{"id":"https://openalex.org/W7141140490","doi":"https://doi.org/10.48550/arxiv.2603.24641","title":"Learning Mesh-Free Discrete Differential Operators with Self-Supervised Graph Neural Networks","display_name":"Learning Mesh-Free Discrete Differential Operators with Self-Supervised Graph Neural Networks","publication_year":2026,"publication_date":"2026-03-25","ids":{"openalex":"https://openalex.org/W7141140490","doi":"https://doi.org/10.48550/arxiv.2603.24641"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.24641","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.24641","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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.2603.24641","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5120641448","display_name":"Lucas Gerken Starepravo","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Starepravo, Lucas Gerken","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062828807","display_name":"Georgios Fourtakas","orcid":"https://orcid.org/0000-0001-8584-3020"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fourtakas, Georgios","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015688321","display_name":"Steven Lind","orcid":"https://orcid.org/0000-0001-9701-6524"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lind, Steven","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069901589","display_name":"Ajay B. Harish","orcid":"https://orcid.org/0000-0001-5234-7047"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Harish, Ajay B.","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039175173","display_name":"Tianning Tang","orcid":"https://orcid.org/0000-0002-6365-9342"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tang, Tianning","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5087330185","display_name":"J.R.C. King","orcid":"https://orcid.org/0000-0002-9731-5556"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"King, Jack R. C.","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5120641448"],"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":0.9501000046730042,"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":0.9501000046730042,"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/T11416","display_name":"Numerical methods for differential equations","score":0.006599999964237213,"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"}},{"id":"https://openalex.org/T11948","display_name":"Machine Learning in Materials Science","score":0.005100000184029341,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/differential-operator","display_name":"Differential operator","score":0.5515000224113464},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.5390999913215637},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.534500002861023},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5113000273704529},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4124000072479248},{"id":"https://openalex.org/keywords/moment","display_name":"Moment (physics)","score":0.37049999833106995},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.36959999799728394},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.35199999809265137}],"concepts":[{"id":"https://openalex.org/C70915906","wikidata":"https://www.wikidata.org/wiki/Q1058681","display_name":"Differential operator","level":2,"score":0.5515000224113464},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.5390999913215637},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.534500002861023},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5113000273704529},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49970000982284546},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45089998841285706},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4156000018119812},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4124000072479248},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38510000705718994},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.37049999833106995},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.36959999799728394},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.35199999809265137},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.3472000062465668},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.3465000092983246},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.32010000944137573},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3059000074863434},{"id":"https://openalex.org/C158946198","wikidata":"https://www.wikidata.org/wiki/Q131187","display_name":"Taylor series","level":2,"score":0.3001999855041504},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.28049999475479126},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.27480000257492065},{"id":"https://openalex.org/C161677786","wikidata":"https://www.wikidata.org/wiki/Q2478475","display_name":"Neighbourhood (mathematics)","level":2,"score":0.2685000002384186},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.2621999979019165},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.2563999891281128}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.24641","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.24641","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2603.24641","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.24641","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"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":{"Mesh-free":[0],"numerical":[1,113],"methods":[2],"provide":[3],"flexible":[4],"discretisations":[5],"for":[6,20,26,35],"complex":[7],"geometries;":[8],"however,":[9],"classical":[10,77],"meshless":[11],"discrete":[12,38,65],"differential":[13,39],"operators":[14,40,89],"typically":[15],"trade":[16],"low":[17],"computational":[18],"cost":[19],"limited":[21],"accuracy":[22,25,118],"or":[23],"high":[24],"substantial":[27],"per-stencil":[28],"computation.":[29],"We":[30,107],"introduce":[31],"a":[32,42,124,130],"parametrised":[33],"framework":[34,110],"learning":[36],"mesh-free":[37,134],"using":[41,111,150],"graph":[43],"neural":[44,73],"network":[45],"trained":[46],"via":[47],"polynomial":[48,78],"moment":[49],"constraints":[50],"derived":[51],"from":[52],"truncated":[53],"Taylor":[54],"expansions.":[55],"The":[56,68,87],"model":[57],"maps":[58],"local":[59,93],"stencils":[60],"relative":[61,128],"positions":[62],"directly":[63],"to":[64,83,129],"operator":[66],"weights.":[67],"current":[69],"work":[70],"demonstrates":[71],"that":[72],"networks":[74],"can":[75,98],"learn":[76],"consistency":[79],"while":[80],"retaining":[81],"robustness":[82],"irregular":[84],"neighbourhood":[85],"geometry.":[86],"learned":[88,152],"depend":[90],"only":[91],"on":[92],"geometry,":[94],"are":[95],"resolution-agnostic,":[96],"and":[97,104,123],"be":[99],"reused":[100],"across":[101],"particle":[102],"configurations":[103],"governing":[105],"equations.":[106],"evaluate":[108],"the":[109,137,145,151],"standard":[112],"analysis":[114],"diagnostics,":[115],"showing":[116],"improved":[117],"over":[119],"Smoothed":[120],"Particle":[121],"Hydrodynamics,":[122],"favourable":[125],"accuracy-cost":[126],"trade-off":[127],"representative":[131],"high-order":[132],"consistent":[133],"method":[135],"in":[136],"moderate-accuracy":[138],"regime.":[139],"Applicability":[140],"is":[141],"demonstrated":[142],"by":[143],"solving":[144],"weakly":[146],"compressible":[147],"Navier-Stokes":[148],"equations":[149],"operators.":[153]},"counts_by_year":[],"updated_date":"2026-03-28T06:16:51.555046","created_date":"2026-03-28T00:00:00"}
