{"id":"https://openalex.org/W7162396824","doi":"https://doi.org/10.48550/arxiv.2605.24041","title":"Iterative Refinement Neural Operators are Learned Fixed-Point Solvers: A Principled Approach to Spectral Bias Mitigation","display_name":"Iterative Refinement Neural Operators are Learned Fixed-Point Solvers: A Principled Approach to Spectral Bias Mitigation","publication_year":2026,"publication_date":"2026-05-21","ids":{"openalex":"https://openalex.org/W7162396824","doi":"https://doi.org/10.48550/arxiv.2605.24041"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.24041","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.24041","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":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.24041","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5137004737","display_name":"Xiaotian Liu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Liu, Xiaotian","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027722754","display_name":"Shuyuan Shang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shang, Shuyuan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5137030633","display_name":"Xiaopeng Wang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, Xiaopeng","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5137064597","display_name":"Pu Ren","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ren, Pu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5137062248","display_name":"Yaoqing Yang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yang, Yaoqing","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"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":0.968999981880188,"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":0.968999981880188,"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/T11948","display_name":"Machine Learning in Materials Science","score":0.007499999832361937,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12611","display_name":"Neural Networks and Reservoir Computing","score":0.005100000184029341,"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/initialization","display_name":"Initialization","score":0.7825999855995178},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.618399977684021},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5548999905586243},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.477400004863739},{"id":"https://openalex.org/keywords/inference","display_name":"Inference","score":0.4740000069141388},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.45840001106262207},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.451200008392334},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.44600000977516174}],"concepts":[{"id":"https://openalex.org/C114466953","wikidata":"https://www.wikidata.org/wiki/Q6034165","display_name":"Initialization","level":2,"score":0.7825999855995178},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.618399977684021},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6150000095367432},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5802000164985657},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5548999905586243},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.477400004863739},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.4740000069141388},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.45840001106262207},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.451200008392334},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.44600000977516174},{"id":"https://openalex.org/C163415756","wikidata":"https://www.wikidata.org/wiki/Q126473","display_name":"Contraction (grammar)","level":2,"score":0.414000004529953},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.36059999465942383},{"id":"https://openalex.org/C117619785","wikidata":"https://www.wikidata.org/wiki/Q6094414","display_name":"Iterative learning control","level":3,"score":0.3522000014781952},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3280999958515167},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3098999857902527},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.30880001187324524},{"id":"https://openalex.org/C2779982483","wikidata":"https://www.wikidata.org/wiki/Q6094420","display_name":"Iterative refinement","level":2,"score":0.30869999527931213},{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.2946999967098236},{"id":"https://openalex.org/C22367795","wikidata":"https://www.wikidata.org/wiki/Q7625208","display_name":"Structured prediction","level":2,"score":0.289000004529953},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.27649998664855957},{"id":"https://openalex.org/C167085575","wikidata":"https://www.wikidata.org/wiki/Q6803654","display_name":"Mean squared prediction error","level":2,"score":0.2637999951839447}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.24041","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.24041","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":"doi:10.48550/arxiv.2605.24041","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.24041","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":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Neural":[0,36],"operators":[1,42],"serve":[2],"as":[3,28],"fast,":[4],"data-driven":[5],"surrogates":[6],"for":[7],"scientific":[8],"modeling":[9],"but":[10],"typically":[11],"rely":[12],"on":[13,102,122],"a":[14,25,44,58,83,94],"monolithic,":[15],"single-pass":[16],"inference":[17],"procedure":[18],"that":[19,98],"struggles":[20],"to":[21,82,119,133,141],"resolve":[22],"high-frequency":[23,90,103],"details,":[24],"limitation":[26],"known":[27],"spectral":[29,96,128],"bias.":[30],"We":[31],"introduce":[32],"the":[33,55,77,136,155],"Iterative":[34],"Refinement":[35],"Operator":[37],"(IRNO),":[38],"which":[39],"augments":[40],"pre-trained":[41],"with":[43,117],"learned":[45],"refinement":[46,106],"module":[47],"iteratively":[48],"applied":[49],"via":[50],"fixed-point":[51],"iteration.":[52],"IRNO":[53,113],"decomposes":[54],"prediction":[56],"into":[57],"coarse":[59],"initialization":[60],"followed":[61],"by":[62],"successive":[63],"residual":[64],"corrections,":[65],"paralleling":[66],"classical":[67],"numerical":[68],"solvers.":[69],"Under":[70],"local":[71],"assumptions,":[72],"we":[73,92],"establish":[74],"contraction":[75],"of":[76],"induced":[78],"operator,":[79,135],"ensuring":[80],"convergence":[81],"unique":[84],"fixed":[85],"point.":[86],"To":[87],"explicitly":[88],"target":[89],"errors,":[91],"propose":[93],"progressive":[95],"loss":[97],"adaptively":[99],"increases":[100],"penalty":[101],"components":[104],"over":[105],"steps":[107],"during":[108],"training.":[109],"Across":[110],"physical":[111],"systems,":[112],"consistently":[114],"lowers":[115],"error,":[116],"up":[118],"56.05%":[120],"improvement":[121],"turbulent":[123],"flow.":[124],"On":[125],"Active":[126],"Matter,":[127],"analysis":[129],"reveals":[130],"that,":[131],"relative":[132],"base":[134],"normalized":[137],"error":[138],"ratios":[139],"decrease":[140],"27.72-36.10%":[142],"in":[143,146,150],"low-,":[144],"5.07-6.68%":[145],"mid-,":[147],"and":[148],"1.48-2.04%":[149],"high-frequencies,":[151],"remaining":[152],"stable":[153],"beyond":[154],"trained":[156],"iteration":[157],"count.":[158],"Code":[159],"is":[160],"available":[161],"at":[162],"https://github.com/xiaotianliu-dartmouth/Iterative_Refinement_Neural_Operator":[163]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-05-27T00:00:00"}