{"id":"https://openalex.org/W7149004066","doi":"https://doi.org/10.1016/j.jcp.2026.114912","title":"Constitutive manifold neural networks","display_name":"Constitutive manifold neural networks","publication_year":2026,"publication_date":"2026-04-03","ids":{"openalex":"https://openalex.org/W7149004066","doi":"https://doi.org/10.1016/j.jcp.2026.114912"},"language":"en","primary_location":{"id":"doi:10.1016/j.jcp.2026.114912","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.jcp.2026.114912","pdf_url":null,"source":{"id":"https://openalex.org/S148709879","display_name":"Journal of Computational Physics","issn_l":"0021-9991","issn":["0021-9991","1090-2716"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Computational Physics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1016/j.jcp.2026.114912","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5107160681","display_name":"Wouter J. Schuttert","orcid":"https://orcid.org/0009-0004-4005-7463"},"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":true,"raw_author_name":"Wouter J. Schuttert","raw_affiliation_strings":["Applied Mechanics and Data Analysis chair Faculty of Engineering Technology Drienerlolaan 5, 7522 NB Enschede University of Twente"],"raw_orcid":"https://orcid.org/0009-0004-4005-7463","affiliations":[{"raw_affiliation_string":"Applied Mechanics and Data Analysis chair Faculty of Engineering Technology Drienerlolaan 5, 7522 NB Enschede University of Twente","institution_ids":["https://openalex.org/I94624287"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039080235","display_name":"Mohammed Rasheed","orcid":"https://orcid.org/0000-0002-0768-2142"},"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":"Mohammed Iqbal Abdul Rasheed","raw_affiliation_strings":["Applied Mechanics and Data Analysis chair Faculty of Engineering Technology Drienerlolaan 5, 7522 NB Enschede University of Twente"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Applied Mechanics and Data Analysis chair Faculty of Engineering Technology Drienerlolaan 5, 7522 NB Enschede University of Twente","institution_ids":["https://openalex.org/I94624287"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5132860251","display_name":"Bojana Rosi\u0107","orcid":null},"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":"Bojana Rosi\u0107","raw_affiliation_strings":["Applied Mechanics and Data Analysis chair Faculty of Engineering Technology Drienerlolaan 5, 7522 NB Enschede University of Twente"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Applied Mechanics and Data Analysis chair Faculty of Engineering Technology Drienerlolaan 5, 7522 NB Enschede University of Twente","institution_ids":["https://openalex.org/I94624287"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5107160681"],"corresponding_institution_ids":["https://openalex.org/I94624287"],"apc_list":{"value":3750,"currency":"USD","value_usd":3750},"apc_paid":{"value":3750,"currency":"USD","value_usd":3750},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.76967624,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"559","issue":null,"first_page":"114912","last_page":"114912"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.4620000123977661,"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"}},"topics":[{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.4620000123977661,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.05990000069141388,"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/T10719","display_name":"3D Shape Modeling and Analysis","score":0.02539999969303608,"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/artificial-neural-network","display_name":"Artificial neural network","score":0.6570000052452087},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.5979999899864197},{"id":"https://openalex.org/keywords/perceptron","display_name":"Perceptron","score":0.541100025177002},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.4970000088214874},{"id":"https://openalex.org/keywords/tangent","display_name":"Tangent","score":0.4092000126838684},{"id":"https://openalex.org/keywords/information-geometry","display_name":"Information geometry","score":0.39489999413490295},{"id":"https://openalex.org/keywords/thermal-conduction","display_name":"Thermal conduction","score":0.3880999982357025},{"id":"https://openalex.org/keywords/tangent-space","display_name":"Tangent space","score":0.38429999351501465},{"id":"https://openalex.org/keywords/riemannian-manifold","display_name":"Riemannian manifold","score":0.3824000060558319},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.3671000003814697}],"concepts":[{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6570000052452087},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.5979999899864197},{"id":"https://openalex.org/C60908668","wikidata":"https://www.wikidata.org/wiki/Q690207","display_name":"Perceptron","level":3,"score":0.541100025177002},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.4970000088214874},{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.4092000126838684},{"id":"https://openalex.org/C109546454","wikidata":"https://www.wikidata.org/wiki/Q3798604","display_name":"Information geometry","level":4,"score":0.39489999413490295},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.39169999957084656},{"id":"https://openalex.org/C172100665","wikidata":"https://www.wikidata.org/wiki/Q7465774","display_name":"Thermal conduction","level":2,"score":0.3880999982357025},{"id":"https://openalex.org/C157157409","wikidata":"https://www.wikidata.org/wiki/Q909601","display_name":"Tangent space","level":2,"score":0.38429999351501465},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3824000060558319},{"id":"https://openalex.org/C2779593128","wikidata":"https://www.wikidata.org/wiki/Q632814","display_name":"Riemannian manifold","level":2,"score":0.3824000060558319},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36880001425743103},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.3671000003814697},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3619999885559082},{"id":"https://openalex.org/C16345878","wikidata":"https://www.wikidata.org/wiki/Q107472979","display_name":"Orientation (vector space)","level":2,"score":0.3587000072002411},{"id":"https://openalex.org/C85725439","wikidata":"https://www.wikidata.org/wiki/Q466686","display_name":"Anisotropy","level":2,"score":0.34450000524520874},{"id":"https://openalex.org/C96469262","wikidata":"https://www.wikidata.org/wiki/Q1324364","display_name":"Homogeneous space","level":2,"score":0.3424000144004822},{"id":"https://openalex.org/C202787564","wikidata":"https://www.wikidata.org/wiki/Q6510488","display_name":"Heat equation","level":2,"score":0.3416999876499176},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.3400999903678894},{"id":"https://openalex.org/C70915906","wikidata":"https://www.wikidata.org/wiki/Q1058681","display_name":"Differential operator","level":2,"score":0.33480000495910645},{"id":"https://openalex.org/C74050887","wikidata":"https://www.wikidata.org/wiki/Q848368","display_name":"Rotation (mathematics)","level":2,"score":0.33160001039505005},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.3124000132083893},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.28760001063346863},{"id":"https://openalex.org/C202973686","wikidata":"https://www.wikidata.org/wiki/Q1937401","display_name":"Constitutive equation","level":3,"score":0.2854999899864197},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.28299999237060547},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.28130000829696655},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.28060001134872437},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.27619999647140503},{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.2651999890804291},{"id":"https://openalex.org/C74750220","wikidata":"https://www.wikidata.org/wiki/Q2662197","display_name":"Differential evolution","level":2,"score":0.2572999894618988},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.2567000091075897},{"id":"https://openalex.org/C47702885","wikidata":"https://www.wikidata.org/wiki/Q5441227","display_name":"Feedforward neural network","level":3,"score":0.2563999891281128},{"id":"https://openalex.org/C192939610","wikidata":"https://www.wikidata.org/wiki/Q188444","display_name":"Differential geometry","level":2,"score":0.2526000142097473},{"id":"https://openalex.org/C83633838","wikidata":"https://www.wikidata.org/wiki/Q1256564","display_name":"Rotation matrix","level":2,"score":0.2522999942302704}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/j.jcp.2026.114912","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.jcp.2026.114912","pdf_url":null,"source":{"id":"https://openalex.org/S148709879","display_name":"Journal of Computational Physics","issn_l":"0021-9991","issn":["0021-9991","1090-2716"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Computational Physics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1016/j.jcp.2026.114912","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.jcp.2026.114912","pdf_url":null,"source":{"id":"https://openalex.org/S148709879","display_name":"Journal of Computational Physics","issn_l":"0021-9991","issn":["0021-9991","1090-2716"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Computational Physics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321800","display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","ror":"https://ror.org/04jsz6e67"},{"id":"https://openalex.org/F4320327247","display_name":"Materials innovation institute","ror":"https://ror.org/00fyemf28"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W1811453145","https://openalex.org/W1983496390","https://openalex.org/W1986964250","https://openalex.org/W1988859494","https://openalex.org/W1994400618","https://openalex.org/W1995875735","https://openalex.org/W1997969642","https://openalex.org/W2032558547","https://openalex.org/W2033622744","https://openalex.org/W2337203680","https://openalex.org/W2619158974","https://openalex.org/W2786232134","https://openalex.org/W2908460620","https://openalex.org/W2970485619","https://openalex.org/W3015176898","https://openalex.org/W3039006016","https://openalex.org/W3101728628","https://openalex.org/W3102100346","https://openalex.org/W3108491918","https://openalex.org/W3110616649","https://openalex.org/W3121900475","https://openalex.org/W3201329906","https://openalex.org/W3215367274","https://openalex.org/W4244360209","https://openalex.org/W4298304695","https://openalex.org/W4309079827","https://openalex.org/W4323922288","https://openalex.org/W4328051924","https://openalex.org/W4387542111","https://openalex.org/W4392310072","https://openalex.org/W4401872115","https://openalex.org/W4402484546"],"related_works":[],"abstract_inverted_index":{"Anisotropic":[0],"material":[1,16,104],"properties,":[2],"such":[3],"as":[4,26,149,154],"the":[5,49,53,58,68,75,88,96,100,102,175,190,194,204,210,241],"thermal":[6,97],"conductivities":[7],"of":[8,57,71,77,90,99,243],"engineering":[9,252],"composites,":[10],"exhibit":[11],"variability":[12],"due":[13],"to":[14,42,158,166,193,233],"inherent":[15],"heterogeneity":[17],"and":[18,52,82,92,206],"manufacturing-related":[19],"uncertainties.":[20],"Mathematically,":[21],"these":[22],"properties":[23],"are":[24,143],"modelled":[25],"symmetric":[27],"positive":[28],"definite":[29],"(SPD)":[30],"tensors,":[31,72,148],"which":[32,73,131,181],"reside":[33],"on":[34,95],"a":[35,43,61,110,132,198],"curved":[36,191],"Riemannian":[37],"manifold.":[38],"Extending":[39],"this":[40,64,171],"description":[41],"stochastic":[44,103,220],"framework":[45],"requires":[46],"preserving":[47,203],"both":[48],"SPD":[50,147,187],"structure":[51],"underlying":[54,161],"spatial":[55],"symmetries":[56],"tensors.":[59],"From":[60],"numerical":[62],"standpoint,":[63],"is":[65,137],"achieved":[66],"through":[67,109],"spectral":[69],"decomposition":[70],"enables":[74],"parameterisation":[76],"uncertainties":[78,94],"into":[79],"scale":[80],"(strength)":[81],"rotation":[83],"(orientation)":[84],"components.":[85],"To":[86,169],"quantify":[87],"impact":[89],"strength":[91],"orientation":[93],"behaviour":[98],"composite,":[101],"tensor":[105,152],"must":[106],"be":[107],"propagated":[108],"physics-based":[111],"forward":[112],"model,":[113],"here":[114],"exemplified":[115],"by":[116],"an":[117],"elliptic":[118],"partial":[119],"differential":[120],"equation":[121],"(PDE).":[122],"This":[123],"process":[124],"necessitates":[125],"computationally":[126],"efficient":[127],"surrogate":[128],"models,":[129],"for":[130,146],"feedforward":[133],"neural":[134,226],"network":[135,227],"(FNN)":[136],"employed.":[138],"However,":[139],"conventional":[140,234],"FNN":[141],"architectures":[142],"not":[144],"well-suited":[145],"directly":[150],"using":[151],"components":[153],"input":[155,183],"features":[156],"fails":[157],"preserve":[159],"their":[160],"geometric":[162,207],"structure,":[163],"often":[164],"leading":[165],"suboptimal":[167],"performance.":[168],"address":[170],"issue,":[172],"we":[173],"introduce":[174],"Constitutive":[176],"Manifold":[177],"Neural":[178],"Network":[179],"(CMNN),":[180],"incorporates":[182],"layers":[184],"that":[185,224],"map":[186],"tensors":[188],"from":[189],"manifold":[192],"local":[195],"tangent":[196],"space,":[197,201],"flat":[199],"vector":[200],"thus":[202],"statistical":[205],"information":[208],"in":[209,251],"dataset.":[211],"A":[212],"case":[213],"study":[214],"involving":[215],"steady-state":[216],"heat":[217],"conduction":[218],"with":[219,248],"anisotropic":[221],"conductivity":[222],"demonstrates":[223],"geometry-preserving":[225],"significantly":[228],"enhance":[229],"learning":[230],"performance":[231],"compared":[232],"multilayer":[235],"perceptrons":[236],"(MLPs).":[237],"These":[238],"findings":[239],"underscore":[240],"importance":[242],"manifold-aware":[244],"methods":[245],"when":[246],"working":[247],"tensor-valued":[249],"data":[250],"applications.":[253]},"counts_by_year":[],"updated_date":"2026-04-08T06:01:36.053099","created_date":"2026-04-04T00:00:00"}
