{"id":"https://openalex.org/W7204917266","doi":"https://doi.org/10.48550/arxiv.2608.30788","title":"Model reduction of port-Hamiltonian systems via neural networks","display_name":"Model reduction of port-Hamiltonian systems via neural networks","publication_year":2026,"publication_date":"2026-08-31","ids":{"openalex":"https://openalex.org/W7204917266","doi":"https://doi.org/10.48550/arxiv.2608.30788"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.30788","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.30788","pdf_url":"https://arxiv.org/pdf/2608.30788","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/2608.30788","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5022294841","display_name":"Silke Glas","orcid":"https://orcid.org/0000-0003-3274-1615","observed_orcids":["https://orcid.org/0000-0003-3274-1615"]},"institutions":[{"id":"https://openalex.org/I94624287","display_name":"University of Twente","ror":"https://ror.org/006hf6230","country_code":"NL","type":"education","lineage":["https://openalex.org/I94624287"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Glas, Silke","raw_affiliation_strings":["Department of Applied Mathematics , University of Twente , Enschede , The Netherlands ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics , University of Twente , Enschede , The Netherlands ,","institution_ids":["https://openalex.org/I94624287"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081654668","display_name":"Alexander Heinlein","orcid":"https://orcid.org/0000-0003-1578-8104","observed_orcids":["https://orcid.org/0000-0003-1578-8104"]},"institutions":[{"id":"https://openalex.org/I94624287","display_name":"University of Twente","ror":"https://ror.org/006hf6230","country_code":"NL","type":"education","lineage":["https://openalex.org/I94624287"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Heinlein, Alexander","raw_affiliation_strings":["Department of Applied Mathematics , University of Twente , Enschede , The Netherlands ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics , University of Twente , Enschede , The Netherlands ,","institution_ids":["https://openalex.org/I94624287"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068988792","display_name":"Harald Monsuur","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I94624287","display_name":"University of Twente","ror":"https://ror.org/006hf6230","country_code":"NL","type":"education","lineage":["https://openalex.org/I94624287"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Monsuur, Harald","raw_affiliation_strings":["Department of Applied Mathematics , University of Twente , Enschede , The Netherlands ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics , University of Twente , Enschede , The Netherlands ,","institution_ids":["https://openalex.org/I94624287"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5159799482","display_name":"Hongliang Mu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I94624287","display_name":"University of Twente","ror":"https://ror.org/006hf6230","country_code":"NL","type":"education","lineage":["https://openalex.org/I94624287"]},{"id":"https://openalex.org/I98358874","display_name":"Delft University of Technology","ror":"https://ror.org/02e2c7k09","country_code":"NL","type":"education","lineage":["https://openalex.org/I98358874"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Mu, Hongliang","raw_affiliation_strings":["Delft Institute of Applied Mathematics , Delft University of Technology , Delft , The Netherlands ,","Department of Applied Mathematics , University of Twente , Enschede , The Netherlands ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Delft Institute of Applied Mathematics , Delft University of Technology , Delft , The Netherlands ,","institution_ids":["https://openalex.org/I98358874"]},{"raw_affiliation_string":"Department of Applied Mathematics , University of Twente , Enschede , The Netherlands ,","institution_ids":["https://openalex.org/I94624287"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"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/T11416","display_name":"Numerical Solvers for Ordinary Differential Equations","score":9.999999747378752e-05,"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/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/port-hamiltonian-systems","display_name":"port-Hamiltonian systems","score":0.9570000171661377},{"id":"https://openalex.org/keywords/model-reduction","display_name":"model reduction","score":0.8820000290870667},{"id":"https://openalex.org/keywords/structure-preserving-model-reduction","display_name":"structure-preserving model reduction","score":0.7929999828338623},{"id":"https://openalex.org/keywords/neural-network","display_name":"artificial neural networks","score":0.9150000214576721},{"id":"https://openalex.org/keywords/skew-symmetric-matrices","display_name":"skew-symmetric matrices","score":0.7070000171661377},{"id":"https://openalex.org/keywords/positive-semidefinite-matrices","display_name":"positive semidefinite matrices","score":0.9599999785423279},{"id":"https://openalex.org/keywords/multi-physics-systems","display_name":"multi-physics systems","score":0.7120000123977661}],"concepts":[{"id":"https://openalex.org/C123745756","wikidata":"https://www.wikidata.org/wiki/Q1665949","display_name":"Interconnection","level":2,"score":0.7807000279426575},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6485999822616577},{"id":"https://openalex.org/C135402231","wikidata":"https://www.wikidata.org/wiki/Q898440","display_name":"Dissipation","level":2,"score":0.5967000126838684},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5910999774932861},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5321000218391418},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.5012000203132629},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.4634000062942505},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4268999993801117},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.423799991607666},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.3944999873638153},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.39010000228881836},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3846000134944916},{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.38269999623298645},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.3749000132083893},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.362199991941452},{"id":"https://openalex.org/C47822265","wikidata":"https://www.wikidata.org/wiki/Q854457","display_name":"Complex system","level":2,"score":0.3443000018596649},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.3208000063896179},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3001999855041504},{"id":"https://openalex.org/C116672817","wikidata":"https://www.wikidata.org/wiki/Q1454986","display_name":"Physical system","level":2,"score":0.29030001163482666},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.28700000047683716},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.27790001034736633},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.27559998631477356},{"id":"https://openalex.org/C31352089","wikidata":"https://www.wikidata.org/wiki/Q3750474","display_name":"Systems design","level":2,"score":0.25440001487731934}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.30788","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.30788","pdf_url":"https://arxiv.org/pdf/2608.30788","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.2608.30788","doi":"https://doi.org/10.48550/arxiv.2608.30788","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.30788","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.30788","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.30788","pdf_url":"https://arxiv.org/pdf/2608.30788","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/F4320321800","display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","ror":"https://ror.org/04jsz6e67"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204917266.pdf","grobid_xml":"https://content.openalex.org/works/W7204917266.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W1526120274","https://openalex.org/W1966447062","https://openalex.org/W1997447880","https://openalex.org/W2016022803","https://openalex.org/W2096876511","https://openalex.org/W2141770513","https://openalex.org/W2526408861","https://openalex.org/W2695202536","https://openalex.org/W2789597342","https://openalex.org/W2793278837","https://openalex.org/W3134999641","https://openalex.org/W4281724062","https://openalex.org/W4376137587","https://openalex.org/W4380878066","https://openalex.org/W4401004083","https://openalex.org/W4416764505","https://openalex.org/W7134849537"],"related_works":["https://openalex.org/W7062152927","https://openalex.org/W7134849537","https://openalex.org/W2963922511","https://openalex.org/W2155402683","https://openalex.org/W4281724062","https://openalex.org/W4320854872","https://openalex.org/W2146678473","https://openalex.org/W1606566422","https://openalex.org/W1977430076","https://openalex.org/W4380878066"],"abstract_inverted_index":{"In":[0,99,178],"this":[1],"paper,":[2],"we":[3,92,101,106,124,182],"consider":[4,183],"structure-preserving":[5,96],"model":[6],"reduction":[7],"of":[8,35,58,67,77,158,171],"port-Hamiltonian":[9],"(pH)":[10],"systems":[11,16,25,40,174],"which":[12],"extend":[13],"classical":[14],"Hamiltonian":[15],"with":[17,53,188,210],"dissipation":[18,57,142],"and":[19,141,168],"an":[20],"input-output":[21],"port.":[22],"These":[23],"pH":[24,45,60,116,154],"are":[26,62,176],"often":[27],"used":[28],"in":[29,43,83],"multi-physics":[30],"systems,":[31],"as":[32],"the":[33,49,54,65,75,78,108,115,119,131,134,138,148,156,159,166,172,197,207],"interconnection":[34,55,140],"one":[36],"or":[37],"more":[38],"\\pH":[39],"results":[41,194],"again":[42,152],"a":[44,59,126,153,179,184,201],"system.":[46],"If":[47],"particularly":[48],"system":[50,61,117,143,187,190],"matrices":[51,175],"associated":[52],"and/or":[56],"state-dependent,":[63],"then":[64,122],"evaluation":[66],"standard":[68],"reduced-order":[69,135,139,173],"models":[70],"(ROMs)":[71],"may":[72],"depend":[73],"on":[74],"dimension":[76],"original":[79,208],"full-order":[80],"model,":[81],"resulting":[82,149],"high":[84,90],"computational":[85,203],"costs.":[86],"To":[87,145],"circumvent":[88],"these":[89],"costs,":[91],"propose":[93],"to":[94,113,129,137,206],"use":[95,107],"neural":[97,127,160],"networks.":[98],"particular,":[100],"perform":[102],"two":[103],"steps:":[104],"(1)":[105],"generalized":[109],"manifold":[110],"Galerkin":[111],"projection":[112],"project":[114],"onto":[118],"reduced":[120],"space;":[121],"(2)":[123],"train":[125],"network":[128,161],"learn":[130],"map":[132],"from":[133],"state":[136],"matrices.":[144,191],"ensure":[146],"that":[147,165,196],"ROM":[150],"is":[151,162],"system,":[155],"architecture":[157],"chosen":[163],"such":[164],"skew-symmetry":[167],"positive":[169],"semi-definiteness":[170],"maintained.":[177],"numerical":[180,193],"example,":[181],"nonlinear":[185],"mass-spring-damper":[186],"state-dependent":[189],"The":[192],"show":[195],"proposed":[198],"method":[199],"achieves":[200],"significant":[202],"speed-up":[204],"compared":[205],"\\ROM":[209],"comparable":[211],"accuracy.":[212]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-02T00:00:00"}
