{"id":"https://openalex.org/W7084137129","doi":"https://doi.org/10.48550/arxiv.2509.25450","title":"Multi-patch isogeometric neural solver for partial differential equations on computer-aided design domains","display_name":"Multi-patch isogeometric neural solver for partial differential equations on computer-aided design domains","publication_year":2025,"publication_date":"2025-09-29","ids":{"openalex":"https://openalex.org/W7084137129","doi":"https://doi.org/10.48550/arxiv.2509.25450"},"language":"en","primary_location":{"id":"pmh:oai:cwi.nl:35943","is_oa":false,"landing_page_url":"https://ir.cwi.nl/pub/35943","pdf_url":null,"source":{"id":"https://openalex.org/S7407055335","display_name":"Centrum Wiskunde & Informatica (CWI), the national research institute for mathematics and computer science in the Netherlands","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":"info:eu-repo/semantics/other"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2509.25450","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"von Tresckow, Moritz","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"von Tresckow, Moritz","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Ion, Ion Gabriel","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ion, Ion Gabriel","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Loukrezis, Dimitrios","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Loukrezis, Dimitrios","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"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":true,"primary_topic":{"id":"https://openalex.org/T12243","display_name":"Research in Cotton Cultivation","score":0.9309999942779541,"subfield":{"id":"https://openalex.org/subfields/1110","display_name":"Plant Science"},"field":{"id":"https://openalex.org/fields/11","display_name":"Agricultural and Biological Sciences"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T12243","display_name":"Research in Cotton Cultivation","score":0.9309999942779541,"subfield":{"id":"https://openalex.org/subfields/1110","display_name":"Plant Science"},"field":{"id":"https://openalex.org/fields/11","display_name":"Agricultural and Biological Sciences"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10869","display_name":"Polysaccharides and Plant Cell Walls","score":0.01850000023841858,"subfield":{"id":"https://openalex.org/subfields/1110","display_name":"Plant Science"},"field":{"id":"https://openalex.org/fields/11","display_name":"Agricultural and Biological Sciences"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T12161","display_name":"Plant Surface Properties and Treatments","score":0.013299999758601189,"subfield":{"id":"https://openalex.org/subfields/1110","display_name":"Plant Science"},"field":{"id":"https://openalex.org/fields/11","display_name":"Agricultural and Biological Sciences"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/isogeometric-analysis","display_name":"Isogeometric analysis","score":0.7943999767303467},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.6559000015258789},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.6557999849319458},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5845000147819519},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5101000070571899},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.47769999504089355},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.4471000134944916},{"id":"https://openalex.org/keywords/partial-derivative","display_name":"Partial derivative","score":0.44670000672340393},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4465999901294708}],"concepts":[{"id":"https://openalex.org/C2780737243","wikidata":"https://www.wikidata.org/wiki/Q17082433","display_name":"Isogeometric analysis","level":3,"score":0.7943999767303467},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.6559000015258789},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.6557999849319458},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5845000147819519},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5101000070571899},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4945000112056732},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.47769999504089355},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4530999958515167},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4471000134944916},{"id":"https://openalex.org/C53846429","wikidata":"https://www.wikidata.org/wiki/Q186475","display_name":"Partial derivative","level":2,"score":0.44670000672340393},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4465999901294708},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3686000108718872},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.36419999599456787},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3619000017642975},{"id":"https://openalex.org/C110167270","wikidata":"https://www.wikidata.org/wiki/Q1193699","display_name":"Dirichlet boundary condition","level":3,"score":0.33629998564720154},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.33379998803138733},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3255999982357025},{"id":"https://openalex.org/C11210021","wikidata":"https://www.wikidata.org/wiki/Q1520713","display_name":"Linearization","level":3,"score":0.3100000023841858},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.30219998955726624},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.3012999892234802},{"id":"https://openalex.org/C63632240","wikidata":"https://www.wikidata.org/wiki/Q1935004","display_name":"Boundary element method","level":3,"score":0.2976999878883362},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.290800005197525},{"id":"https://openalex.org/C64057670","wikidata":"https://www.wikidata.org/wiki/Q4381442","display_name":"First-order partial differential equation","level":3,"score":0.2856000065803528},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.2797999978065491},{"id":"https://openalex.org/C113843644","wikidata":"https://www.wikidata.org/wiki/Q901882","display_name":"Interface (matter)","level":4,"score":0.2648000121116638},{"id":"https://openalex.org/C191640071","wikidata":"https://www.wikidata.org/wiki/Q5377056","display_name":"Energy functional","level":2,"score":0.2556999921798706},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.2531000077724457}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:cwi.nl:35943","is_oa":false,"landing_page_url":"https://ir.cwi.nl/pub/35943","pdf_url":null,"source":{"id":"https://openalex.org/S7407055335","display_name":"Centrum Wiskunde & Informatica (CWI), the national research institute for mathematics and computer science in the Netherlands","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":"info:eu-repo/semantics/other"},{"id":"doi:10.48550/arxiv.2509.25450","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2509.25450","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":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2509.25450","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2509.25450","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":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[{"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7","score":0.5706742405891418}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"This":[0],"work":[1],"develops":[2],"a":[3,107,112,116,125],"computational":[4],"framework":[5,74],"that":[6,31],"combines":[7],"physics-informed":[8],"neural":[9,29,66,149],"networks":[10,30],"with":[11,137],"multi-patch":[12],"isogeometric":[13,38],"analysis":[14],"to":[15,133,151],"solve":[16],"partial":[17,87],"differential":[18,88],"equations":[19],"on":[20,33,98],"complex":[21,153],"computer-aided":[22,159],"design":[23,160],"geometries.":[24],"The":[25,90,128],"method":[26,95],"utilizes":[27],"patch-local":[28],"operate":[32],"the":[34,45,72,77,82,86,93,144,147,157],"reference":[35,134],"domain":[36],"of":[37,48,85,92,111,124,146],"analysis.":[39],"A":[40],"custom":[41],"output":[42],"layer":[43],"enables":[44],"strong":[46],"imposition":[47],"Dirichlet":[49],"boundary":[50],"conditions.":[51],"Solution":[52],"conformity":[53],"across":[54],"interfaces":[55],"between":[56],"non-uniform":[57],"rational":[58],"B-spline":[59],"patches":[60],"is":[61,69,96],"enforced":[62],"using":[63,71],"dedicated":[64],"interface":[65],"networks.":[67],"Training":[68],"performed":[70],"variational":[73],"by":[75],"minimizing":[76],"energy":[78],"functional":[79],"derived":[80],"after":[81],"weak":[83],"form":[84],"equation.":[89],"effectiveness":[91],"suggested":[94,148],"demonstrated":[97],"two":[99],"highly":[100],"non-trivial":[101],"and":[102,115,120],"practically":[103],"relevant":[104],"use-cases,":[105],"namely,":[106],"2D":[108],"magnetostatics":[109],"model":[110,123],"quadrupole":[113],"magnet":[114],"3D":[117],"nonlinear":[118],"solid":[119],"contact":[121],"mechanics":[122],"mechanical":[126],"holder.":[127],"results":[129],"show":[130],"excellent":[131],"agreement":[132],"solutions":[135],"obtained":[136],"high-fidelity":[138],"finite":[139],"element":[140],"solvers,":[141],"thus":[142],"highlighting":[143],"potential":[145],"solver":[150],"tackle":[152],"engineering":[154],"problems":[155],"given":[156],"corresponding":[158],"models.":[161]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
