{"id":"https://openalex.org/W7165671556","doi":"https://doi.org/10.48550/arxiv.2606.20771","title":"ELADO: Elliptic PDE Assessment Datasets for Operator Learning","display_name":"ELADO: Elliptic PDE Assessment Datasets for Operator Learning","publication_year":2026,"publication_date":"2026-06-18","ids":{"openalex":"https://openalex.org/W7165671556","doi":"https://doi.org/10.48550/arxiv.2606.20771"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.20771","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.20771","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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.2606.20771","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5115718622","display_name":"Frank Ehebrecht","orcid":"https://orcid.org/0009-0001-5680-0256"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ehebrecht, Frank","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039798111","display_name":"Toni Scharle","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Scharle, Toni","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5011835245","display_name":"Martin Atzmueller","orcid":"https://orcid.org/0000-0002-2480-6901"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Atzmueller, Martin","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":0.7440000176429749,"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":0.7440000176429749,"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":0.02419999986886978,"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/T11636","display_name":"Artificial Intelligence in Healthcare and Education","score":0.02319999970495701,"subfield":{"id":"https://openalex.org/subfields/2718","display_name":"Health Informatics"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.64410001039505},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5875999927520752},{"id":"https://openalex.org/keywords/sensitivity","display_name":"Sensitivity (control systems)","score":0.5745000243186951},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.5253999829292297},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4171000123023987},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.4088999927043915},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.4041999876499176},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.4018999934196472},{"id":"https://openalex.org/keywords/hilbert\u2013huang-transform","display_name":"Hilbert\u2013Huang transform","score":0.3887999951839447}],"concepts":[{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.64410001039505},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5875999927520752},{"id":"https://openalex.org/C21200559","wikidata":"https://www.wikidata.org/wiki/Q7451068","display_name":"Sensitivity (control systems)","level":2,"score":0.5745000243186951},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.5253999829292297},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5037999749183655},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.44519999623298645},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4171000123023987},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.4088999927043915},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4041999876499176},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.4018999934196472},{"id":"https://openalex.org/C25570617","wikidata":"https://www.wikidata.org/wiki/Q1006462","display_name":"Hilbert\u2013Huang transform","level":3,"score":0.3887999951839447},{"id":"https://openalex.org/C70610323","wikidata":"https://www.wikidata.org/wiki/Q427625","display_name":"Elliptic operator","level":2,"score":0.3822999894618988},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.37630000710487366},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.36649999022483826},{"id":"https://openalex.org/C79581498","wikidata":"https://www.wikidata.org/wiki/Q1367530","display_name":"Suite","level":2,"score":0.36469998955726624},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.3506999909877777},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.34060001373291016},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.33559998869895935},{"id":"https://openalex.org/C110342517","wikidata":"https://www.wikidata.org/wiki/Q1129902","display_name":"Constant coefficients","level":2,"score":0.32429999113082886},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.3160000145435333},{"id":"https://openalex.org/C18591234","wikidata":"https://www.wikidata.org/wiki/Q860615","display_name":"Helmholtz equation","level":3,"score":0.3127000033855438},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.3091000020503998},{"id":"https://openalex.org/C2779843651","wikidata":"https://www.wikidata.org/wiki/Q7390335","display_name":"SIGNAL (programming language)","level":2,"score":0.2897000014781952},{"id":"https://openalex.org/C104267543","wikidata":"https://www.wikidata.org/wiki/Q208163","display_name":"Signal processing","level":3,"score":0.2892000079154968},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.2865999937057495},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.27059999108314514},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.26579999923706055},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.26440000534057617},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.25110000371932983}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.20771","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.20771","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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.2606.20771","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.20771","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,76,159],"introduce":[1],"ELADO":[2,44],"(Elliptic":[3],"PDE":[4,56],"Assessment":[5],"Datasets":[6],"for":[7],"Operator":[8],"Learning),":[9],"a":[10,78,90],"systematic":[11],"benchmark":[12],"suite":[13],"constructed":[14,47],"to":[15,48,82,88],"show":[16,169],"and":[17,68,144,168,175,189],"quantify":[18],"failure":[19],"modes":[20],"of":[21,29,35,93,112,123,134,148,182],"neural":[22,162],"operator":[23,163],"architectures":[24,164],"when":[25],"learning":[26],"solution":[27,100],"operators":[28],"elliptic":[30,55],"PDEs.":[31],"While":[32],"the":[33,43,69,113,120,146,183,192],"benchmarks":[34],"existing":[36],"datasets":[37,45,63,167,188],"focus":[38],"on":[39,152],"average":[40],"case":[41],"performance,":[42],"are":[46,86,97],"highlight":[49],"challenges":[50],"that":[51,85,170,186],"arise":[52],"naturally":[53],"in":[54,119],"problems.":[57],"In":[58],"particular,":[59],"we":[60],"construct":[61],"several":[62,161],"built":[64],"around":[65],"Poisson's":[66],"equation":[67],"Helmholtz":[70],"equation,":[71],"each":[72,178],"with":[73],"non-constant":[74],"coefficients.":[75],"define":[77],"controllable":[79],"data-generating":[80],"process":[81],"create":[83],"datasets,":[84],"designed":[87],"isolate":[89],"distinct":[91],"source":[92],"difficulty.":[94],"Specifically,":[95],"these":[96],"(1)":[98],"heavy-tailed":[99,117,171],"distributions":[101,118],"arising":[102,125],"from":[103,126],"light-tailed":[104,127],"coefficient":[105,128],"field":[106,129],"distributions,":[107,130],"(2)":[108],"spectral":[109,173],"distribution":[110],"shift":[111],"input":[114,132,149,176],"data,":[115],"(3)":[116],"frequency":[121],"domain":[122],"solutions,":[124],"(4)":[131],"sensitivity":[133,177],"learned":[135],"operators,":[136],"quantified":[137],"by":[138],"an":[139],"empirical":[140],"local":[141],"Lipschitz":[142],"analysis,":[143],"(5)":[145],"effect":[147],"signal":[150],"complexity":[151],"prediction":[153,184],"accuracy":[154,185],"under":[155],"controlled":[156],"amplitude":[157],"normalization.":[158],"evaluate":[160],"across":[165],"all":[166],"targets,":[172],"shift,":[174],"cause":[179],"substantial":[180],"degradation":[181],"standard":[187],"metrics":[190],"(e.g.,":[191],"mean":[193],"relative":[194],"$L^2$":[195],"error)":[196],"may":[197],"obscure.":[198]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-06-24T00:00:00"}
