{"id":"https://openalex.org/W7160317574","doi":"https://doi.org/10.48550/arxiv.2605.02310","title":"A Variational Kolosov--Muskhelishvili Network for Elasticity and Fracture","display_name":"A Variational Kolosov--Muskhelishvili Network for Elasticity and Fracture","publication_year":2026,"publication_date":"2026-05-04","ids":{"openalex":"https://openalex.org/W7160317574","doi":"https://doi.org/10.48550/arxiv.2605.02310"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.02310","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.02310","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"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.02310","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5135290680","display_name":"Shuwei Zhou","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Zhou, Shuwei","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5130582366","display_name":"Christian H\u00e4ffner","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"H\u00e4ffner, Christian","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135326409","display_name":"Sophie Stebner","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Stebner, Sophie","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135410701","display_name":"Niklas Fehlemann","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fehlemann, Niklas","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027265282","display_name":"Zhichao Wei","orcid":"https://orcid.org/0000-0002-5002-6415"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wei, Zhichao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5026259562","display_name":"Sebastian M\u00fcnstermann","orcid":"https://orcid.org/0000-0002-6251-2429"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"M\u00fcnstermann, Sebastian","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5135290680"],"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":0.9624999761581421,"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":0.9624999761581421,"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/T10514","display_name":"Numerical methods in engineering","score":0.018400000408291817,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11115","display_name":"Topology Optimization in Engineering","score":0.002300000051036477,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural 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/classification-of-discontinuities","display_name":"Classification of discontinuities","score":0.6758999824523926},{"id":"https://openalex.org/keywords/singularity","display_name":"Singularity","score":0.6592000126838684},{"id":"https://openalex.org/keywords/displacement-field","display_name":"Displacement field","score":0.6187000274658203},{"id":"https://openalex.org/keywords/linear-elasticity","display_name":"Linear elasticity","score":0.5889999866485596},{"id":"https://openalex.org/keywords/elasticity","display_name":"Elasticity (physics)","score":0.5835999846458435},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5221999883651733},{"id":"https://openalex.org/keywords/stress-intensity-factor","display_name":"Stress intensity factor","score":0.4903999865055084},{"id":"https://openalex.org/keywords/stress-field","display_name":"Stress field","score":0.4832000136375427}],"concepts":[{"id":"https://openalex.org/C15627037","wikidata":"https://www.wikidata.org/wiki/Q541961","display_name":"Classification of discontinuities","level":2,"score":0.6758999824523926},{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.6592000126838684},{"id":"https://openalex.org/C29660869","wikidata":"https://www.wikidata.org/wiki/Q5282615","display_name":"Displacement field","level":3,"score":0.6187000274658203},{"id":"https://openalex.org/C3161131","wikidata":"https://www.wikidata.org/wiki/Q14097093","display_name":"Linear elasticity","level":3,"score":0.5889999866485596},{"id":"https://openalex.org/C121854251","wikidata":"https://www.wikidata.org/wiki/Q62932","display_name":"Elasticity (physics)","level":2,"score":0.5835999846458435},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5221999883651733},{"id":"https://openalex.org/C54303661","wikidata":"https://www.wikidata.org/wiki/Q1754376","display_name":"Stress intensity factor","level":3,"score":0.4903999865055084},{"id":"https://openalex.org/C2778414698","wikidata":"https://www.wikidata.org/wiki/Q7623438","display_name":"Stress field","level":3,"score":0.4832000136375427},{"id":"https://openalex.org/C9259290","wikidata":"https://www.wikidata.org/wiki/Q745215","display_name":"Variational principle","level":2,"score":0.4657000005245209},{"id":"https://openalex.org/C59085676","wikidata":"https://www.wikidata.org/wiki/Q957852","display_name":"Fracture mechanics","level":2,"score":0.4643999934196472},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42969998717308044},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4027999937534332},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.392300009727478},{"id":"https://openalex.org/C107551265","wikidata":"https://www.wikidata.org/wiki/Q1458245","display_name":"Displacement (psychology)","level":2,"score":0.37959998846054077},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3741999864578247},{"id":"https://openalex.org/C43369102","wikidata":"https://www.wikidata.org/wiki/Q2307625","display_name":"Fracture (geology)","level":2,"score":0.34389999508857727},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.32820001244544983},{"id":"https://openalex.org/C64618476","wikidata":"https://www.wikidata.org/wiki/Q164296","display_name":"Variational method","level":2,"score":0.30959999561309814},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.2890999913215637},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2678999900817871},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.2671999931335449},{"id":"https://openalex.org/C21036866","wikidata":"https://www.wikidata.org/wiki/Q181767","display_name":"Stress (linguistics)","level":2,"score":0.26669999957084656},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.260699987411499},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.259799987077713},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.25029999017715454}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.02310","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.02310","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.2605.02310","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.02310","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","score":0.6505887508392334,"id":"https://metadata.un.org/sdg/7"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Physics-informed":[0],"neural":[1,58,90,181,199,222],"networks":[2],"provide":[3],"a":[4,74,86,135,164],"mesh-free":[5],"framework":[6,92,160,231],"for":[7,43,93,232],"solving":[8],"partial":[9],"differential":[10],"equation-governed":[11],"problems":[12,45,97,168],"in":[13,20,104,212],"solid":[14],"mechanics.":[15],"However,":[16],"most":[17],"existing":[18,55],"formulations":[19,60],"linear":[21,95,234],"elasticity":[22,39],"still":[23,61],"learn":[24],"the":[25,34,125,145,155,213,217],"displacement":[26,188],"field":[27,189],"directly,":[28],"which":[29],"does":[30],"not":[31,78],"explicitly":[32],"exploit":[33],"analytic":[35],"structure":[36],"of":[37,127,166],"two-dimensional":[38,94,233],"and":[40,50,70,99,116,149,187,209,227],"becomes":[41],"restrictive":[42],"fracture":[44,236],"with":[46,67,98,169,197],"crack":[47,51,133,146,150,172],"face":[48,147],"discontinuities":[49],"tip":[52,151],"singularities.":[53],"Moreover,":[54],"Kolosov--Muskhelishvili":[56,88,114,179,220],"informed":[57,89,180,221],"network":[59,91,182,200,223],"rely":[62],"on":[63,163],"residual-based":[64],"loss":[65,121,207],"functions":[66],"multiple":[68],"boundary":[69],"interface":[71],"terms,":[72],"whereas":[73],"variational":[75,87,178,219,230],"concept":[76],"has":[77],"yet":[79],"been":[80],"established.":[81],"To":[82],"address":[83],"these":[84],"issues,":[85],"elastic":[96,235],"without":[100,171],"cracks":[101],"is":[102,109,140,161],"proposed":[103,159,218],"this":[105],"work.":[106],"The":[107,158,174],"solution":[108,156],"represented":[110],"by":[111],"two":[112],"holomorphic":[113],"potentials":[115],"trained":[117],"through":[118],"an":[119,225],"energy-based":[120],"function":[122],"derived":[123],"from":[124],"principle":[126],"minimum":[128],"total":[129],"potential":[130,138],"energy.":[131],"For":[132],"problems,":[134],"discontinuous":[136],"stress":[137,186,193],"representation":[139],"further":[141],"introduced":[142],"to":[143],"embed":[144],"condition":[148],"singularity":[152],"directly":[153],"into":[154],"ansatz.":[157],"validated":[162],"series":[165],"benchmark":[167],"or":[170],"problems.":[173],"results":[175],"show":[176],"that":[177],"can":[183],"accurately":[184],"predict":[185],"as":[190,192],"well":[191],"intensity":[194],"factors.":[195],"Compared":[196],"traditional":[198],"models,":[201],"it":[202],"achieves":[203],"higher":[204],"accuracy,":[205],"simpler":[206],"construction,":[208],"faster":[210],"convergence":[211],"considered":[214],"cases.":[215],"Overall,":[216],"provides":[224],"effective":[226],"physically":[228],"consistent":[229],"analysis.":[237]},"counts_by_year":[],"updated_date":"2026-05-06T06:10:43.113611","created_date":"2026-05-06T00:00:00"}