{"id":"https://openalex.org/W7215107706","doi":"https://doi.org/10.48550/arxiv.2609.39291","title":"Physics-Informed Method of Group Data Handling: Adaptive Construction of Functional Representations with an Application to the Navier-Stokes Equations","display_name":"Physics-Informed Method of Group Data Handling: Adaptive Construction of Functional Representations with an Application to the Navier-Stokes Equations","publication_year":2026,"publication_date":"2026-09-30","ids":{"openalex":"https://openalex.org/W7215107706","doi":"https://doi.org/10.48550/arxiv.2609.39291"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.39291","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.39291","pdf_url":"https://arxiv.org/pdf/2609.39291","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,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.39291","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5154010412","display_name":"Mykhailo Minin","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Minin, Mykhailo","raw_affiliation_strings":["JSC KIEP , Kyiv , Ukraine"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"JSC KIEP , Kyiv , Ukraine","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5154010412"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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":1.0,"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":1.0,"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/T10320","display_name":"Neural Networks and Applications","score":0.0,"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"}},{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/incompressible-navier-stokes-equations","display_name":"incompressible Navier-Stokes equations","score":0.8370000123977661},{"id":"https://openalex.org/keywords/taylor-green-flow","display_name":"Taylor-Green flow","score":0.7900000214576721},{"id":"https://openalex.org/keywords/physics-informed-neural-networks","display_name":"physics-informed neural networks","score":0.7739999890327454}],"concepts":[{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.7157999873161316},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5601999759674072},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.4950000047683716},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46630001068115234},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.44440001249313354},{"id":"https://openalex.org/C21424316","wikidata":"https://www.wikidata.org/wiki/Q718621","display_name":"Chebyshev filter","level":2,"score":0.43070000410079956},{"id":"https://openalex.org/C51820054","wikidata":"https://www.wikidata.org/wiki/Q5508814","display_name":"Functional data analysis","level":2,"score":0.42719998955726624},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.40779998898506165},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.35359999537467957},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.34619998931884766},{"id":"https://openalex.org/C135925592","wikidata":"https://www.wikidata.org/wiki/Q2637908","display_name":"Orthogonal functions","level":2,"score":0.3418000042438507},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.3314000070095062},{"id":"https://openalex.org/C129785596","wikidata":"https://www.wikidata.org/wiki/Q619511","display_name":"Chebyshev polynomials","level":2,"score":0.3052000105381012},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3041999936103821},{"id":"https://openalex.org/C55037315","wikidata":"https://www.wikidata.org/wiki/Q5421151","display_name":"Experimental data","level":2,"score":0.2824999988079071},{"id":"https://openalex.org/C81299745","wikidata":"https://www.wikidata.org/wiki/Q334269","display_name":"Transfer function","level":2,"score":0.2768999934196472},{"id":"https://openalex.org/C16910744","wikidata":"https://www.wikidata.org/wiki/Q7705759","display_name":"Test data","level":2,"score":0.27219998836517334},{"id":"https://openalex.org/C116409475","wikidata":"https://www.wikidata.org/wiki/Q1385056","display_name":"External Data Representation","level":2,"score":0.2635999917984009},{"id":"https://openalex.org/C178009071","wikidata":"https://www.wikidata.org/wiki/Q93344","display_name":"Trigonometric functions","level":2,"score":0.26109999418258667},{"id":"https://openalex.org/C184389593","wikidata":"https://www.wikidata.org/wiki/Q603159","display_name":"Curve fitting","level":2,"score":0.2513999938964844},{"id":"https://openalex.org/C11516046","wikidata":"https://www.wikidata.org/wiki/Q1055807","display_name":"Group representation","level":3,"score":0.25099998712539673}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.39291","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.39291","pdf_url":"https://arxiv.org/pdf/2609.39291","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,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.39291","doi":"https://doi.org/10.48550/arxiv.2609.39291","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.39291","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,"listed_in":[],"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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.39291","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.39291","pdf_url":"https://arxiv.org/pdf/2609.39291","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,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306113","display_name":"U.S. Department of State","ror":"https://ror.org/03vvynj75"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7215107706.pdf","grobid_xml":"https://content.openalex.org/works/W7215107706.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W1490180844","https://openalex.org/W1678356000","https://openalex.org/W1696703109","https://openalex.org/W2000769684","https://openalex.org/W2150913357","https://openalex.org/W2898526471","https://openalex.org/W2899283552","https://openalex.org/W3163993681","https://openalex.org/W3200673624","https://openalex.org/W3205073660","https://openalex.org/W4410635455","https://openalex.org/W4413950903","https://openalex.org/W4415059772","https://openalex.org/W7171715841","https://openalex.org/W7171848508"],"related_works":["https://openalex.org/W7125942533","https://openalex.org/W4399797801","https://openalex.org/W7131742949","https://openalex.org/W4309258063","https://openalex.org/W7208798165","https://openalex.org/W4414098613","https://openalex.org/W2899283552","https://openalex.org/W7124212203","https://openalex.org/W6941145770","https://openalex.org/W4407962679"],"abstract_inverted_index":{"Physics-informed":[0],"computational":[1],"methods":[2],"usually":[3],"optimize":[4],"parameters":[5],"within":[6],"a":[7,19,80,151,167],"functional":[8,40],"representation":[9,156],"whose":[10],"structure":[11],"is":[12,68,163],"fixed":[13],"in":[14,27,56],"advance.":[15],"This":[16],"work":[17],"proposes":[18],"Physics-Informed":[20],"Method":[21],"of":[22,30,48,97,133,154,169],"Group":[23],"Data":[24],"Handling":[25],"(PI-GMDH),":[26],"which":[28],"representations":[29],"coupled":[31],"physical":[32,51],"fields":[33],"are":[34,42,127],"progressively":[35],"constructed":[36],"during":[37],"solution.":[38],"Candidate":[39],"directions":[41],"evaluated":[43],"through":[44],"the":[45,49,75,86,131],"first":[46],"variation":[47],"complete":[50],"and":[52,58,93,99,104,111,115,123,158],"observational":[53],"objective,":[54],"introduced":[55],"packages,":[57],"followed":[59],"by":[60],"block-coordinate":[61],"damped":[62],"Gauss-Newton":[63],"coefficient":[64],"optimization.":[65],"The":[66,137,161],"framework":[67],"demonstrated":[69],"with":[70,101,120],"tensor-product":[71],"Chebyshev":[72],"functions":[73,107],"on":[74],"incompressible":[76],"Navier-Stokes":[77],"equations":[78],"using":[79],"two-dimensional":[81],"time-dependent":[82],"Taylor-Green":[83],"benchmark.":[84],"Under":[85],"tested":[87],"configuration,":[88],"adaptive":[89],"PI-GMDH":[90,117],"reached":[91],"validation":[92],"held-out":[94],"test":[95],"losses":[96],"5.299e-19":[98],"5.296e-19":[100],"204,":[102],"201,":[103],"175":[105],"active":[106],"for":[108,141],"u,":[109],"v,":[110],"p.":[112],"Complete":[113],"degree-by-degree":[114],"all-terms":[116],"variants,":[118],"together":[119],"selected":[121],"PINN":[122],"KAN":[124],"reference":[125],"configurations,":[126],"used":[128],"to":[129],"examine":[130],"effect":[132],"structural":[134],"construction":[135,148],"policy.":[136],"results":[138],"show":[139],"that,":[140],"this":[142],"controlled":[143],"synthetic":[144],"benchmark,":[145],"selective":[146],"progressive":[147],"can":[149],"provide":[150],"favorable":[152],"combination":[153],"accuracy,":[155],"size,":[157],"wall-clock":[159],"time.":[160],"comparison":[162],"illustrative":[164],"rather":[165],"than":[166],"claim":[168],"universal":[170],"superiority":[171],"over":[172],"alternative":[173],"physics-informed":[174],"approaches.":[175]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-02T00:00:00"}