":"Helmholtz equation","level":3,"score":0.31459999084472656},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3028999865055084},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.29739999771118164},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.28859999775886536},{"id":"https://openalex.org/C28006648","wikidata":"https://www.wikidata.org/wiki/Q6934509","display_name":"Multi-task learning","level":3,"score":0.2874999940395355},{"id":"https://openalex.org/C126042441","wikidata":"https://www.wikidata.org/wiki/Q1324888","display_name":"Frame (networking)","level":2,"score":0.28630000352859497},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.28369998931884766},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.2831000089645386},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.28110000491142273},{"id":"https://openalex.org/C70915906","wikidata":"https://www.wikidata.org/wiki/Q1058681","display_name":"Differential operator","level":2,"score":0.2759999930858612},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.2741999924182892},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.2630999982357025},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.2630999982357025},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.26010000705718994},{"id":"https://openalex.org/C175154964","wikidata":"https://www.wikidata.org/wiki/Q380077","display_name":"Task analysis","level":3,"score":0.2596000134944916},{"id":"https://openalex.org/C49766605","wikidata":"https://www.wikidata.org/wiki/Q207643","display_name":"Linear map","level":2,"score":0.2563000023365021}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.04061","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.04061","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":"doi:10.48550/arxiv.2604.04061","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.04061","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":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[{"score":0.5257270932197571,"id":"https://metadata.un.org/sdg/9","display_name":"Industry, innovation and infrastructure"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Solving":[0],"Partial":[1],"Differential":[2],"Equation":[3],"(PDE)":[4],"interface":[5,39,60],"problems":[6,40],"on":[7,32],"varying":[8],"domains":[9],"is":[10,68],"a":[11,135],"critical":[12],"task":[13],"in":[14],"design":[15],"and":[16,86,110,129],"optimization,":[17],"yet":[18],"it":[19],"remains":[20],"computationally":[21],"prohibitive":[22],"for":[23,37,115,139,145],"traditional":[24],"solvers.":[25],"Although":[26],"operator":[27,54,104],"learning":[28],"has":[29,41],"shown":[30],"promise":[31],"fixed":[33],"geometries,":[34],"its":[35],"potential":[36],"geometry-dependent":[38],"been":[42],"largely":[43],"unexplored.":[44],"To":[45],"bridge":[46],"this":[47,132],"gap,":[48],"we":[49,97],"propose":[50],"an":[51],"extension-based":[52],"neural":[53],"framework":[55,125],"applicable":[56],"to":[57,107],"general":[58],"linear":[59],"problems.":[61],"A":[62],"key":[63],"innovation":[64],"of":[65,71,91,101],"our":[66,79,124],"method":[67],"the":[69,72,89,94,99,102,116],"integration":[70],"Tailored":[73],"Finite":[74],"Point":[75],"Method":[76],"(TFPM)":[77],"with":[78,105],"base":[80],"network,":[81],"which":[82],"reduces":[83],"memory":[84],"consumption":[85],"effectively":[87],"alleviates":[88],"curse":[90],"dimensionality.":[92],"On":[93],"theoretical":[95],"front,":[96],"establish":[98],"continuity":[100],"Helmholtz":[103],"respect":[106],"domain":[108],"perturbations":[109],"provide":[111],"rigorous":[112],"error":[113],"estimates":[114],"proposed":[117],"encodings.":[118],"Comprehensive":[119],"numerical":[120],"experiments":[121],"demonstrate":[122],"that":[123],"achieves":[126],"state-of-the-art":[127],"accuracy":[128],"robustness.":[130],"Consequently,":[131],"work":[133],"provides":[134],"powerful,":[136],"data-efficient":[137],"tool":[138],"varying-domain":[140],"simulations,":[141],"offering":[142],"new":[143],"possibilities":[144],"real-time":[146],"shape":[147],"optimization.":[148]},"counts_by_year":[],"updated_date":"2026-04-08T06:07:18.267832","created_date":"2026-04-08T00:00:00"}