卷積神經(jīng)網(wǎng)絡(luò)機(jī)器學(xué)習(xí)外文文獻(xiàn)翻譯中英文2020

#卷積神經(jīng)網(wǎng)絡(luò)機(jī)器學(xué)習(xí)相關(guān)外文翻譯中英文2020英文Predictionofcompositemicrostructurestress-straincurvesusing

convolutionalneuralnetworksCharlesYang，YoungsooKim，SeunghwaRyu，GraceGuAbstractStress-straincurvesareanimportantrepresentationofamaterial'smechanicalproperties,fromwhichimportantpropertiessuchaselasticmodulus,strength,andtoughness,aredefined.However,generatingstress-straincurvesfromnumericalmethodssuchasfiniteelementmethod(FEM)iscomputationallyintensive,especiallywhenconsideringtheentirefailurepathforamaterial.Asaresult,itisdifficulttoperformhighthroughputcomputationaldesignofmaterialswithlargedesignspaces,especiallywhenconsideringmechanicalresponsesbeyondtheelasticlimit.Inthiswork,acombinationofprincipalcomponentanalysis(PCA)andconvolutionalneuralnetworks(CNN)areusedtopredicttheentirestress-strainbehaviorofbinarycompositesevaluatedovertheentirefailurepath,motivatedbythesignificantlyfasterinferencespeedofempiricalmodels.WeshowthatPCAtransformsthestress-straincurvesintoaneffectivelatentspacebyvisualizingtheeigenbasisofPCA.Despitehavingadatasetofonly10-27%ofpossiblemicrostructureconfigurations,themeanabsoluteerrorofthepredictionis<10%oftherangeofvaluesinthedataset,whenmeasuringmodelperformancebasedonderivedmaterialdescriptors,suchasmodulus,strength,andtoughness.Ourstudydemonstratesthepotentialtousemachinelearningtoacceleratematerialdesign,characterization,andoptimization.Keywords：Machinelearning，Convolutionalneuralnetworks，Mechanicalproperties，Microstructure，ComputationalmechanicsIntroductionUnderstandingtherelationshipbetweenstructureandpropertyformaterialsisaseminalprobleminmaterialscience,withsignificantapplicationsfordesigningnext-generationmaterials.Aprimary??*!?*!????/"*motivatingexampleisdesigningcompositemicrostructuresforload-bearingapplications,ascompositesofferadvantageouslyhighspecificstrengthandspecifictoughness.Recentadvancementsinadditivemanufacturinghavefacilitatedthefabricationofcomplexcompositestructures,andasaresult,avarietyofcomplexdesignshavebeenfabricatedandtestedvia3D-printingmethods.Whilemoreadvancedmanufacturingtechniquesareopeningupunprecedentedopportunitiesforadvancedmaterialsandnovelfunctionalities,identifyingmicrostructureswithdesirablepropertiesisadifficultoptimizationproblem.Onemethodofidentifyingoptimalcompositedesignsisbyconstructinganalyticaltheories.Forconventionalparticulate/fiber-reinforcedcomposites,avarietyofhomogenizationtheorieshavebeendevelopedtopredictthemechanicalpropertiesofcompositesasafunctionofvolumefraction,aspectratio,andorientationdistributionofreinforcements.Becausemanynaturalcomposites,synthesizedviaself-assemblyprocesses,haverelativelyperiodicandregularstructures,theirmechanicalpropertiescanbepredictediftheloadtransfermechanismofarepresentativeunitcellandtheroleoftheself-similarhierarchicalstructureareunderstood.However,theapplicabilityofanalyticaltheoriesislimitedinquantitativelypredictingcompositepropertiesbeyondtheelasticlimitinthepresenceofdefects,becausesuchtheoriesrelyontheconceptofrepresentativevolumeelement(RVE),astatisticalrepresentationofmaterialproperties,whereasthestrengthandfailureisdeterminedbytheweakestdefectintheentiresampledomain.Numericalmodelingbasedonfiniteelementmethods(FEM)cancomplementanalyticalmethodsforpredictinginelasticpropertiessuchasstrengthandtoughnessmodulus(referredtoastoughness,hereafter)whichcanonlybeobtainedfromfullstress-straincurves.However,numericalschemescapableofmodelingtheinitiationandpropagationofthecurvilinearcracks,suchasthecrackphasefieldmodel,arecomputationallyexpensiveandtime-consumingbecauseaveryfinemeshisrequiredtoaccommodatehighlyconcentratedstressfieldnearcracktipandtherapidvariationofdamageparameterneardiffusivecracksurface.Meanwhile,analyticalmodelsrequiresignificanthumaneffortanddomainexpertiseandfailtogeneralizetosimilardomainproblems.Inordertoidentifyhigh-performingcompositesinthemidstoflargedesignspaceswithinrealistictime-frames,weneedmodelsthatcanrapidlydescribethemechanicalpropertiesofcomplexsystemsandbegeneralizedeasilytoanalogoussystems.Machinelearningoffersthebenefitofextremelyfastinferencetimesandrequiresonlytrainingdatatolearnrelationshipsbetweeninputsandoutputse.g.,compositemicrostructuresandtheirmechanicalproperties.Machinelearninghasalreadybeenappliedtospeeduptheoptimizationofseveraldifferentphysicalsystems,includinggraphenekirigamicuts,fine-tuningspinqubitparameters,andprobemicroscopytuning.Suchmodelsdonotrequiresignificanthumaninterventionorknowledge,learnrelationshipsefficientlyrelativetotheinputdesignspace,andcanbegeneralizedtodifferentsystems.Inthispaper,weutilizeacombinationofprincipalcomponentanalysis(PCA)andconvolutionalneuralnetworks(CNN)topredicttheentirestress-straincurveofcompositefailuresbeyondtheelasticlimit.Stress-straincurvesarechosenasthemodel'stargetbecausetheyaredifficulttopredictgiventheirhighdimensionality.Inaddition,stress-straincurvesareusedtoderiveimportantmaterialdescriptorssuchasmodulus,strength,andtoughness.Inthissense,predictingstress-straincurvesisamoregeneraldescriptionofcompositespropertiesthananycombinationofscalermaterialdescriptors.Adatasetof100,000differentcompositemicrostructuresandtheircorrespondingstress-straincurvesareusedtotrainandevaluatemodelperformance.Duetothehighdimensionalityofthestress-straindataset,severaldimensionalityreductionmethodsareused,includingPCA,featuringablendofdomainunderstandingandtraditionalmachinelearning,tosimplifytheproblemwithoutlossofgeneralityforthemodel.Wewillfirstdescribeourmodelingmethodologyandtheparametersofourfinite-elementmethod(FEM)usedtogeneratedata.VisualizationsofthelearnedPCAlatentspacearethenpresented,alongwithmodelperformanceresults.CNNimplementationandtrainingAconvolutionalneuralnetworkwastrainedtopredictthislowerdimensionalrepresentationofthestressvector.TheinputtotheCNNwasabinarymatrixrepresentingthecompositedesign,with0'scorrespondingtosoftblocksand1'scorrespondingtostiffblocks.PCAwasimplementedwiththeopen-sourcePythonpackagescikit-learn,usingthedefaulthyperparameters.CNNwasimplementedusingKeraswithaTensorFlowbackend.Thebatchsizeforallexperimentswassetto16andthenumberofepochsto30;theAdamoptimizerwasusedtoupdatetheCNNweightsduringbackpropagation.Atrain/testsplitratioof95:5isused—wejustifyusingasmallerratiothanthestandard80:20becauseofarelativelylargedataset.Witharatioof95:5andadatasetwith100,000instances,thetestsetsizestillhasenoughdatapoints,roughlyseveralthousands,foritsresultstogeneralize.EachcolumnofthetargetPCA-representationwasnormalizedtohaveameanof0andastandarddeviationof1topreventinstabletraining.FiniteelementmethoddatagenerationFEMwasusedtogeneratetrainingdatafortheCNNmodel.Althoughinitiallyobtainedtrainingdataiscompute-intensive,ittakesmuchlesstimetotraintheCNNmodelandevenlesstimetomakehigh-throughputinferencesoverthousandsofnew,randomlygeneratedcomposites.Thecrackphasefieldsolverwasbasedonthehybridformulationforthequasi-staticfractureofelasticsolidsandimplementedinthecommercialFEMsoftwareABAQUSwithauser-elementsubroutine(UEL).VisualizingPCAInordertobetterunderstandtherolePCAplaysineffectivelycapturingtheinformationcontainedinstress-straincurves,theprincipalcomponentrepresentationofstress-straincurvesisplottedin3dimensions.Specifically,wetakethefirstthreeprincipalcomponents,whichhaveacumulativeexplainedvariance~85%,andplotstress-straincurvesinthatbasisandprovideseveraldifferentanglesfromwhichtoviewthe3Dplot.Eachpointrepresentsastress-straincurveinthePCAlatentspaceandiscoloredbasedontheassociatedmodulusvalue.itseemsthatthePCAisabletospreadoutthecurvesinthelatentspacebasedonmodulusvalues,whichsuggeststhatthisisausefullatentspaceforCNNtomakepredictionsin.CNNmodeldesignandperformanceOurCNNwasafullyconvolutionalneuralnetworki.e.theonlydenselayerwastheoutputlayer.Allconvolutionlayersused16filterswithastrideof1,withaLeakyReLUactivationfollowedbyBatchNormalization.Thefirst3Convblocksdidnothave2DMaxPooling,followedby9convblockswhichdidhavea2DMaxPoolinglayer,placedaftertheBatchNormalizationlayer.AGlobalAveragePoolingwasusedtoreducethedimensionalityoftheoutputtensorfromthesequentialconvolutionblocksandthefinaloutputlayerwasaDenselayerwith15nodes,whereeachnodecorrespondedtoaprincipalcomponent.Intotal,ourmodelhad26,319trainableweights.Ourarchitecturewasmotivatedbytherecentdevelopmentandconvergenceontofully-convolutionalarchitecturesfortraditionalcomputervisionapplications,whereconvolutionsareempiricallyobservedtobemoreefficientandstableforlearningasopposedtodenselayers.Inaddition,inourpreviouswork,wehadshownthatCNN'swereacapablearchitectureforlearningtopredictmechanicalpropertiesof2Dcomposites[30].Theconvolutionoperationisanintuitivelygoodfitforpredictingcrackpropagationbecauseitisalocaloperation,allowingittoimplicitlyfeaturizeandlearnthelocalspatialeffectsofcrackpropagation.AfterapplyingPCAtransformationtoreducethedimensionalityofthetargetvariable,CNNisusedtopredictthePCArepresentationofthestress-straincurveofagivenbinarycompositedesign.AftertrainingtheCNNonatrainingset,itsabilitytogeneralizetocompositedesignsithasnotseenisevaluatedbycomparingitspredictionsonanunseentestset.However,anaturalquestionthatemergesishowtoevaluateamodel'sperformanceatpredictingstress-straincurvesinareal-worldengineeringcontext.Whilesimplescalermetricssuchasmeansquarederror(MSE)andmeanabsoluteerror(MAE)generalizeeasilytovectortargets,itisnotclearhowtointerprettheseaggregatesummariesofperformance.Itisdifficulttousesuchmetricstoaskquestionssuchas“Isthismodelgoodenoughtouseintherealworld”and“Onaverage,howpoorlywillagivenpredictionbeincorrectrelativetosomegivenspecification”.Althoughbeingabletopredictstress-straincurvesisanimportantapplicationofFEMandahighlydesirablepropertyforanymachinelearningmodeltolearn,itdoesnoteasilylenditselftointerpretation.Specifically,thereisnosimplequantitativewaytodefinewhethertwostress-straincurvesare“close”or“simi-lwaro”rlduwniittsh.realGiventhatstress-straincurvesareoftentimesintermediaryrepresentationsofacompositepropertythatareusedtoderivemoremeaningfuldescriptorssuchasmodulus,strength,andtoughness,wedecidedtoevaluatethemodelinananalogousfashion.TheCNNpredictioninthePCAlatentspacerepresentationistransformedbacktoastress-straincurveusingPCA,andusedtoderivethepredictedmodulus,strength,andtoughnessofthecomposite.Thepredictedmaterialdescriptorsarethencomparedwiththeactualmaterialdescriptors.Inthisway,MSEandMAEnowhaveclearlyinterpretableunitsandmeanings.Theaverageperformanceofthemodelwithrespecttotheerrorbetweentheactualandpredictedmaterialdescriptorvaluesderivedfromstress-straincurvesarepresentedinTable.TheMAEformaterialdescriptorsprovidesaneasilyinterpretablemetricofmodelperformanceandcaneasilybeusedinanydesignspecificationtoprovideconfidenceestimatesofamodelprediction.Whencomparingthemeanabsoluteerror(MAE)totherangeofvaluestakenonbythedistributionofmaterialdescriptors,wecanseethattheMAEisrelativelysmallcomparedtotherange.TheMAEcomparedtotherangeis<10%forallmaterialdescriptors.Relativelytightconfidenceintervalsontheerrorindicatethatthismodelarchitectureisstable,themodelperformanceisnotheavilydependentoninitialization,andthatourresultsarerobusttodifferenttrain-testsplitsofthedata.FutureworkFutureworkincludescombiningempiricalmodelswithoptimizationalgorithms,suchasgradient-basedmethods,toidentifycompositedesignsthatyieldcomplementarymechanicalproperties.Theabilityofatrainedempiricalmodeltomakehigh-throughputpredictionsoverdesignsithasneverseenbeforeallowsforlargeparameterspaceoptimizationthatwouldbecomputationallyinfeasibleforFEM.Inaddition,weplantoexploredifferentvisualizationsofempiricalmodelsinaneffortto“openuptheblack-box”ofsuchmodels.Applyingmachinelearningtofinite-elementmethodsisarapidlygrowingfieldwiththepotentialtodiscovernovelnext-generationmaterialstailoredforavarietyofapplications.Wealsonotethattheproposedmethodcanbereadilyappliedtopredictotherphysicalpropertiesrepresentedinasimilarvectorizedformat,suchaselectron/phonondensityofstates,andsound/lightabsorptionspectrum.ConclusionInconclusion,weappliedPCAandCNNtorapidlyandaccuratelypredictthestress-straincurvesofcompositesbeyondtheelasticlimit.Indoingso,severalnovelmethodologicalapproachesweredeveloped,includingusingthederivedmaterialdescriptorsfromthestress-straincurvesasinterpretablemetricsformodelperformanceanddimensionalityreductiontechniquestostress-straincurves.Thismethodhasthepotentialtoenablecompositedesignwithrespecttomechanicalresponsebeyondtheelasticlimit,whichwaspreviouslycomputationallyinfeasible,andcangeneralizeeasilytorelatedproblemsoutsideofmicrostructuraldesignforenhancingmechanicalproperties.中文基于卷積神經(jīng)網(wǎng)絡(luò)的復(fù)合材料微結(jié)構(gòu)應(yīng)力-應(yīng)變曲線預(yù)測(cè)

查爾斯，吉姆，瑞恩，格瑞斯摘要應(yīng)力-應(yīng)變曲線是材料機(jī)械性能的重要代表，從中可以定義重要的性能，例如彈性模量，強(qiáng)度和韌性。但是，從數(shù)值方法（例如有限兀方法（FEM））生成應(yīng)力-應(yīng)變曲線的計(jì)算量很大，尤其是在考慮材料的整個(gè)失效路徑時(shí)。結(jié)果，難以對(duì)具有較大設(shè)計(jì)空間的材料進(jìn)行高通量計(jì)算設(shè)計(jì)，尤其是在考慮超出彈性極限的機(jī)械響應(yīng)時(shí)。在這項(xiàng)工作中，主成分分析（PCA）和卷積神經(jīng)網(wǎng)絡(luò)（CNN）的組合被用于預(yù)測(cè)在整個(gè)失效路徑上評(píng)估的二兀復(fù)合材料的整體應(yīng)力-應(yīng)變行為，這是由于經(jīng)驗(yàn)?zāi)Ｐ偷耐茢嗨俣蕊@著加快的緣故。我們展示了PCA通過可視化PCA的本征基礎(chǔ)將應(yīng)力-應(yīng)變曲線轉(zhuǎn)換為有效的潛在空間。盡管只有可能的微觀結(jié)構(gòu)配置的10-27％的數(shù)據(jù)集，但在基于派生的材料描述符（例如模量，強(qiáng)度）測(cè)量模型性能時(shí)，預(yù)測(cè)的平均絕對(duì)誤差小于數(shù)據(jù)集中值范圍的10％和韌性。我們的研究表明使用機(jī)器學(xué)習(xí)來加速材料設(shè)計(jì)，表征和優(yōu)化的潛力。關(guān)鍵詞：機(jī)器學(xué)習(xí)，卷積神經(jīng)網(wǎng)絡(luò)，力學(xué)性能，微觀結(jié)構(gòu)，計(jì)算力學(xué)引言理解材料的結(jié)構(gòu)與性能之間的關(guān)系是材料科學(xué)中的一個(gè)重要問題，在設(shè)計(jì)下一代材料方面有重要的應(yīng)用。一個(gè)主要的動(dòng)機(jī)示例是設(shè)計(jì)用于承重應(yīng)用的復(fù)合材料微結(jié)構(gòu)，因?yàn)閺?fù)合材料可提供有利的高比強(qiáng)度和比韌性。增材制造的最新進(jìn)展促進(jìn)了復(fù)雜復(fù)合結(jié)構(gòu)的制造，結(jié)果，通過3D打印方法制造并測(cè)試了各種復(fù)雜設(shè)計(jì)。盡管更先進(jìn)的制造技術(shù)為先進(jìn)的材料和新穎的功能性開辟了前所未有的機(jī)遇，但要確定具有所需性能的微結(jié)構(gòu)卻是一個(gè)困難的優(yōu)化問題。確定最佳組合設(shè)計(jì)的一種方法是構(gòu)建分析理論。對(duì)于常規(guī)的顆粒/纖維增強(qiáng)復(fù)合材料，已開發(fā)出多種均質(zhì)化理論來預(yù)測(cè)復(fù)合材料的機(jī)械性能隨增強(qiáng)材料的體積分?jǐn)?shù)，縱橫比和取向分布的變化。由于許多通過自組裝過程合成的天然復(fù)合材料具有相對(duì)周期性和規(guī)則的結(jié)構(gòu)，因此，如果了解代表性單位晶格的載荷傳遞機(jī)理和自相似分層結(jié)構(gòu)的作用，則可以預(yù)測(cè)其機(jī)械性能。但是，在存在缺陷的情況下，分析理論的應(yīng)用范圍僅限于定量預(yù)測(cè)超出彈性極限的復(fù)合材料性能，因?yàn)榇祟惱碚撘蕾囉诖眢w積元素（RVE）的概念，即材料性能的統(tǒng)計(jì)表示，而強(qiáng)度和強(qiáng)度失敗取決于整個(gè)樣本域中最弱的缺陷。基于有限元方法（FEM）的數(shù)值建?？梢匝a(bǔ)充用于預(yù)測(cè)非彈性屬性（例如強(qiáng)度和韌性模量，以下簡(jiǎn)稱韌性）的分析方法，這些方法只能從完整的應(yīng)力-應(yīng)變曲線獲得。但是，由于需要非常細(xì)的網(wǎng)格來適應(yīng)裂紋尖端附近的高度集中的應(yīng)力場(chǎng)，因此能夠模擬曲線裂紋的萌生和擴(kuò)展的數(shù)值模式（例如裂紋相場(chǎng)模型）在計(jì)算上是昂貴且費(fèi)時(shí)的。擴(kuò)散裂紋表面附近損傷參數(shù)的變化。同時(shí)，分析模型需要大量的人力和領(lǐng)域?qū)I(yè)知識(shí)，并且不能推廣到類似的領(lǐng)域問題。為了在現(xiàn)實(shí)的時(shí)間內(nèi)在大型設(shè)計(jì)空間中識(shí)別出高性能的復(fù)合材料，我們需要能夠快速描述復(fù)雜系統(tǒng)的機(jī)械性能并易于推廣到類似系統(tǒng)的模型。機(jī)器學(xué)習(xí)提供了極快的推理時(shí)間的優(yōu)勢(shì)，并且僅需訓(xùn)練數(shù)據(jù)即可學(xué)習(xí)輸入和輸出之間的關(guān)系，例如復(fù)合微結(jié)構(gòu)及其機(jī)械性能。機(jī)器學(xué)習(xí)已被應(yīng)用來加速幾個(gè)不同物理系統(tǒng)的優(yōu)化，包括石墨烯kirigami切割，微調(diào)自旋qubit參數(shù)和探針顯微鏡微調(diào)。這樣的模型不需要大量的人工干預(yù)或知識(shí)，不需要相對(duì)于輸入設(shè)計(jì)空間有效地學(xué)習(xí)關(guān)系，并且可以推廣到不同的系統(tǒng)。在本文中，我們結(jié)合主成分分析（PCA）和卷積神經(jīng)網(wǎng)絡(luò)（CNN）來預(yù)測(cè)超出彈性極限的復(fù)合材料破壞的整個(gè)應(yīng)力-應(yīng)變曲線。選擇應(yīng)力-應(yīng)變曲線作為模型的目標(biāo)，因?yàn)殍b于它們的高維數(shù)，它們很難預(yù)測(cè)。另外，應(yīng)力-應(yīng)變曲線用于導(dǎo)出重要的材料描述，如模量，強(qiáng)度和韌性。從這個(gè)意義上講，預(yù)測(cè)應(yīng)力-應(yīng)變曲線是比定標(biāo)器材料描述符的任何組合更全面的復(fù)合材料性能描述。100,000個(gè)不同的復(fù)合微結(jié)構(gòu)及其對(duì)應(yīng)的應(yīng)力-應(yīng)變曲線的數(shù)據(jù)集用于訓(xùn)練和評(píng)估模型性能。由于應(yīng)力-應(yīng)變數(shù)據(jù)集的高維性，因此使用了多種降維方法，包括PCA，該方法將領(lǐng)域理解和傳統(tǒng)機(jī)器學(xué)習(xí)相結(jié)合，從而簡(jiǎn)化了問題，而又不損失模型的一般性。我們將首先描述建模方法和用于生成數(shù)據(jù)的有限元方法（FEM）的參數(shù)。然后呈現(xiàn)學(xué)習(xí)到的PCA潛在空間的可視化以及模型性能結(jié)果。CNN的實(shí)施和培訓(xùn)卷積神經(jīng)網(wǎng)絡(luò)經(jīng)過訓(xùn)練可以預(yù)測(cè)應(yīng)力向量的這種較低維表示。CNN的輸入是代表復(fù)合設(shè)計(jì)的二進(jìn)制矩陣，其中0對(duì)應(yīng)于軟塊，而1對(duì)應(yīng)于硬塊。PCA是使用默認(rèn)的超參數(shù)通過開源Python軟件包scikit-learn實(shí)現(xiàn)的。CNN是使用Keras與TensorFlow后端實(shí)現(xiàn)的。所有實(shí)驗(yàn)的批次大小均設(shè)置為16，歷時(shí)數(shù)設(shè)置為30。Adam優(yōu)化器用于在反向傳播期間更新CNN權(quán)重。使用的火車/測(cè)試拆分比率為95：5-由于數(shù)據(jù)集相對(duì)較大，因此我們使用比標(biāo)準(zhǔn)80:20小的比率進(jìn)行驗(yàn)證。比率為95：5且具有100,000個(gè)實(shí)例的數(shù)據(jù)集，測(cè)試集大小仍然具有足夠的數(shù)據(jù)點(diǎn)（大約幾千個(gè)），以便將其結(jié)果推廣。將目標(biāo)PCA表示的每一列標(biāo)準(zhǔn)化為平均值為0，標(biāo)準(zhǔn)差為1，以防止訓(xùn)練不穩(wěn)定。有限元方法數(shù)據(jù)生成FEM用于生成CNN模型的訓(xùn)練數(shù)據(jù)。盡管最初獲得的訓(xùn)練數(shù)據(jù)是計(jì)算密集型的，但訓(xùn)練CNN模型所需的時(shí)間要少得多，并且可以對(duì)成千上萬個(gè)新的，隨機(jī)生成的復(fù)合物進(jìn)行高吞吐量推斷的時(shí)間更少。裂紋相場(chǎng)求解器基于用于彈性固體準(zhǔn)靜態(tài)斷裂的混合公式，并在帶有用戶元素子例程（UEL）的商業(yè)FEM軟件ABAQUS中實(shí)現(xiàn)。可視化PCA為了更好地理解PCA在有效捕獲應(yīng)力-應(yīng)變曲線中包含的信息中所起的作用，應(yīng)力-應(yīng)變曲線的主成分表示形式分為3維。具體來說，我們采用前三個(gè)主要成分，它們具有85％的累積解釋方差，并在此基礎(chǔ)上繪制應(yīng)力-應(yīng)變曲線，并提供幾個(gè)不同的角度來查看3D繪圖。每個(gè)點(diǎn)代表PCA潛在空間中的應(yīng)力-應(yīng)變曲線，并根據(jù)關(guān)聯(lián)的模量值進(jìn)行著色。似乎PCA能夠基于模量值在潛在空間中展開曲線，這表明這是CNN進(jìn)行預(yù)測(cè)的有用潛在空間。CNN模型設(shè)計(jì)與性能我們的CNN是一個(gè)全卷積神經(jīng)網(wǎng)絡(luò)，即唯一的密集層是輸出層。所有卷積層都使用16個(gè)步幅為1的濾波器，并激活LeakyReLU，然后進(jìn)行BatchNormalization。前三個(gè)Conv塊沒有2DMaxPooling，然后