{"id":"https://openalex.org/W4408865928","doi":"https://doi.org/10.1090/mcom/4086","title":"A hybrid iterative method based on MIONet for PDEs: Theory and numerical examples","display_name":"A hybrid iterative method based on MIONet for PDEs: Theory and numerical examples","publication_year":2025,"publication_date":"2025-03-26","ids":{"openalex":"https://openalex.org/W4408865928","doi":"https://doi.org/10.1090/mcom/4086"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/4086","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/4086","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"preprint","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5028500115","display_name":"Jun Hu","orcid":"https://orcid.org/0000-0002-4565-3000"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jun Hu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5009632487","display_name":"Pengzhan Jin","orcid":"https://orcid.org/0000-0002-2169-1491"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pengzhan Jin","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":9,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":"95","issue":"359","first_page":"1327","last_page":"1359"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.6376000046730042,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.6376000046730042,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.6065000295639038,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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/T11416","display_name":"Numerical methods for differential equations","score":0.5709999799728394,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5592836737632751},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4612831473350525},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.44225233793258667},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.39328399300575256},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.36394333839416504},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3313589096069336},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3133684992790222}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5592836737632751},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4612831473350525},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.44225233793258667},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.39328399300575256},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.36394333839416504},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3313589096069336},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3133684992790222},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/mcom/4086","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/4086","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2519258023","display_name":null,"funder_award_id":"12288101","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W1549748890","https://openalex.org/W2037159403","https://openalex.org/W2075536798","https://openalex.org/W2151317657","https://openalex.org/W2749028154","https://openalex.org/W2760972773","https://openalex.org/W2899283552","https://openalex.org/W2914483840","https://openalex.org/W2963889991","https://openalex.org/W2978175238","https://openalex.org/W2979786244","https://openalex.org/W3128157635","https://openalex.org/W3133338006","https://openalex.org/W3163993681","https://openalex.org/W3186384563","https://openalex.org/W3201666041","https://openalex.org/W3204708751","https://openalex.org/W4200096621","https://openalex.org/W4221154881","https://openalex.org/W4226057880","https://openalex.org/W4253937035","https://openalex.org/W4320488531","https://openalex.org/W4362480129","https://openalex.org/W4382519581","https://openalex.org/W6600175564","https://openalex.org/W6600407735","https://openalex.org/W6600566992","https://openalex.org/W6601160810","https://openalex.org/W6601430172","https://openalex.org/W6601613822","https://openalex.org/W6602332119","https://openalex.org/W6603860191","https://openalex.org/W6723418815"],"related_works":["https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2053286651","https://openalex.org/W2181743346","https://openalex.org/W2187401768","https://openalex.org/W2057289358","https://openalex.org/W2040941802","https://openalex.org/W2412311587","https://openalex.org/W4238207569","https://openalex.org/W2339251345"],"abstract_inverted_index":{"We":[0,64,79],"propose":[1],"a":[2,99,139],"hybrid":[3,90,105,114],"iterative":[4,20],"method":[5,28,91],"based":[6],"on":[7],"multiple-input":[8],"operator":[9],"network":[10],"for":[11,69,118,149],"partial":[12],"differential":[13],"equations,":[14],"which":[15,97],"combines":[16],"the":[17,23,40,43,49,55,58,61,66,70,85,89,93,104,113,119],"traditional":[18],"numerical":[19,110],"solver":[21],"and":[22,32,60,77,131],"recent":[24],"powerful":[25],"machine":[26],"learning":[27],"of":[29,54,57,84,88],"neural":[30],"operator,":[31],"further":[33],"systematically":[34],"analyzes":[35],"its":[36],"theoretical":[37,67,129],"properties,":[38],"including":[39,112],"convergence":[41,50,86],"condition,":[42],"spectral":[44],"behavior,":[45],"as":[46,48],"well":[47],"rate,":[51],"in":[52],"terms":[53],"errors":[56],"discretization":[59],"model":[62,94],"inference.":[63],"show":[65],"results":[68],"frequently-used":[71],"smoothers,":[72],"i.e.":[73],"Richardson":[74,115],"(damped":[75],"Jacobi)":[76],"Gauss-Seidel.":[78],"give":[80],"an":[81,134],"upper":[82],"bound":[83],"rate":[87],"w.r.t.":[92],"correction":[95],"period,":[96],"indicates":[98],"minimum":[100],"point":[101],"to":[102,126],"make":[103],"iteration":[106,117],"converge":[107],"fastest.":[108],"Several":[109],"examples":[111],"(Gauss-Seidel)":[116],"1-d":[120],"(2-d)":[121],"Poisson":[122],"equation":[123],"are":[124],"presented":[125],"verify":[127],"our":[128],"results,":[130],"also":[132],"reflect":[133],"excellent":[135],"acceleration":[136,141],"effect.":[137],"As":[138],"meshless":[140],"method,":[142],"it":[143],"is":[144],"provided":[145],"with":[146],"enormous":[147],"potentials":[148],"practice":[150],"applications.":[151]},"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2025,"cited_by_count":4}],"updated_date":"2026-08-28T12:50:07.497085","created_date":"2025-10-10T00:00:00"}