{"id":"https://openalex.org/W7150754415","doi":"https://doi.org/10.48550/arxiv.2604.03034","title":"Learning Contractive Integral Operators with Fredholm Integral Neural Operators","display_name":"Learning Contractive Integral Operators with Fredholm Integral Neural Operators","publication_year":2026,"publication_date":"2026-04-03","ids":{"openalex":"https://openalex.org/W7150754415","doi":"https://doi.org/10.48550/arxiv.2604.03034"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.03034","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.03034","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.2604.03034","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035240394","display_name":"Kyriakos Georgiou","orcid":"https://orcid.org/0000-0001-7549-2298"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Georgiou, Kyriakos C.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090389995","display_name":"Constantinos Siettos","orcid":"https://orcid.org/0000-0002-9568-3355"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Siettos, Constantinos","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5020073636","display_name":"Athanasios N. Yannacopoulos","orcid":"https://orcid.org/0000-0001-9489-4268"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yannacopoulos, Athanasios N.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"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":0.8650000095367432,"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":0.8650000095367432,"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":0.015799999237060547,"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/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.01080000028014183,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/fredholm-theory","display_name":"Fredholm theory","score":0.6628999710083008},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.6589999794960022},{"id":"https://openalex.org/keywords/fredholm-integral-equation","display_name":"Fredholm integral equation","score":0.616599977016449},{"id":"https://openalex.org/keywords/operator-theory","display_name":"Operator theory","score":0.5867999792098999},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5415999889373779},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5134000182151794},{"id":"https://openalex.org/keywords/fourier-integral-operator","display_name":"Fourier integral operator","score":0.49810001254081726},{"id":"https://openalex.org/keywords/elliptic-operator","display_name":"Elliptic operator","score":0.4821999967098236},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.4318999946117401}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7282999753952026},{"id":"https://openalex.org/C518188847","wikidata":"https://www.wikidata.org/wiki/Q4455098","display_name":"Fredholm theory","level":4,"score":0.6628999710083008},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.6589999794960022},{"id":"https://openalex.org/C89285879","wikidata":"https://www.wikidata.org/wiki/Q2991898","display_name":"Fredholm integral equation","level":3,"score":0.616599977016449},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.5867999792098999},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5415999889373779},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5134000182151794},{"id":"https://openalex.org/C191832335","wikidata":"https://www.wikidata.org/wiki/Q4262191","display_name":"Fourier integral operator","level":3,"score":0.49810001254081726},{"id":"https://openalex.org/C70610323","wikidata":"https://www.wikidata.org/wiki/Q427625","display_name":"Elliptic operator","level":2,"score":0.4821999967098236},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.4318999946117401},{"id":"https://openalex.org/C2779219991","wikidata":"https://www.wikidata.org/wiki/Q573631","display_name":"Fredholm operator","level":4,"score":0.42899999022483826},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.42500001192092896},{"id":"https://openalex.org/C134810832","wikidata":"https://www.wikidata.org/wiki/Q2996956","display_name":"Daniell integral","level":4,"score":0.4156000018119812},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.3865000009536743},{"id":"https://openalex.org/C200052193","wikidata":"https://www.wikidata.org/wiki/Q877802","display_name":"Integral transform","level":2,"score":0.35519999265670776},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.34470000863075256},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.32440000772476196},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3228999972343445},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.31850001215934753},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.3109000027179718},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.3034000098705292},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.302700012922287},{"id":"https://openalex.org/C129683796","wikidata":"https://www.wikidata.org/wiki/Q430450","display_name":"Microlocal analysis","level":4,"score":0.2971000075340271},{"id":"https://openalex.org/C117204833","wikidata":"https://www.wikidata.org/wiki/Q7233207","display_name":"Positive-definite kernel","level":4,"score":0.27900001406669617},{"id":"https://openalex.org/C152306953","wikidata":"https://www.wikidata.org/wiki/Q621744","display_name":"Approximation property","level":3,"score":0.2718999981880188},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.271699994802475},{"id":"https://openalex.org/C3019018024","wikidata":"https://www.wikidata.org/wiki/Q207643","display_name":"Linear operators","level":3,"score":0.26739999651908875},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.26260000467300415}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.03034","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.03034","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.2604.03034","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.03034","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":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,26,55,107],"generalize":[1],"the":[2,20,29,59,70,75,78,93,109],"framework":[3],"of":[4,19,45,77,96],"Fredholm":[5,15,31],"Neural":[6,33],"Networks,":[7],"to":[8,64,91],"learn":[9,92],"non-expansive":[10],"integral":[11,49],"operators":[12,50,61],"arising":[13],"in":[14,23,121,131],"Integral":[16,32,103],"Equations":[17],"(FIEs)":[18],"second":[21],"kind":[22],"arbitrary":[24,122],"dimensions.":[25],"first":[27],"present":[28],"proposed":[30,110],"Operators":[34],"(FREDINOs),":[35],"for":[36,74,150],"FIEs":[37,120],"and":[38,47,51,118,143],"prove":[39,57],"that":[40,58],"they":[41],"are":[42,62],"universal":[43],"approximators":[44],"linear":[46,117],"non-linear":[48,97,119,128],"corresponding":[52],"solution":[53,94],"operators.":[54],"furthermore":[56],"learned":[60],"guaranteed":[63],"be":[65,89],"contractive,":[66],"thereby":[67],"strictly":[68],"satisfying":[69],"mathematical":[71],"property":[72],"required":[73],"convergence":[76],"fixed":[79],"point":[80],"scheme.":[81],"Finally,":[82],"we":[83],"also":[84],"demonstrate":[85],"how":[86],"FREDINOs":[87,139],"can":[88],"used":[90],"operator":[95],"elliptic":[98,129],"PDEs,":[99],"via":[100,113],"a":[101,127],"Boundary":[102],"Equation":[104],"(BIE)":[105],"formulation.":[106],"assess":[108],"methodology":[111],"numerically,":[112],"several":[114],"benchmark":[115],"problems:":[116],"dimensions,":[123],"as":[124,126],"well":[125,148],"PDE":[130],"2D.":[132],"Built":[133],"on":[134],"tailored":[135],"mathematical/numerical":[136],"analysis":[137,154],"theory,":[138],"offer":[140],"high-accuracy":[141],"approximations":[142],"interpretable":[144],"schemes,":[145],"making":[146],"them":[147],"suited":[149],"scientific":[151],"machine":[152],"learning/numerical":[153],"computations.":[155]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-04-07T00:00:00"}