Lecture25-SurrogateModeling

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2020-07-14

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1ASE6002:SystemsDesignandAnalysis2008-2012Copyright©GeorgiaTech.AllRightsReserved.Module:OptimizationinDesignLecture:SurrogateModelingChrisParedisMBSEModel-BasedSystemsEngineeringCenter2ASE6002:SystemsDesignandAnalysis2008-2012Copyright©GeorgiaTech.AllRightsReserved.LectureOverviewMotivatingquestions:–WhatareSurrogateModels?–Whyaretheyimportant?–Whenshouldtheybeused?KindsofSurrogateModels(akaresponsesurfacemodelsormeta-models)–PolynomialFits—LinearRegression–ArtificialNeuralNetworks–RadialBasisFunctions–KrigingInterpolationCreatingSurrogateModelsinModelCenter3ASE6002:SystemsDesignandAnalysis2008-2012Copyright©GeorgiaTech.AllRightsReserved.Introduction&MotivationAssumethat=istheresultofarelativelycomplexandexpensivesimulation(e.g.1minuteperexecution)Further,assumeisuncertainxyAssume1,000iterationsinoptimizationand10,000iterationsperMonte-Carlosimulation…⇒10millionminutes=19yearsofruntime!!!Whatarethecomputationalrequirements?4ASE6002:SystemsDesignandAnalysis2008-2012Copyright©GeorgiaTech.AllRightsReserved.SurrogateModelsWhatisit?Amathematicallytractablecomputationalmodelthatapproximatestheunderlying(simulation)modelWhydoesitwork?–Costofapproxcostofunderlyingmodel–Iftheunderlyingmodelissmooth,thenfewdatapointsareneededtoapproximatethemodelwelleverywherexyE.g.replacethesimulationmodelwithapolynomial:0.2µsperevaluation⇒2secondsruntimeintotal!5ASE6002:SystemsDesignandAnalysis2008-2012Copyright©GeorgiaTech.AllRightsReserved.KindsofSurrogateModelsFitting:surrogateisapproximationevenatdatapoints–PolynomialFits—LinearRegression–ArtificialNeuralNetworks–…Interpolation:surrogateisexactatdatapoints–RadialBasisFunctions–KrigingInterpolation–…Let’stakeacloserlookatsomeofthese…6ASE6002:SystemsDesignandAnalysis2008-2012Copyright©GeorgiaTech.AllRightsReserved.051015051015xy=f(x)polynomialfitofdegree1PolynomialFit—LinearRegressionFitbecomesincreasingoscillatoryasdegreeincreasesForlargedegrees,averylargenumberofpointsareneededGoodformodelinggeneraltrendsinnoisydataNOTGOODforapproximatingdesignobjectivesPolynomialofdegree17ASE6002:SystemsDesignandAnalysis2008-2012Copyright©GeorgiaTech.AllRightsReserved.051015051015xy=f(x)polynomialfitofdegree2PolynomialFit—LinearRegressionFitbecomesincreasingoscillatoryasdegreeincreasesForlargedegrees,averylargenumberofpointsareneededGoodformodelinggeneraltrendsinnoisydataNOTGOODforapproximatingdesignobjectivesPolynomialofdegree28ASE6002:SystemsDesignandAnalysis2008-2012Copyright©GeorgiaTech.AllRightsReserved.051015051015xy=f(x)polynomialfitofdegree3PolynomialFit—LinearRegressionFitbecomesincreasingoscillatoryasdegreeincreasesForlargedegrees,averylargenumberofpointsareneededGoodformodelinggeneraltrendsinnoisydataNOTGOODforapproximatingdesignobjectivesPolynomialofdegree39ASE6002:SystemsDesignandAnalysis2008-2012Copyright©GeorgiaTech.AllRightsReserved.051015051015xy=f(x)polynomialfitofdegree4PolynomialFit—LinearRegressionFitbecomesincreasingoscillatoryasdegreeincreasesForlargedegrees,averylargenumberofpointsareneededGoodformodelinggeneraltrendsinnoisydataNOTGOODforapproximatingdesignobjectivesPolynomialofdegree410ASE6002:SystemsDesignandAnalysis2008-2012Copyright©GeorgiaTech.AllRightsReserved.051015051015xy=f(x)polynomialfitofdegree5PolynomialFit—LinearRegressionFitbecomesincreasingoscillatoryasdegreeincreasesForlargedegrees,averylargenumberofpointsareneededGoodformodelinggeneraltrendsinnoisydataNOTGOODforapproximatingdesignobjectivesPolynomialofdegree511ASE6002:SystemsDesignandAnalysis2008-2012Copyright©GeorgiaTech.AllRightsReserved.051015051015xy=f(x)polynomialfitofdegree6PolynomialFit—LinearRegressionFitbecomesincreasingoscillatoryasdegreeincreasesForlargedegrees,averylargenumberofpointsareneededGoodformodelinggeneraltrendsinnoisydataNOTGOODforapproximatingdesignobjectivesPolynomialofdegree612ASE6002:SystemsDesignandAnalysis2008-2012Copyright©GeorgiaTech.AllRightsReserved.051015051015xy=f(x)polynomialfitofdegree7PolynomialFit—LinearRegressionFitbecomesincreasingoscillatoryasdegreeincreasesForlargedegrees,averylargenumberofpointsareneededGoodformodelinggeneraltrendsinnoisydataNOTGOODforapproximatingdesignobjectivesPolynomialofdegree713ASE6002:SystemsDesignandAnalysis2008-2012Copyright©GeorgiaTech.AllRightsReserved.051015051015xy=f(x)polynomialfitofdegree8PolynomialFit—LinearRegressionFitbecomesincreasingoscillatoryasdegreeincreasesForlargedegrees,averylargenumberofpointsareneededGoodformodelinggeneraltrendsinnoisydataNOTGOODforapproximatingdesignobjectivesPolynomialofdegree814ASE6002:SystemsDesignandAnalysis2008-2012Copyright©GeorgiaTech.AllRightsReserved.PolynomialFit—LinearRegressionFitbecomesincreasingoscillatoryasdegreeincreasesForlargedegrees,averylargenumberofpointsareneededGoodformodelinggeneraltrendsinnoisydataNOTGOODforapproximatingdesignobjectives051015051015xy=f(x)polynomialfitofdegree9Polynomialofdegree915ASE6002:SystemsDesignandAnalysis2008-2012Copyright©GeorgiaTech.AllRightsReserved.KindsofSurrogateModelsFitting:surrogateisappr