{"id":"https://openalex.org/W4415309817","doi":"https://doi.org/10.1137/25m1777700","title":"RONOM: Reduced-Order Neural Operator Modeling","display_name":"RONOM: Reduced-Order Neural Operator Modeling","publication_year":2026,"publication_date":"2026-06-23","ids":{"openalex":"https://openalex.org/W4415309817","doi":"https://doi.org/10.1137/25m1777700"},"language":"en","primary_location":{"id":"doi:10.1137/25m1777700","is_oa":false,"landing_page_url":"https://doi.org/10.1137/25m1777700","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2507.12814","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038306747","display_name":"Sven Dummer","orcid":"https://orcid.org/0000-0002-5276-4155"},"institutions":[{"id":"https://openalex.org/I94624287","display_name":"University of Twente","ror":"https://ror.org/006hf6230","country_code":"NL","type":"education","lineage":["https://openalex.org/I94624287"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Sven Dummer","raw_affiliation_strings":["Mathematics of Imaging & AI, Department of Applied Mathematics, University of Twente, Enschede, Overijssei 7522 NB, The Netherlands"],"raw_orcid":"https://orcid.org/0000-0002-5276-4155","affiliations":[{"raw_affiliation_string":"Mathematics of Imaging & AI, Department of Applied Mathematics, University of Twente, Enschede, Overijssei 7522 NB, The Netherlands","institution_ids":["https://openalex.org/I94624287"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5120047491","display_name":"Dongwei Ye","orcid":null},"institutions":[{"id":"https://openalex.org/I69356397","display_name":"Xi\u2019an Jiaotong-Liverpool University","ror":"https://ror.org/03zmrmn05","country_code":"CN","type":"education","lineage":["https://openalex.org/I69356397"]},{"id":"https://openalex.org/I94624287","display_name":"University of Twente","ror":"https://ror.org/006hf6230","country_code":"NL","type":"education","lineage":["https://openalex.org/I94624287"]}],"countries":["CN","NL"],"is_corresponding":false,"raw_author_name":"Dongwei Ye","raw_affiliation_strings":["Mathematics of Imaging & AI, Department of Applied Mathematics, University of Twente, Enschede, Overijssei 7522 NB, The Netherlands, and Department of Applied Mathematics, School of Mathematics and Physics, Xi\u2019an Jiaotong-Liverpool University, Suzhou, Jiangsu 215123, People\u2019s Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics of Imaging & AI, Department of Applied Mathematics, University of Twente, Enschede, Overijssei 7522 NB, The Netherlands, and Department of Applied Mathematics, School of Mathematics and Physics, Xi\u2019an Jiaotong-Liverpool University, Suzhou, Jiangsu 215123, People\u2019s Republic of China","institution_ids":["https://openalex.org/I69356397","https://openalex.org/I94624287"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078725649","display_name":"Christoph Br\u00fcne","orcid":"https://orcid.org/0000-0003-0145-5069"},"institutions":[{"id":"https://openalex.org/I94624287","display_name":"University of Twente","ror":"https://ror.org/006hf6230","country_code":"NL","type":"education","lineage":["https://openalex.org/I94624287"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Christoph Brune","raw_affiliation_strings":["Mathematics of Imaging & AI, Department of Applied Mathematics, University of Twente, Enschede, Overijssei 7522 NB, The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics of Imaging & AI, Department of Applied Mathematics, University of Twente, Enschede, Overijssei 7522 NB, The Netherlands","institution_ids":["https://openalex.org/I94624287"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.01428187,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"48","issue":"3","first_page":"C604","last_page":"C634"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.22360000014305115,"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"}},"topics":[{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.22360000014305115,"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/discretization","display_name":"Discretization","score":0.8400999903678894},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5697000026702881},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.555400013923645},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4699999988079071},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.45329999923706055},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.44029998779296875},{"id":"https://openalex.org/keywords/discretization-error","display_name":"Discretization error","score":0.3840000033378601}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.8400999903678894},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5884000062942505},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5697000026702881},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.555400013923645},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4699999988079071},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.45329999923706055},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.44029998779296875},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.39149999618530273},{"id":"https://openalex.org/C126148662","wikidata":"https://www.wikidata.org/wiki/Q3890355","display_name":"Discretization error","level":3,"score":0.3840000033378601},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.37709999084472656},{"id":"https://openalex.org/C70915906","wikidata":"https://www.wikidata.org/wiki/Q1058681","display_name":"Differential operator","level":2,"score":0.37040001153945923},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3650999963283539},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.35839998722076416},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3357999920845032},{"id":"https://openalex.org/C105427703","wikidata":"https://www.wikidata.org/wiki/Q665193","display_name":"Discretization of continuous features","level":4,"score":0.33559998869895935},{"id":"https://openalex.org/C2780598303","wikidata":"https://www.wikidata.org/wiki/Q65921492","display_name":"Flexibility (engineering)","level":2,"score":0.3352000117301941},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.32199999690055847},{"id":"https://openalex.org/C91873725","wikidata":"https://www.wikidata.org/wiki/Q3445816","display_name":"Function approximation","level":3,"score":0.31150001287460327},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.2797999978065491},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.25839999318122864},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.25049999356269836}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/25m1777700","is_oa":false,"landing_page_url":"https://doi.org/10.1137/25m1777700","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2507.12814","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2507.12814","pdf_url":"https://arxiv.org/pdf/2507.12814","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":null,"raw_type":"text"},{"id":"pmh:oai:ris.utwente.nl:openaire/deefec15-33aa-47d7-9e55-348291ae42c2","is_oa":false,"landing_page_url":"https://research.utwente.nl/en/publications/deefec15-33aa-47d7-9e55-348291ae42c2","pdf_url":null,"source":{"id":"https://openalex.org/S4406922991","display_name":"University of Twente Research Information","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":"Dummer, S, Ye, D & Brune, C 2025 'RONOM : Reduced-Order Neural Operator Modeling' ArXiv.org. https://doi.org/10.48550/arXiv.2507.12814","raw_type":"info:eu-repo/semantics/preprint"},{"id":"doi:10.48550/arxiv.2507.12814","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2507.12814","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":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2507.12814","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2507.12814","pdf_url":"https://arxiv.org/pdf/2507.12814","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":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320335322","display_name":"European Regional Development Fund","ror":"https://ror.org/00k4n6c32"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Time-dependent":[0],"partial":[1,158],"differential":[2,159],"equations":[3],"are":[4,147],"ubiquitous":[5],"in":[6,14,131,175,182],"physics-based":[7],"modeling,":[8],"but":[9,38],"they":[10],"remain":[11],"computationally":[12],"intensive":[13],"many-query":[15],"scenarios,":[16],"such":[17,55],"as":[18,56],"real-time":[19],"forecasting,":[20],"optimal":[21],"control,":[22],"and":[23,91,100,119,133,140,178,186,198],"uncertainty":[24],"quantification.":[25],"Reduced-order":[26],"modeling":[27,111],"(ROM)":[28],"addresses":[29],"these":[30],"challenges":[31],"by":[32,62],"constructing":[33],"a":[34,41,124],"low-dimensional":[35],"surrogate":[36],"model":[37],"relies":[39],"on":[40,88,203],"fixed":[42],"discretization,":[43],"which":[44,114],"limits":[45],"flexibility":[46],"across":[47,73],"varying":[48],"meshes":[49],"during":[50],"evaluation.":[51],"Operator":[52],"learning":[53,85,202],"approaches,":[54],"neural":[57,83,109,154,169],"operators,":[58],"offer":[59],"an":[60],"alternative":[61],"parameterizing":[63],"mappings":[64],"between":[65,97],"infinite-dimensional":[66,99],"function":[67],"spaces,":[68],"enabling":[69],"adaptation":[70],"to":[71,129,152],"data":[72],"different":[74],"resolutions.":[75],"Whereas":[76],"ROM":[77,118],"provides":[78],"rigorous":[79],"numerical":[80,145],"error":[81,96,126],"estimates,":[82],"operator":[84,110,120],"largely":[86],"focuses":[87],"discretization":[89,125,138,141,187],"convergence":[90,139],"invariance":[92],"without":[93],"quantifying":[94],"the":[95,98,101,107],"discretized":[102],"operators.":[103],"This":[104],"work":[105],"introduces":[106],"reduced-order":[108],"(RONOM)":[112],"framework,":[113],"bridges":[115],"concepts":[116],"from":[117],"learning.":[121],"We":[122],"establish":[123],"bound":[127],"analogous":[128],"those":[130],"ROM,":[132],"get":[134],"insights":[135,193],"into":[136,194],"RONOM's":[137],"robustness.":[142],"Moreover,":[143],"three":[144],"examples":[146],"presented":[148],"that":[149,164],"compare":[150],"RONOM":[151,165],"existing":[153],"operators":[155],"for":[156,201],"solving":[157],"equations.":[160],"The":[161],"results":[162],"demonstrate":[163],"using":[166],"standard":[167],"vector-to-vector":[168],"networks":[170],"can":[171],"achieve":[172],"comparable":[173],"performance":[174,181],"input":[176],"generalization":[177],"achieves":[179],"superior":[180],"both":[183],"spatial":[184],"super-resolution":[185,196],"robustness,":[188],"while":[189],"also":[190],"offering":[191],"novel":[192],"temporal":[195],"scenarios":[197],"ROM-based":[199],"approaches":[200],"time-dependent":[204],"data.":[205]},"counts_by_year":[],"updated_date":"2026-06-25T06:16:34.145877","created_date":"2025-10-18T00:00:00"}