卷积神经网络机器学习外文文献翻译中英文2020.docx

卷积神经网络机器学习外文文献翻译中英文2020.docx

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卷积神经网络机器学习相关外文翻译中英文2020

英文

Predictionofcompositemicrostructurestress-straincurvesusing

convolutionalneuralnetworks

CharlesYang,YoungsooKim,SeunghwaRyu,GraceGuAbstract

Stress-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,Computationalmechanics

Introduction

Understandingtherelationshipbetweenstructureandpropertyformaterialsisaseminalprobleminmaterialscience,withsignificantapplicationsfordesigningnext-generationmaterials.Aprimarymotivatingexampleisdesigningcompositemicrostructuresforload-bearingapplications,ascompositesofferadvantageouslyhighspecificstrengthandspecifictoughness.Recentadvancementsinadditivemanufacturinghavefacilitatedthefabricationofcomplexcompositestructures,andasaresult,avarietyofcomplexdesignshavebeenfabricatedandtestedvia3D-printingmethods.Whilemoreadvancedmanufacturingtechniquesareopeningupunprecedentedopportunitiesforadvancedmaterialsandnovelfunctionalities,identifyingmicrostructureswithdesirablepropertiesisadifficultoptimizationproblem.

Onemethodofidentifyingoptimalcompositedesignsisbyconstructinganalyticaltheories.Forconventionalparticulate/fiber-reinforcedcomposites,avarietyofhomogenizationtheorieshavebeendevelopedtopredictthemechanicalpropertiesofcompositesasafunctionofvolumefraction,aspectratio,andorientationdistributionofreinforcements.Becausemanynaturalcomposites,synthesizedviaseif-assemblyprocesses,haverelativelyperiodicandregularstructures,theirmechanicalpropertiescanbepredictediftheloadtransfermechanismofarepresentativeunitcellandtheroleoftheself-similarhierarchicalstructureareunderstood.However,theapplicabilityofanalyticaltheoriesislimitedinquantitativelypredictingcompositepropertiesbeyondtheelasticlimitinthepresenceofdefects,becausesuchtheoriesrelyontheconceptofrepresentativevolumeelement（RVE）,astatisticalrepresentationofmaterialproperties,whereasthestrengthandfailureisdeterminedbytheweakestdefectintheentiresampledomain.Numericalmodelingbasedonfiniteelementmethods（FEM）cancomplementanalyticalmethodsforpredictinginelasticpropertiessuchasstrengthandtoughnessmodulus（referredtoastoughness,hereafter）whichcanonlybeobtainedfromfullstress-straincurves.

However,numericalschemescapableofmodelingtheinitiationandpropagationofthecurvilinearcracks,suchasthecrackphasefieldmodel,arecomputationallyexpensiveandtime-consumingbeeauseaveryfinemeshisrequiredtoaccommodatehighlyconcentratedstressfieldnearcracktipandtherapidvariationofdamageparameterneardiffusivecracksurface.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,predietingstress-straincurvesisamoregeneraldescriptionofcompositespropertiesthananycombinationofscalermaterialdescriptors.Adatasetof100,000differentcompositemicrostructuresandtheircorrespondingstress-straincurvesareusedtotrainandevaluatemodelperformance.Duetothehighdimensionalityofthestress-straindataset,severaldimensionalityreductionmethodsareused,includingPCA,featuringablendofdomainunderstandingandtraditionalmachinelearning,tosimplifytheproblemwithoutlossofgeneralityforthemodel.

Wewillfirstdescribeourmodelingmethodologyandtheparametersofourfinite-elementmethod（FEM）usedtogeneratedata.VisualizationsofthelearnedPCAlatentspacearethenpresented,alongwithmodelperformanceresults.

CNNimplementationandtraining

Aconvolutionalneuralnetworkwastrainedtopredictthislowerdimensionalrepresentationofthestressvector.TheinputtotheCNNwasabinarymatrixrepresentingthecompositedesign,with0'scorrespondingtosoftblocksandl'scorrespondingtostiffblocks.PCAwasimplementedwiththeopen-sourcePythonpackagescikit-learn,usingthedefaulthyperparameters.CNNwasimplementedusingKeraswithaTensorFlowbackend.Thebatchsizeforallexperimentswassetto16andthenumberofepochsto30;theAdamoptimizerwasusedtoupdatetheCNNweightsduringbackpropagation.

Atrain/testsplitratioof95:

5isused—wejustifyusingasmallerratiothanthestandard80:

20becauseofarelativelylargedataset.Witharatioof95:

5andadatasetwith100,000instances,thetestsetsizestillhasenoughdatapoints,roughlyseveralthousands,foritsresultstogeneralize.EachcolumnofthetargetPCA-representationwasnormalizedtohaveameanof0andastandarddeviationof1topreventinstabletraining.

Finiteelementmethoddatageneration

FEMwasusedtogeneratetrainingdatafortheCNNmodel.Althoughinitiallyobtainedtrainingdataiscompute-intensive,ittakesmuchlesstimetotraintheCNNmodelandevenlesstimetomakehigh-throughputinferencesoverthousandsofnew,randomlygeneratedcomposites.Thecrackphasefieldsolverwasbasedonthehybridformulationforthequasi-staticfractureofelasticsolidsandimplementedinthecommercialFEMsoftwareABAQUSwithauser-elementsubroutine（UEL）.

VisualizingPCA

InordertobetterunderstandtherolePCAplaysineffectivelycapturingtheinformationcontainedinstress-straincurves,theprincipalcomponentrepresentationofstress-straincurvesisplottedin3dimensions.Specifically,wetakethefirstthreeprincipalcomponents,whichhaveacumulativeexplainedvariance-85%,andplotstress-straincurvesinthatbasisandprovideseveraldifferentanglesfromwhichtoviewthe3Dplot.Eachpointrepresentsastress-straincurveinthePCAlatentspaceandiscoloredbasedontheassociatedmodulusvalue,itseemsthatthePCAisabletospreadoutthecurvesinthelatentspacebasedonmodulusvalues,whichsuggeststhatthisisausefullatentspaceforCNNtomakepredictionsin.

CNNmodeldesignandperformance

OurCNNwasafullyconvolutionalneuralnetworki.e.theonlydenselayerwastheoutputlayer.Allconvolutionlayersused16filterswithastrideof1,withaLeakyReLUactivationfollowedbyBatchNormalization.Thefirst3Convblocksdidnothave2DMaxPooling,followedby9convblockswhichdidhavea2DMaxPoolinglayer,placedaftertheBatchNormalizationlayer.AGlobalAveragePoolingwasusedtoreducethedimensionalityoftheoutputtensorfromthesequentialconvolutionblocksandthefinaloutputlayerwasaDenselayerwith15nodes,whereeachnodecorrespondedtoaprincipalcomponent.Intotal,ourmodelhad26,319trainable

weights.

Ourarchitecturewasmotivatedbytherecentdevelopmentandconvergenceontofully-convolutionalarchitecturesfortraditionalcomputervisionapplications,whereconvolutionsareempiricallyobservedtobemoreefficientandstableforlearningasopposedtodenselayers.Inaddition,inourpreviouswork,wehadshownthatCNN'swereacapablearchitecturefor