{"id":"https://openalex.org/W7152588426","doi":"https://doi.org/10.48550/arxiv.2604.06519","title":"Multiscale topology optimization of compressible and nearly incompressible anisotropic hyperelastic structures using physics-augmented neural networks","display_name":"Multiscale topology optimization of compressible and nearly incompressible anisotropic hyperelastic structures using physics-augmented neural networks","publication_year":2026,"publication_date":"2026-04-07","ids":{"openalex":"https://openalex.org/W7152588426","doi":"https://doi.org/10.48550/arxiv.2604.06519"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.06519","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.06519","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.2604.06519","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5133238700","display_name":"Asghar A. Jadoon","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Jadoon, Asghar A.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5133247927","display_name":"Aryan Tyagi","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tyagi, Aryan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5133285837","display_name":"L. River Spencer","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Spencer, L. River","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5133262062","display_name":"Reese E. Jones","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jones, Reese E.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014059790","display_name":"Manuel K. Rausch","orcid":"https://orcid.org/0000-0003-1337-6472"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rausch, Manuel K.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049100071","display_name":"Ryan Alberdi","orcid":"https://orcid.org/0000-0002-5836-948X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Alberdi, Ryan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5133279509","display_name":"D. Thomas Seidl","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Seidl, D. Thomas","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5133265847","display_name":"Jan N. Fuhg","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fuhg, Jan N.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":8,"corresponding_author_ids":["https://openalex.org/A5133238700"],"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/T11115","display_name":"Topology Optimization in Engineering","score":0.9819999933242798,"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"}},"topics":[{"id":"https://openalex.org/T11115","display_name":"Topology Optimization in Engineering","score":0.9819999933242798,"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"}},{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.003599999938160181,"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/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.00279999990016222,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/hyperelastic-material","display_name":"Hyperelastic material","score":0.8580999970436096},{"id":"https://openalex.org/keywords/topology-optimization","display_name":"Topology optimization","score":0.6527000069618225},{"id":"https://openalex.org/keywords/isotropy","display_name":"Isotropy","score":0.5860000252723694},{"id":"https://openalex.org/keywords/microscale-chemistry","display_name":"Microscale chemistry","score":0.5656999945640564},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5256999731063843},{"id":"https://openalex.org/keywords/compressibility","display_name":"Compressibility","score":0.5012999773025513},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.49140000343322754},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.4722999930381775},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4129999876022339}],"concepts":[{"id":"https://openalex.org/C147370603","wikidata":"https://www.wikidata.org/wiki/Q3801506","display_name":"Hyperelastic material","level":3,"score":0.8580999970436096},{"id":"https://openalex.org/C189216461","wikidata":"https://www.wikidata.org/wiki/Q2443456","display_name":"Topology optimization","level":3,"score":0.6527000069618225},{"id":"https://openalex.org/C184050105","wikidata":"https://www.wikidata.org/wiki/Q273163","display_name":"Isotropy","level":2,"score":0.5860000252723694},{"id":"https://openalex.org/C179428855","wikidata":"https://www.wikidata.org/wiki/Q1069216","display_name":"Microscale chemistry","level":2,"score":0.5656999945640564},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5256999731063843},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.5012999773025513},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.49140000343322754},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.4722999930381775},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4401000142097473},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4129999876022339},{"id":"https://openalex.org/C141123601","wikidata":"https://www.wikidata.org/wiki/Q6935072","display_name":"Multiscale modeling","level":2,"score":0.4072999954223633},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.39969998598098755},{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.3971000015735626},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.3930000066757202},{"id":"https://openalex.org/C202973686","wikidata":"https://www.wikidata.org/wiki/Q1937401","display_name":"Constitutive equation","level":3,"score":0.38929998874664307},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.35659998655319214},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33799999952316284},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.3337000012397766},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.3285999894142151},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3276999890804291},{"id":"https://openalex.org/C85725439","wikidata":"https://www.wikidata.org/wiki/Q466686","display_name":"Anisotropy","level":2,"score":0.32580000162124634},{"id":"https://openalex.org/C101842124","wikidata":"https://www.wikidata.org/wiki/Q2449817","display_name":"Transverse isotropy","level":3,"score":0.31709998846054077},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3158999979496002},{"id":"https://openalex.org/C2778722038","wikidata":"https://www.wikidata.org/wiki/Q17030643","display_name":"Homogenization (climate)","level":3,"score":0.313400000333786},{"id":"https://openalex.org/C31555180","wikidata":"https://www.wikidata.org/wiki/Q3523867","display_name":"Material properties","level":2,"score":0.2874000072479248},{"id":"https://openalex.org/C20192703","wikidata":"https://www.wikidata.org/wiki/Q17106073","display_name":"Strain energy density function","level":3,"score":0.26930001378059387},{"id":"https://openalex.org/C178295079","wikidata":"https://www.wikidata.org/wiki/Q919765","display_name":"Tangent stiffness matrix","level":4,"score":0.2667999863624573},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.25619998574256897}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.06519","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.06519","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.2604.06519","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.06519","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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Multiscale":[0],"topology":[1,28,202],"optimization":[2,29,51,203],"(TO)":[3],"of":[4,15,52,123,135,178,204],"hyperelastic":[5,108],"materials":[6],"remains":[7],"computationally":[8],"prohibitive":[9],"due":[10],"to":[11,187],"the":[12,49,83,114,136,165],"repeated":[13],"solution":[14],"microscale":[16,57,115],"boundary":[17,116],"value":[18,117],"problems.":[19],"In":[20],"this":[21,33],"work,":[22],"we":[23],"present":[24],"a":[25,60,196],"concurrent":[26],"multiscale":[27,142,170,201],"framework":[30,145],"that":[31,76,164],"overcomes":[32],"limitation":[34],"by":[35],"leveraging":[36],"physics-augmented":[37],"neural":[38,73,137],"networks":[39,74],"(PANNs)":[40],"as":[41,195],"surrogate":[42,67],"constitutive":[43],"models.":[44],"The":[45,66,110,144,161],"proposed":[46,166],"approach":[47],"enables":[48,173],"simultaneous":[50],"macroscale":[53],"material":[54,88,179],"distribution":[55],"and":[56,87,93,100,119,125,132,156,172],"descriptors,":[58],"within":[59,82],"unified":[61],"nonlinear":[62,205],"finite":[63],"strain":[64],"setting.":[65],"models":[68],"are":[69],"constructed":[70],"using":[71,129],"input-specific":[72],"(ISNNs)":[75],"enforce":[77],"key":[78],"physical":[79],"principles":[80],"directly":[81],"architecture,":[84],"including":[85],"convexity":[86],"symmetry":[89],"through":[90],"invariant-based":[91],"representations":[92],"structural":[94],"tensors.":[95],"This":[96],"ensures":[97],"thermodynamic":[98],"consistency":[99],"numerical":[101],"stability":[102],"while":[103,181],"accurately":[104],"representing":[105],"homogenized":[106],"anisotropic":[107,206],"responses.":[109],"trained":[111],"PANNs":[112,194],"replace":[113],"problem":[118],"provide":[120],"efficient":[121],"evaluations":[122],"stresses":[124],"consistent":[126],"tangent":[127],"moduli":[128],"analytical":[130],"first":[131],"second":[133],"derivatives":[134],"network,":[138],"enabling":[139],"tractable":[140],"large-scale":[141],"optimization.":[143],"is":[146],"demonstrated":[147],"on":[148],"representative":[149],"microstructures":[150],"exhibiting":[151],"transversely":[152],"isotropic,":[153],"cubic":[154],"anisotropic,":[155],"nearly":[157],"incompressible":[158],"isotropic":[159],"behavior.":[160],"results":[162],"show":[163],"method":[167],"captures":[168],"complex":[169],"interactions":[171],"physically":[174],"meaningful":[175],"spatial":[176],"tailoring":[177],"properties,":[180],"significantly":[182],"reducing":[183],"computational":[184],"cost":[185],"compared":[186],"classical":[188],"FE$^2$":[189],"approaches.":[190],"These":[191],"findings":[192],"establish":[193],"powerful":[197],"tool":[198],"for":[199],"high-fidelity":[200],"materials.":[207]},"counts_by_year":[],"updated_date":"2026-05-05T08:41:31.759640","created_date":"2026-04-10T00:00:00"}
