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首页 SIAM Uncertainty Quantification.pdf

SIAM Uncertainty Quantification.pdf

SIAM Uncertainty Quantification…

上传者: 缄默浅读 2013-12-28 评分 0 0 0 0 0 0 暂无简介 简介 举报

简介:本文档为《SIAM Uncertainty Quantificationpdf》,可适用于高等教育领域,主题内容包含IntroductiontoUncertaintyQuantificationSIAMCSEConference,Miami,FL,Gianluca符等。

IntroductiontoUncertaintyQuantificationSIAMCSEConference,Miami,FL,GianlucaIaccarinoMichaelEldredAlirezaDoostanOmarGhattas"Ifamanwillbeginwithcertainties,heshallendindoubtsbutifhewillbecontenttobeginwithdoubts,heshallendincertainties"FBaconPlanfortheMiniTutorialAgendaGIaccarino:StanfordUniversityIntroductionandmotivationsMEldred:SANDIANationalLabNonintrusiveUQpropagationmethodsADoostan:StanfordUniversityIntrusiveUQpropagationmethodsOGhattas:UniversityofTexas,AustinBayesianmethodsforstatisticalinversionGIaccarino:StanfordUniversityNonprobabilisticmethodsandconclusiveremarksObjectivesIIntroduceUncertaintyQuantificationMethodologiesIDefinitionsandmotivationsIClassificationofvarioustechniquesIApplicationexamplesICharacterizemysteriousconceptssuchas:IpolynomialchaosIstochasticcollocationIsurrogatesamplingIepistemicuncertaintyIIIdentifytheresearchareasandtheconnectionstootherfieldsIConveythechallengesandtheopportunityinUQIPresentationsareatanintroductorylevelandwewillnottrytobecomprehensiveObjectivesIIntroduceUncertaintyQuantificationMethodologiesIDefinitionsandmotivationsIClassificationofvarioustechniquesIApplicationexamplesICharacterizemysteriousconceptssuchas:IpolynomialchaosIstochasticcollocationIsurrogatesamplingIepistemicuncertaintyIIIdentifytheresearchareasandtheconnectionstootherfieldsIConveythechallengesandtheopportunityinUQIPresentationsareatanintroductorylevelandwewillnottrytobecomprehensiveObjectivesIIntroduceUncertaintyQuantificationMethodologiesIDefinitionsandmotivationsIClassificationofvarioustechniquesIApplicationexamplesICharacterizemysteriousconceptssuchas:IpolynomialchaosIstochasticcollocationIsurrogatesamplingIepistemicuncertaintyIIIdentifytheresearchareasandtheconnectionstootherfieldsIConveythechallengesandtheopportunityinUQIPresentationsareatanintroductorylevelandwewillnottrytobecomprehensiveObjectivesIIntroduceUncertaintyQuantificationMethodologiesIDefinitionsandmotivationsIClassificationofvarioustechniquesIApplicationexamplesICharacterizemysteriousconceptssuchas:IpolynomialchaosIstochasticcollocationIsurrogatesamplingIepistemicuncertaintyIIIdentifytheresearchareasandtheconnectionstootherfieldsIConveythechallengesandtheopportunityinUQIPresentationsareatanintroductorylevelandwewillnottrytobecomprehensiveObjectivesIIntroduceUncertaintyQuantificationMethodologiesIDefinitionsandmotivationsIClassificationofvarioustechniquesIApplicationexamplesICharacterizemysteriousconceptssuchas:IpolynomialchaosIstochasticcollocationIsurrogatesamplingIepistemicuncertaintyIIIdentifytheresearchareasandtheconnectionstootherfieldsIConveythechallengesandtheopportunityinUQIPresentationsareatanintroductorylevelandwewillnottrytobecomprehensiveIntroductionMotivationsGianlucaIaccarinoDepartmentofMechanicalEngineeringInstituteforComputationalandMathematicalEngineering(ICME)StanfordUniversityCSEMinitutorialOnUncertaintyQuantificationMarch,Miami,FLWhyUncertaintyQuantificationWhyUncertaintyQuantificationUQforDecisionMakingIInspiteofthewidespreaduseofModelingandSimulation(MS)toolsitremainsdifficulttoprovideobjectiveconfidencelevelsinthequantitativeinformationobtainedfromnumericalpredictionsIThecomplexityarisesfromtheuncertaintiesrelatedtotheinputsofanycomputationattemptingtorepresentarealphysicalsystemIUseofMSpredictionsinhighimpactdecisionsrequirearigorousevaluationoftheconfidenceWhyUncertaintyQuantificationUQforDecisionMakingExample:hurricaneforecastingImagefromNOAAWhyUncertaintyQuantificationUQforValidationITheacceptedprocessofevaluatingMStoolsandsolutionsisbasedonthegeneralconceptofVerificationandValidation(VV)IThelaststepoftheprocessisinvariablybasedoncomparisonsbetweennumericalpredictionsandphysicalobservationsIPrecisequantificationoftheerrorsanduncertaintiesisrequiredtoestablishpredictivecapabilities:UQisakeyingredientofvalidation!WhyUncertaintyQuantificationUQforValidationExample:measurementsofthespeedoflight()ImagefromChristieetal,LosAlamosScience,#,WhyUncertaintyQuantificationUQforDesignOptimizationIArobustdesignisonewheresystemperformanceremainsrelativelyunchanged(stable)whenexposedtouncertaintiesintheoperatingconditionsIRobustdesignoptimizationisapowerfultoolformanagingthetradeoffsbetweenoptimalperformanceandperformancestabilityIAreliabilitybaseddesignisonewheretheprobabilityoffailureislessthansomeacceptablevalueWhyUncertaintyQuantificationUQforDesignOptimizationExample:wingshapeoptimizationImagefromTZang,WhyUncertaintyQuantificationSimplisticView:Errorbarsonthenumericalresults,justlikeexperimentsTheresultsprovideanintuitivenotionofconfidenceUnsteadyturbulentheatconvectionwithuncertainwallheatingConstantineIaccarino,OneimportantobjectiveofUQistomaketheintuitivenotionofconfidencemathematicallysound!WhyUncertaintyQuantificationSimplisticView:Errorbarsonthenumericalresults,justlikeexperimentsTheresultsprovideanintuitivenotionofconfidenceUnsteadyturbulentheatconvectionwithuncertainwallheatingConstantineIaccarino,OneimportantobjectiveofUQistomaketheintuitivenotionofconfidencemathematicallysound!DefinitionsVerificationandValidationDefinitionsTheAmericanInstituteforAeronauticsandAstronautics(AIAA)hasdevelopedthe“GuidefortheVerificationandValidation(VV)ofComputationalFluidDynamicsSimulations”()WhatisVVIVerification:Theprocessofdeterminingthatamodelimplementationaccuratelyrepresentsthedeveloper’sconceptualdescriptionofthemodelIValidationTheprocessofdeterminingthedegreetowhichamodelisanaccuraterepresentationoftherealworldfortheintendedusesofthemodelErrorsvsUncertaintiesDefinitionsTheAIAA“GuidefortheVerificationandValidation(VV)ofCFDSimulations”()definesIerrorsasrecognisabledeficienciesofthemodelsorthealgorithmsemployedIuncertaintiesasapotentialdeficiencythatisduetolackofknowledgeWhatistherelationwithVVIVerificationaimsatansweringthequestion“arewesolvingtheequationscorrectly”–itisanexerciseinmathematicsIValidationaimsatansweringthequestion“arewesolvingthecorrectequations”–itisanexerciseinphysicsErrorsvsUncertaintiesDefinitionsTheAIAA“GuidefortheVerificationandValidation(VV)ofCFDSimulations”()definesIerrorsasrecognisabledeficienciesofthemodelsorthealgorithmsemployedIuncertaintiesasapotentialdeficiencythatisduetolackofknowledgeWhatistherelationwithVVIVerificationaimsatansweringthequestion“arewesolvingtheequationscorrectly”–itisanexerciseinmathematicsIValidationaimsatansweringthequestion“arewesolvingthecorrectequations”–itisanexerciseinphysicsErrorsvsUncertaintiesDefinitionsTheAIAA“GuidefortheVerificationandValidation(VV)ofCFDSimulations”()definesIerrorsasrecognisabledeficienciesofthemodelsorthealgorithmsemployedIuncertaintiesasapotentialdeficiencythatisduetolackofknowledgeWhatistherelationwithVVIVerificationaimsatansweringthequestion“arewesolvingtheequationscorrectly”–itisanexerciseinmathematicsIValidationaimsatansweringthequestion“arewesolvingthecorrectequations”–itisanexerciseinphysicsErrorsvsUncertaintiesDefinitionsTheAIAA“GuidefortheVerificationandValidation(VV)ofCFDSimulations”()definesIerrorsasrecognisabledeficienciesofthemodelsorthealgorithmsemployedIuncertaintiesasapotentialdeficiencythatisduetolackofknowledgeWhatistherelationwithVVIVerificationaimsatansweringthequestion“arewesolvingtheequationscorrectly”–itisanexerciseinmathematicsIValidationaimsatansweringthequestion“arewesolvingthecorrectequations”–itisanexerciseinphysicsErrorsvsUncertaintiesDefinitionsTheAIAAdefinitionisnotveryprecise:itdoesnotclearlydistinguishbetweenthemathematicsandthephysicsIWhatareerrorserrorsareassociatedtothetranslationofamathematicalformulationintoanumericalalgorithmandacomputationalcodeIAcknowledgederrorsareknowntobepresentbuttheireffectontheresultsisdeemednegligible(roundoff,limitedconvergenceofiterativealgorithms)IUnacknowledgederrorsarenotrecognizablebutmightbepresent,egimplementationmistakes(bugs)IWhatareuncertaintiesuncertaintiesareassociatedtothespecificationoftheinputphysicalparametersrequiredforperformingtheanalysisI"anuncertaininputparameterwillleadnotonlytoanuncertainsolutionbuttoanuncertainsolutionerroraswell"Trucano,ErrorsvsUncertaintiesDefinitionsTheAIAAdefinitionisnotveryprecise:itdoesnotclearlydistinguishbetweenthemathematicsandthephysicsIWhatareerrorserrorsareassociatedtothetranslationofamathematicalformulationintoanumericalalgorithmandacomputationalcodeIAcknowledgederrorsareknowntobepresentbuttheireffectontheresultsisdeemednegligible(roundoff,limitedconvergenceofiterativealgorithms)IUnacknowledgederrorsarenotrecognizablebutmightbepresent,egimplementationmistakes(bugs)IWhatareuncertaintiesuncertaintiesareassociatedtothespecificationoftheinputphysicalparametersrequiredforperformingtheanalysisI"anuncertaininputparameterwillleadnotonlytoanuncertainsolutionbuttoanuncertainsolutionerroraswell"Trucano,ErrorsvsUncertaintiesDefinitionsTheAIAAdefinitionisnotveryprecise:itdoesnotclearlydistinguishbetweenthemathematicsandthephysicsIWhatareerrorserrorsareassociatedtothetranslationofamathematicalformulationintoanumericalalgorithmandacomputationalcodeIAcknowledgederrorsareknowntobepresentbuttheireffectontheresultsisdeemednegligible(roundoff,limitedconvergenceofiterativealgorithms)IUnacknowledgederrorsarenotrecognizablebutmightbepresent,egimplementationmistakes(bugs)IWhatareuncertaintiesuncertaintiesareassociatedtothespecificationoftheinputphysicalparametersrequiredforperformingtheanalysisI"anuncertaininputparameterwillleadnotonlytoanuncertainsolutionbuttoanuncertainsolutionerroraswell"Trucano,ErrorsvsUncertaintiesDefinitionsTheAIAAdefinitionisnotveryprecise:itdoesnotclearlydistinguishbetweenthemathematicsandthephysicsIWhatareerrorserrorsareassociatedtothetranslationofamathematicalformulationintoanumericalalgorithmandacomputationalcodeIAcknowledgederrorsareknowntobepresentbuttheireffectontheresultsisdeemednegligible(roundoff,limitedconvergenceofiterativealgorithms)IUnacknowledgederrorsarenotrecognizablebutmightbepresent,egimplementationmistakes(bugs)IWhatareuncertaintiesuncertaintiesareassociatedtothespecificationoftheinputphysicalparametersrequiredforperformingtheanalysisI"anuncertaininputparameterwillleadnotonlytoanuncertainsolutionbuttoanuncertainsolutionerroraswell"Trucano,UncertaintiesAleatory:itisthephysicalvariabilitypresentinthesystemoritsenvironmentIItisnotstrictlyduetoalackofknowledgeandcannotbereduced(alsoreferredtoasvariability,stochasticuncertaintyorirreducibleuncertainty)IItisnaturallydefinedinaprobabilisticframeworkIExamplesare:materialproperties,operatingconditionsmanufacturingtolerances,etcIInmathematicalmodelingitisalsostudiedasnoiseUncertaintiesAleatory:itisthephysicalvariabilitypresentinthesystemoritsenvironmentIItisnotstrictlyduetoalackofknowledgeandcannotbereduced(alsoreferredtoasvariability,stochasticuncertaintyorirreducibleuncertainty)IItisnaturallydefinedinaprobabilisticframeworkIExamplesare:materialproperties,operatingconditionsmanufacturingtolerances,etcIInmathematicalmodelingitisalsostudiedasnoiseUncertaintiesAleatory:itisthephysicalvariabilitypresentinthesystemoritsenvironmentIItisnotstrictlyduetoalackofknowledgeandcannotbereduced(alsoreferredtoasvariability,stochasticuncertaintyorirreducibleuncertainty)IItisnaturallydefinedinaprobabilisticframeworkIExamplesare:materialproperties,operatingconditionsmanufacturingtolerances,etcIInmathematicalmodelingitisalsostudiedasnoiseAleatoryUncertaintyManufacturingprocessCourtesyofNASAUncertaintiesEpistemic:itisapotentialdeficiencythatisduetoalackofknowledgeIItcanarisefromassumptionsintroducedinthederivationofthemathematicalmodel(itisalsocalledreducibleuncertaintyorincertitude)IExamplesare:turbulencemodelassumptionsorsurrogatechemicalmodelsIItisNOTnaturallydefinedinaprobabilisticframeworkICanleadtostrongbiasofthepredictionsUncertaintiesEpistemic:itisapotentialdeficiencythatisduetoalackofknowledgeIItcanarisefromassumptionsintroducedinthederivationofthemathematicalmodel(itisalsocalledreducibleuncertaintyorincertitude)IExamplesare:turbulencemodelassumptionsorsurrogatechemicalmodelsIItisNOTnaturallydefinedinaprobabilisticframeworkICanleadtostrongbiasofthepredictionsUncertaintiesEpistemic:itisapotentialdeficiencythatisduetoalackofknowledgeIItcanarisefromassumptionsintroducedinthederivationofthemathematicalmodel(itisalsocalledreducibleuncertaintyorincertitude)IExamplesare:turbulencemodelassumptionsorsurrogatechemicalmodelsIItisNOTnaturallydefinedinaprobabilisticframeworkICanleadtostrongbiasofthepredictionsEpistemicUncertaintyModeluncertaintyCBOPredictionsofdeficitasapercentageofGDPSource:CongressionalBudgetOfficeReduciblevsIrreducibleUncertaintyIEpistemicuncertaintycanbereducedbyincreasingourknowledge,egperformingmoreexperimentalinvestigationsandordevelopingnewphysicalmodelsIAleatoryuncertaintycannotbereducedasitarisesnaturallyfromobservationsofthesystemAdditionalexperimentscanonlybeusedtobettercharacterizethevariabilitySensitivityAnalysisvsUQISensitivityanalysis(SA)investigatestheconnectionbetweeninputsandoutputsofa(computational)modelITheobjectiveofSAistoidentifyhowthevariabilityinanoutputquantityofinterest(q)isconnectedtoaninput(ξ)inthemodeltheresultisasensitivityderivativeqξISAallowstobuildarankingoftheinputsourceswhichmightdominatetheresponseofthesystemINotethatstronglargesensitivitiesderivativesdonotnecessarilytranslateincriticaluncertaintiesbecausetheinputvariabilitymightbeverysmallinaspecificdeviceofinterestComputationsUnderUncertaintyUncertaintyQuantificationComputationalFrameworkConsideragenericcomputationalmodel(y<dwithdlarge)HowdowehandletheuncertaintiesDataassimilation:characterizeuncertaintiesintheinputsUncertaintypropagation:performsimulationsaccountingfortheidentifieduncertaintiesCertification:establishacceptancecriteriaforpredictionsUncertaintyQuantificationComputationalFrameworkConsideragenericcomputationalmodel(y<dwithdlarge)HowdowehandletheuncertaintiesDataassimilation:characterizeuncertaintiesintheinputsUncertaintypropagation:performsimulationsaccountingfortheidentifieduncertaintiesCertification:establishacceptancecriteriaforpredictionsUncertaintyQuantificationComputationalFrameworkConsideragenericcomputationalmodel(y<dwithdlarge)HowdowehandletheuncertaintiesDataassimilation:characterizeuncertaintiesintheinputsUncertaintypropagation:performsimulationsaccountingfortheidentifieduncertaintiesCertification:establishacceptancecriteriaforpredictionsUncertaintyQuantificationComputationalFrameworkConsideragenericcomputationalmodel(y<dwithdlarge)HowdowehandletheuncertaintiesDataassimilation:characterizeuncertaintiesintheinputsUncertaintypropagation:performsimulationsaccountingfortheidentifieduncertaintiesCertification:establishacceptancecriteriaforpredictionsUncertaintyQuantificationComputationalFrameworkConsideragenericcomputationalmodel(y<dwithdlarge)HowdowehandletheuncertaintiesDataassimilation:characterizeuncertaintiesintheinputsUncertaintypropagation:performsimulationsaccountingfortheidentifieduncertaintiesCertification:establishacceptancecriteriaforpredictionsDataassimilationTheobjectiveischaracterizeuncertaintiesinsimulationinputs,basedonavailableinformationIDatasourcesExperimentalobservationsTheoreticalargumentsExpertopinionsetcIMathematicalframeworkfordataassimilationIMethodsareafunctionoftheamountofdataavailableDatarichenvironments:egstockmarketSparsedataenvironments:egplanetaryexplorationIinference:determinationofthestatisticalinputparametersthatbestrepresenttheavailableinformationIBayesianinversion::OGhattasDataassimilationTheobjectiveischaracterizeuncertaintiesinsimulationinputs,basedonavailableinformationIDatasourcesExperimentalobservationsTheoreticalargumentsExpertopinionsetcIMathematicalframeworkfordataassimilationIMethodsareafunctionoftheamountofdataavailableDatarichenvironments:egstockmarketSparsedataenvironments:egplanetaryexplorationIinference:determinationofthestatisticalinputparametersthatbestrepresenttheavailableinformationIBayesianinversion::OGhattasDataassimilationTheobjectiveischaracterizeuncertaintiesinsimulationinputs,basedonavailableinformationIDatasourcesExperimentalobservationsTheoreticalargumentsExpertopinionsetcIMathematicalframeworkfordataassimilationIMethodsareafunctionoftheamountofdataavailableDatarichenvironments:egstockmarketSparsedataenvironments:egplanetaryexplorationIinference:determinationofthestatisticalinputparametersthatbestrepresenttheavailableinformationIBayesianinversion::OGhattasDataassimilationTheobjectiveischaracterizeuncertaintiesinsimulationinputs,basedonavailableinformationIDatasourcesExperimentalobservationsTheoreticalargumentsExpertopinionsetcIMathematicalframeworkfordataassimilationIMethodsareafunctionoftheamou

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