{"id":"https://openalex.org/W7213520004","doi":"https://doi.org/10.48550/arxiv.2609.17841","title":"Hybrid coupling with numerics-informed neural networks and the overlapping Schwarz alternating method","display_name":"Hybrid coupling with numerics-informed neural networks and the overlapping Schwarz alternating method","publication_year":2026,"publication_date":"2026-09-15","ids":{"openalex":"https://openalex.org/W7213520004","doi":"https://doi.org/10.48550/arxiv.2609.17841"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.17841","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.17841","pdf_url":"https://arxiv.org/pdf/2609.17841","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.17841","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5151994578","display_name":"George Chumbipuma","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I74775410","display_name":"Rice University","ror":"https://ror.org/008zs3103","country_code":"US","type":"education","lineage":["https://openalex.org/I74775410"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Chumbipuma, George","raw_affiliation_strings":["Rice University ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Rice University ,","institution_ids":["https://openalex.org/I74775410"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049294766","display_name":"Irina Tezaur","orcid":"https://orcid.org/0000-0002-0918-5553","observed_orcids":["https://orcid.org/0000-0002-0918-5553"]},"institutions":[{"id":"https://openalex.org/I4210104735","display_name":"Sandia National Laboratories","ror":"https://ror.org/01apwpt12","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I198811213","https://openalex.org/I4210104735"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Tezaur, Irina","raw_affiliation_strings":["Sandia National Laboratories ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Sandia National Laboratories ,","institution_ids":["https://openalex.org/I4210104735"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5125968313","display_name":"Alejandro Diaz","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210104735","display_name":"Sandia National Laboratories","ror":"https://ror.org/01apwpt12","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I198811213","https://openalex.org/I4210104735"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Diaz, Alejandro","raw_affiliation_strings":["Sandia National Laboratories ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Sandia National Laboratories ,","institution_ids":["https://openalex.org/I4210104735"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5046673531","display_name":"Beatrice M. Rivi\u00e8re","orcid":"https://orcid.org/0000-0003-4230-2528","observed_orcids":["https://orcid.org/0000-0003-4230-2528"]},"institutions":[{"id":"https://openalex.org/I74775410","display_name":"Rice University","ror":"https://ror.org/008zs3103","country_code":"US","type":"education","lineage":["https://openalex.org/I74775410"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Riviere, Beatrice","raw_affiliation_strings":["Rice University ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Rice University ,","institution_ids":["https://openalex.org/I74775410"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"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":1.0,"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":1.0,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":9.999999747378752e-05,"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"}},{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.0,"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/physics-informed-neural-networks","display_name":"physics-informed neural networks","score":0.8389999866485596},{"id":"https://openalex.org/keywords/overlapping-schwarz-methods","display_name":"overlapping Schwarz methods","score":0.7630000114440918},{"id":"https://openalex.org/keywords/domain-decomposition","display_name":"domain decomposition","score":0.8080000281333923},{"id":"https://openalex.org/keywords/hybrid-modeling","display_name":"hybrid modeling","score":0.5690000057220459},{"id":"https://openalex.org/keywords/full-order-model","display_name":"full-order model","score":0.8299999833106995},{"id":"https://openalex.org/keywords/convection-diffusion-equation","display_name":"advection-diffusion equation","score":0.9679999947547913},{"id":"https://openalex.org/keywords/peclet-number","display_name":"Peclet number","score":0.8130000233650208}],"concepts":[{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.713699996471405},{"id":"https://openalex.org/C31278502","wikidata":"https://www.wikidata.org/wiki/Q7433186","display_name":"Schwarz alternating method","level":4,"score":0.6953999996185303},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6851999759674072},{"id":"https://openalex.org/C174819683","wikidata":"https://www.wikidata.org/wiki/Q4681340","display_name":"Additive Schwarz method","level":4,"score":0.6704000234603882},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5467000007629395},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5242000222206116},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4867999851703644},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.486299991607666},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.45719999074935913},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.3822999894618988},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3571999967098236},{"id":"https://openalex.org/C103824480","wikidata":"https://www.wikidata.org/wiki/Q185889","display_name":"Time domain","level":2,"score":0.33739998936653137},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3353999853134155},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.30880001187324524},{"id":"https://openalex.org/C12713177","wikidata":"https://www.wikidata.org/wiki/Q1900281","display_name":"Perspective (graphical)","level":2,"score":0.3061000108718872},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.28209999203681946},{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.2809999883174896},{"id":"https://openalex.org/C50897621","wikidata":"https://www.wikidata.org/wiki/Q2665508","display_name":"Hybrid system","level":2,"score":0.27649998664855957},{"id":"https://openalex.org/C126780896","wikidata":"https://www.wikidata.org/wiki/Q899871","display_name":"Distortion (music)","level":4,"score":0.274399995803833},{"id":"https://openalex.org/C172100665","wikidata":"https://www.wikidata.org/wiki/Q7465774","display_name":"Thermal conduction","level":2,"score":0.2721000015735626},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.2703999876976013},{"id":"https://openalex.org/C2987642246","wikidata":"https://www.wikidata.org/wiki/Q5452196","display_name":"First order","level":2,"score":0.26030001044273376},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.25459998846054077}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.17841","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.17841","pdf_url":"https://arxiv.org/pdf/2609.17841","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.17841","doi":"https://doi.org/10.48550/arxiv.2609.17841","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.17841","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.17841","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.17841","pdf_url":"https://arxiv.org/pdf/2609.17841","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G11630931","display_name":null,"funder_award_id":"DENA0003525","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G1166951225","display_name":null,"funder_award_id":"DE-NA-0003525","funder_id":"https://openalex.org/F4320337506","funder_display_name":"Advanced Scientific Computing Research"},{"id":"https://openalex.org/G1859920734","display_name":null,"funder_award_id":"NA0003525","funder_id":"https://openalex.org/F4320337547","funder_display_name":"Laboratory Directed Research and Development"},{"id":"https://openalex.org/G2214935549","display_name":null,"funder_award_id":"NA0003525","funder_id":"https://openalex.org/F4320338291","funder_display_name":"Sandia National Laboratories"},{"id":"https://openalex.org/G2234472222","display_name":null,"funder_award_id":"22-025291","funder_id":"https://openalex.org/F4320337506","funder_display_name":"Advanced Scientific Computing Research"},{"id":"https://openalex.org/G2270046793","display_name":null,"funder_award_id":"NA0003525","funder_id":"https://openalex.org/F4320337506","funder_display_name":"Advanced Scientific Computing Research"},{"id":"https://openalex.org/G280414146","display_name":null,"funder_award_id":"DE-NA0003525","funder_id":"https://openalex.org/F4320332359","funder_display_name":"Office of Science"},{"id":"https://openalex.org/G363632689","display_name":null,"funder_award_id":"22\u2010025291","funder_id":"https://openalex.org/F4320332359","funder_display_name":"Office of Science"},{"id":"https://openalex.org/G413247060","display_name":null,"funder_award_id":"DE\u2010NA,0003525","funder_id":"https://openalex.org/F4320338291","funder_display_name":"Sandia National Laboratories"},{"id":"https://openalex.org/G4903105778","display_name":null,"funder_award_id":"NA0003525","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G5339743583","display_name":null,"funder_award_id":"NA0003525","funder_id":"https://openalex.org/F4320332369","funder_display_name":"National Nuclear Security Administration"},{"id":"https://openalex.org/G70797072","display_name":null,"funder_award_id":"DE-NA0003525","funder_id":"https://openalex.org/F4320337547","funder_display_name":"Laboratory Directed Research and Development"},{"id":"https://openalex.org/G855168022","display_name":null,"funder_award_id":"DENA-0003525","funder_id":"https://openalex.org/F4320332369","funder_display_name":"National Nuclear Security Administration"},{"id":"https://openalex.org/G8922552302","display_name":null,"funder_award_id":"NA0003525","funder_id":"https://openalex.org/F4320332359","funder_display_name":"Office of Science"}],"funders":[{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320332359","display_name":"Office of Science","ror":"https://ror.org/00mmn6b08"},{"id":"https://openalex.org/F4320332369","display_name":"National Nuclear Security Administration","ror":"https://ror.org/03sk1we31"},{"id":"https://openalex.org/F4320337506","display_name":"Advanced Scientific Computing Research","ror":"https://ror.org/0012c7r22"},{"id":"https://openalex.org/F4320337547","display_name":"Laboratory Directed Research and Development","ror":"https://ror.org/01e41cf67"},{"id":"https://openalex.org/F4320338291","display_name":"Sandia National Laboratories","ror":"https://ror.org/01apwpt12"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213520004.pdf","grobid_xml":"https://content.openalex.org/works/W7213520004.grobid-xml"},"referenced_works_count":4,"referenced_works":["https://openalex.org/W4310280894","https://openalex.org/W4388275294","https://openalex.org/W4407571348","https://openalex.org/W4416777428"],"related_works":["https://openalex.org/W4388275294","https://openalex.org/W7116331365","https://openalex.org/W7213499593","https://openalex.org/W7212177894","https://openalex.org/W4413734447","https://openalex.org/W7204994149","https://openalex.org/W4306742185","https://openalex.org/W4385261611","https://openalex.org/W4400027595","https://openalex.org/W3209422647"],"abstract_inverted_index":{"We":[0,25,37,62,92],"develop":[1],"a":[2,48,69,74,79,101,111,120,128],"hybrid":[3,149],"modeling":[4],"framework":[5],"for":[6,72,97],"coupling":[7,73],"pre-trained":[8],"numerics-informed":[9],"neural":[10,45],"networks":[11],"(NINNs)":[12],"with":[13,78,82,119,154,160],"classical":[14],"full":[15,117],"order":[16],"models":[17],"(FOMs)":[18],"using":[19],"the":[20,27,32,42,83,89,98,116,139,155,161],"overlapping":[21,65],"Schwarz":[22,67,90,113,158],"alternating":[23],"method.":[24],"consider":[26,93],"two-dimensional":[28],"advection-diffusion":[29],"equation":[30],"in":[31,104,131],"advection-dominated,":[33],"Peclet-number":[34],"10^6":[35],"regime.":[36],"first":[38],"demonstrate":[39],"that,":[40],"unlike":[41],"corresponding":[43,156],"physics-informed":[44],"network":[46],"(PINN),":[47],"monolithic":[49],"NINN":[50,77,84,140],"can":[51],"be":[52],"accurately":[53],"trained":[54],"on":[55,115,122,138],"our":[56],"model":[57],"problem":[58],"without":[59,142],"domain":[60,118],"decomposition.":[61],"then":[63],"employ":[64],"multiplicative":[66],"as":[68],"deployment":[70],"mechanism":[71],"pre-trained,":[75],"subdomain-local":[76,99],"neighboring":[80],"FOM,":[81],"weights":[85],"held":[86],"fixed":[87],"throughout":[88],"iteration.":[91],"two":[94],"training":[95,165],"approaches":[96,166],"NINNs:":[100],"top-down":[102,162],"approach,":[103,130],"which":[105,132],"boundary":[106,133],"data":[107],"are":[108,135],"obtained":[109],"from":[110],"coupled":[112],"solve":[114],"FOM":[121],"each":[123],"subdomain":[124,141],"(FOM-FOM":[125],"Schwarz),":[126],"and":[127,163],"bottom-up":[129,164],"traces":[134],"generated":[136],"synthetically":[137],"requiring":[143],"any":[144],"full-domain":[145],"solves.":[146],"The":[147],"resulting":[148],"NINN-FOM":[150],"solutions":[151],"agree":[152],"closely":[153],"FOM-FOM":[157],"solutions,":[159],"yielding":[167],"comparable":[168],"accuracy.":[169]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-18T00:00:00"}
