{"id":"https://openalex.org/W7131869952","doi":"https://doi.org/10.48550/arxiv.2602.23113","title":"Learning Physical Operators using Neural Operators","display_name":"Learning Physical Operators using Neural Operators","publication_year":2026,"publication_date":"2026-02-26","ids":{"openalex":"https://openalex.org/W7131869952","doi":"https://doi.org/10.48550/arxiv.2602.23113"},"language":null,"primary_location":{"id":"pmh:doi:10.48550/arxiv.2602.23113","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","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":null,"raw_type":"Article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":null,"any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5025230700","display_name":"Vignesh Gopakumar","orcid":"https://orcid.org/0000-0003-0904-3448"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gopakumar, Vignesh","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045565430","display_name":"Ander Gray","orcid":"https://orcid.org/0000-0002-1585-0900"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gray, Ander","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111142721","display_name":"Dan Giles","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Giles, Dan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5125143239","display_name":"Lorenzo Zanisi","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zanisi, Lorenzo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5106577629","display_name":"Matt J. Kusner","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kusner, Matt J.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078044622","display_name":"Timo Betcke","orcid":"https://orcid.org/0000-0002-3323-2110"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Betcke, Timo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5126989117","display_name":"Stanislas Pamela","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pamela, Stanislas","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5001763022","display_name":"Marc Peter Deisenroth","orcid":"https://orcid.org/0000-0003-1503-680X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Deisenroth, Marc Peter","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":0.9887999892234802,"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":0.9887999892234802,"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":0.002300000051036477,"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/T11804","display_name":"Quantum many-body systems","score":0.0017000000225380063,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/extrapolation","display_name":"Extrapolation","score":0.6096000075340271},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5838000178337097},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5139999985694885},{"id":"https://openalex.org/keywords/ode","display_name":"Ode","score":0.49380001425743103},{"id":"https://openalex.org/keywords/operator-theory","display_name":"Operator theory","score":0.4618000090122223},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.4578000009059906},{"id":"https://openalex.org/keywords/modular-design","display_name":"Modular design","score":0.43309998512268066},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.42890000343322754}],"concepts":[{"id":"https://openalex.org/C132459708","wikidata":"https://www.wikidata.org/wiki/Q744069","display_name":"Extrapolation","level":2,"score":0.6096000075340271},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5838000178337097},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5139999985694885},{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.49380001425743103},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.4618000090122223},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4611000120639801},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.4578000009059906},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4487999975681305},{"id":"https://openalex.org/C101468663","wikidata":"https://www.wikidata.org/wiki/Q1620158","display_name":"Modular design","level":2,"score":0.43309998512268066},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.42890000343322754},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.4016000032424927},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3970000147819519},{"id":"https://openalex.org/C35958075","wikidata":"https://www.wikidata.org/wiki/Q1425077","display_name":"Spectral theorem","level":3,"score":0.3619000017642975},{"id":"https://openalex.org/C191832335","wikidata":"https://www.wikidata.org/wiki/Q4262191","display_name":"Fourier integral operator","level":3,"score":0.3540000021457672},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3379000127315521},{"id":"https://openalex.org/C3019018024","wikidata":"https://www.wikidata.org/wiki/Q207643","display_name":"Linear operators","level":3,"score":0.3303000032901764},{"id":"https://openalex.org/C2780451532","wikidata":"https://www.wikidata.org/wiki/Q759676","display_name":"Task (project management)","level":2,"score":0.3111000061035156},{"id":"https://openalex.org/C125411270","wikidata":"https://www.wikidata.org/wiki/Q18653","display_name":"Encoding (memory)","level":2,"score":0.3100999891757965},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.30889999866485596},{"id":"https://openalex.org/C70915906","wikidata":"https://www.wikidata.org/wiki/Q1058681","display_name":"Differential operator","level":2,"score":0.30809998512268066},{"id":"https://openalex.org/C129683796","wikidata":"https://www.wikidata.org/wiki/Q430450","display_name":"Microlocal analysis","level":4,"score":0.29760000109672546},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.290800005197525},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.2888999879360199},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.28130000829696655},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2770000100135803},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.2558000087738037}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:doi:10.48550/arxiv.2602.23113","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","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":null,"raw_type":"Article"},{"id":"doi:10.48550/arxiv.2602.23113","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.23113","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:doi:10.48550/arxiv.2602.23113","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","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":null,"raw_type":"Article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Neural":[0],"operators":[1,51,57,61,98],"have":[2],"emerged":[3],"as":[4,88],"promising":[5],"surrogate":[6],"models":[7],"for":[8],"solving":[9],"partial":[10],"differential":[11,92],"equations":[12],"(PDEs),":[13],"but":[14],"struggle":[15],"to":[16,25,52,72,132],"generalise":[17],"beyond":[18,142],"training":[19,35,48,143],"distributions":[20],"and":[21,110,118,127,145],"are":[22],"often":[23],"constrained":[24],"a":[26,33,89],"fixed":[27,63],"temporal":[28,140],"discretisation.":[29],"This":[30,66],"work":[31],"introduces":[32],"physics-informed":[34],"framework":[36],"that":[37],"addresses":[38],"these":[39,96],"limitations":[40],"by":[41,76],"decomposing":[42],"PDEs":[43],"using":[44],"operator":[45,81],"splitting":[46],"methods,":[47],"separate":[49],"neural":[50,90],"learn":[53],"individual":[54],"non-linear":[55],"physical":[56,74],"while":[58],"approximating":[59],"linear":[60],"with":[62],"finite-difference":[64],"convolutions.":[65],"modular":[67],"mixture-of-experts":[68],"architecture":[69],"enables":[70],"generalisation":[71],"novel":[73],"regimes":[75],"explicitly":[77],"encoding":[78],"the":[79,85,100],"underlying":[80],"structure.":[82],"We":[83],"formulate":[84],"modelling":[86],"task":[87],"ordinary":[91],"equation":[93],"(ODE)":[94],"where":[95],"learned":[97],"constitute":[99],"right-hand":[101],"side,":[102],"enabling":[103,139],"continuous-in-time":[104],"predictions":[105],"through":[106],"standard":[107],"ODE":[108],"solvers":[109],"implicitly":[111],"enforcing":[112],"PDE":[113],"constraints.":[114],"Demonstrated":[115],"on":[116],"incompressible":[117],"compressible":[119],"Navier--Stokes":[120],"equations,":[121],"our":[122],"approach":[123],"achieves":[124],"better":[125],"convergence":[126],"superior":[128],"performance":[129],"when":[130],"generalising":[131],"unseen":[133],"physics.":[134,156],"The":[135],"method":[136],"remains":[137],"parameter-efficient,":[138],"extrapolation":[141],"horizons,":[144],"provides":[146],"interpretable":[147],"components":[148],"whose":[149],"behaviour":[150],"can":[151],"be":[152],"verified":[153],"against":[154],"known":[155]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-02-28T00:00:00"}