{"id":"https://openalex.org/W7140658779","doi":"https://doi.org/10.48550/arxiv.2603.24143","title":"Linear-Nonlinear Fusion Neural Operator for Partial Differential Equations","display_name":"Linear-Nonlinear Fusion Neural Operator for Partial Differential Equations","publication_year":2026,"publication_date":"2026-03-25","ids":{"openalex":"https://openalex.org/W7140658779","doi":"https://doi.org/10.48550/arxiv.2603.24143"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.24143","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.24143","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.2603.24143","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5130650790","display_name":"Heng Wu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wu, Heng","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5130639435","display_name":"Junjie Wang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, Junjie","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5123330772","display_name":"Benzhuo Lu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lu, Benzhuo","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":0.9904000163078308,"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":0.9904000163078308,"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":0.0038999998942017555,"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":0.0005000000237487257,"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/nonlinear-system","display_name":"Nonlinear system","score":0.6776000261306763},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.6161999702453613},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5878999829292297},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.574999988079071},{"id":"https://openalex.org/keywords/decoupling","display_name":"Decoupling (probability)","score":0.5622000098228455},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4300000071525574},{"id":"https://openalex.org/keywords/linear-map","display_name":"Linear map","score":0.39890000224113464},{"id":"https://openalex.org/keywords/semi-elliptic-operator","display_name":"Semi-elliptic operator","score":0.36250001192092896},{"id":"https://openalex.org/keywords/partial-derivative","display_name":"Partial derivative","score":0.35670000314712524}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6776000261306763},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.6161999702453613},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5878999829292297},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.574999988079071},{"id":"https://openalex.org/C205606062","wikidata":"https://www.wikidata.org/wiki/Q5249645","display_name":"Decoupling (probability)","level":2,"score":0.5622000098228455},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.46889999508857727},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4336000084877014},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4300000071525574},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4300000071525574},{"id":"https://openalex.org/C49766605","wikidata":"https://www.wikidata.org/wiki/Q207643","display_name":"Linear map","level":2,"score":0.39890000224113464},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.392300009727478},{"id":"https://openalex.org/C24902271","wikidata":"https://www.wikidata.org/wiki/Q7449297","display_name":"Semi-elliptic operator","level":3,"score":0.36250001192092896},{"id":"https://openalex.org/C53846429","wikidata":"https://www.wikidata.org/wiki/Q186475","display_name":"Partial derivative","level":2,"score":0.35670000314712524},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.34279999136924744},{"id":"https://openalex.org/C158525013","wikidata":"https://www.wikidata.org/wiki/Q2593739","display_name":"Fusion","level":2,"score":0.3287999927997589},{"id":"https://openalex.org/C70915906","wikidata":"https://www.wikidata.org/wiki/Q1058681","display_name":"Differential operator","level":2,"score":0.3260999917984009},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.30799999833106995},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.2858000099658966},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.28110000491142273},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.27219998836517334},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.26510000228881836},{"id":"https://openalex.org/C33954974","wikidata":"https://www.wikidata.org/wiki/Q486494","display_name":"Sensor fusion","level":2,"score":0.26249998807907104},{"id":"https://openalex.org/C207864730","wikidata":"https://www.wikidata.org/wiki/Q179467","display_name":"Fourier series","level":2,"score":0.2624000012874603},{"id":"https://openalex.org/C175291020","wikidata":"https://www.wikidata.org/wiki/Q1156822","display_name":"Offset (computer science)","level":2,"score":0.26190000772476196},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.2590000033378601},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.25119999051094055}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.24143","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.24143","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.2603.24143","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.24143","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":[0,78,198],"operator":[1,61,83,116,166],"learning":[2,66],"directly":[3],"constructs":[4],"the":[5,9,14,25,75,86,115,179,195],"mapping":[6],"relationship":[7],"from":[8],"equation":[10],"parameter":[11],"space":[12],"to":[13,41,64,132,160],"solution":[15,29,112],"space,":[16],"enabling":[17],"efficient":[18,108],"direct":[19],"inference":[20],"in":[21],"practical":[22],"applications":[23],"without":[24],"need":[26],"for":[27],"repeated":[28],"of":[30,89,110,143],"partial":[31],"differential":[32],"equations":[33,150],"(PDEs)":[34],"--":[35],"an":[36],"advantage":[37],"that":[38,52],"is":[39,130,156],"difficult":[40],"achieve":[42],"with":[43],"traditional":[44],"numerical":[45],"methods.":[46],"In":[47],"this":[48],"work,":[49],"we":[50],"find":[51],"explicitly":[53],"decoupling":[54,106],"linear":[55,91],"and":[56,93,101,121,129,136,151,200],"nonlinear":[57,95,148],"effects":[58],"within":[59],"such":[60],"mappings":[62,84],"leads":[63],"improved":[65,172],"efficiency.":[67],"This":[68,104],"yields":[69],"a":[70,90,94,99,140],"novel":[71],"network":[72],"structure,":[73],"namely":[74],"Linear-Nonlinear":[76],"Fusion":[77],"Operator":[79,199],"(LNF-NO),":[80],"which":[81],"models":[82],"via":[85],"multiplicative":[87],"fusion":[88],"component":[92],"component,":[96],"thus":[97],"achieving":[98,169],"lightweight":[100],"interpretable":[102],"representation.":[103],"linear-nonlinear":[105],"enables":[107],"capture":[109],"complex":[111],"features":[113],"at":[114],"level":[117],"while":[118,168,188],"maintaining":[119],"stability":[120],"generality.":[122],"LNF-NO":[123,155,184],"naturally":[124],"supports":[125],"multiple":[126],"functional":[127],"inputs":[128],"applicable":[131],"both":[133],"regular":[134],"grids":[135],"irregular":[137],"geometries.":[138],"Across":[139],"diverse":[141],"suite":[142],"PDE":[144],"operator-learning":[145],"benchmarks,":[146],"including":[147],"Poisson-Boltzmann":[149,182],"multi-physics":[152],"coupled":[153],"systems,":[154],"typically":[157],"substantially":[158,190],"faster":[159],"train":[161],"than":[162,194],"several":[163],"representative":[164],"neural":[165],"baselines,":[167],"comparable":[170],"or":[171],"accuracy":[173,187],"across":[174],"most":[175],"tested":[176,180],"cases.":[177],"On":[178],"3D":[181],"case,":[183],"achieves":[185],"strong":[186],"requiring":[189],"less":[191],"training":[192],"time":[193],"three-dimensional":[196],"Fourier":[197],"Transolver":[201],"baselines.":[202]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-03-27T00:00:00"}