Lecture25-SurrogateModeling

1ASE6002:SystemsDesignandAnalysis2008-2012Copyright©GeorgiaTech.AllRightsReserved.Module:OptimizationinDesignLecture:SurrogateModelingChrisParedisMBSEModel-BasedSystemsEngineeringCenter2ASE6002:SystemsDesignandAnalysis2008-2012Copyright©GeorgiaTech.AllRightsReserved.LectureOverview
Motivatingquestions:–WhatareSurrogateModels?–Whyaretheyimportant?–Whenshouldtheybeused?
KindsofSurrogateModels(akaresponsesurfacemodelsormeta-models)–PolynomialFits—LinearRegression–ArtificialNeuralNetworks–RadialBasisFunctions–KrigingInterpolation
CreatingSurrogateModelsinModelCenter3ASE6002:SystemsDesignandAnalysis2008-2012Copyright©GeorgiaTech.AllRightsReserved.Introduction&Motivation
Assumethat
=istheresultofarelativelycomplexandexpensivesimulation(e.g.1minuteperexecution)
Further,assumeisuncertainxyAssume1,000iterationsinoptimizationand10,000iterationsperMonte-Carlosimulation…⇒10millionminutes=19yearsofruntime!!!Whatarethecomputationalrequirements?4ASE6002:SystemsDesignandAnalysis2008-2012Copyright©GeorgiaTech.AllRightsReserved.SurrogateModels
Whatisit?Amathematicallytractablecomputationalmodelthatapproximatestheunderlying(simulation)model
Whydoesitwork?–Costofapproxcostofunderlyingmodel–Iftheunderlyingmodelissmooth,thenfewdatapointsareneededtoapproximatethemodelwelleverywherexyE.g.replacethesimulationmodelwithapolynomial:0.2µsperevaluation⇒2secondsruntimeintotal!5ASE6002:SystemsDesignandAnalysis2008-2012Copyright©GeorgiaTech.AllRightsReserved.KindsofSurrogateModels
Fitting:surrogateisapproximationevenatdatapoints–PolynomialFits—LinearRegression–ArtificialNeuralNetworks–…
Interpolation:surrogateisexactatdatapoints–RadialBasisFunctions–KrigingInterpolation–…Let’stakeacloserlookatsomeofthese…6ASE6002:SystemsDesignandAnalysis2008-2012Copyright©GeorgiaTech.AllRightsReserved.051015051015xy=f(x)polynomialfitofdegree1PolynomialFit—LinearRegression
Fitbecomesincreasingoscillatoryasdegreeincreases
Forlargedegrees,averylargenumberofpointsareneeded
Goodformodelinggeneraltrendsinnoisydata
NOTGOODforapproximatingdesignobjectivesPolynomialofdegree17ASE6002:SystemsDesignandAnalysis2008-2012Copyright©GeorgiaTech.AllRightsReserved.051015051015xy=f(x)polynomialfitofdegree2PolynomialFit—LinearRegression
Fitbecomesincreasingoscillatoryasdegreeincreases
Forlargedegrees,averylargenumberofpointsareneeded
Goodformodelinggeneraltrendsinnoisydata
NOTGOODforapproximatingdesignobjectivesPolynomialofdegree28ASE6002:SystemsDesignandAnalysis2008-2012Copyright©GeorgiaTech.AllRightsReserved.051015051015xy=f(x)polynomialfitofdegree3PolynomialFit—LinearRegression
Fitbecomesincreasingoscillatoryasdegreeincreases
Forlargedegrees,averylargenumberofpointsareneeded
Goodformodelinggeneraltrendsinnoisydata
NOTGOODforapproximatingdesignobjectivesPolynomialofdegree39ASE6002:SystemsDesignandAnalysis2008-2012Copyright©GeorgiaTech.AllRightsReserved.051015051015xy=f(x)polynomialfitofdegree4PolynomialFit—LinearRegression
Fitbecomesincreasingoscillatoryasdegreeincreases
Forlargedegrees,averylargenumberofpointsareneeded
Goodformodelinggeneraltrendsinnoisydata
NOTGOODforapproximatingdesignobjectivesPolynomialofdegree410ASE6002:SystemsDesignandAnalysis2008-2012Copyright©GeorgiaTech.AllRightsReserved.051015051015xy=f(x)polynomialfitofdegree5PolynomialFit—LinearRegression
Fitbecomesincreasingoscillatoryasdegreeincreases
Forlargedegrees,averylargenumberofpointsareneeded
Goodformodelinggeneraltrendsinnoisydata
NOTGOODforapproximatingdesignobjectivesPolynomialofdegree511ASE6002:SystemsDesignandAnalysis2008-2012Copyright©GeorgiaTech.AllRightsReserved.051015051015xy=f(x)polynomialfitofdegree6PolynomialFit—LinearRegression
Fitbecomesincreasingoscillatoryasdegreeincreases
Forlargedegrees,averylargenumberofpointsareneeded
Goodformodelinggeneraltrendsinnoisydata
NOTGOODforapproximatingdesignobjectivesPolynomialofdegree612ASE6002:SystemsDesignandAnalysis2008-2012Copyright©GeorgiaTech.AllRightsReserved.051015051015xy=f(x)polynomialfitofdegree7PolynomialFit—LinearRegression
Fitbecomesincreasingoscillatoryasdegreeincreases
Forlargedegrees,averylargenumberofpointsareneeded
Goodformodelinggeneraltrendsinnoisydata
NOTGOODforapproximatingdesignobjectivesPolynomialofdegree713ASE6002:SystemsDesignandAnalysis2008-2012Copyright©GeorgiaTech.AllRightsReserved.051015051015xy=f(x)polynomialfitofdegree8PolynomialFit—LinearRegression
Fitbecomesincreasingoscillatoryasdegreeincreases
Forlargedegrees,averylargenumberofpointsareneeded
Goodformodelinggeneraltrendsinnoisydata
NOTGOODforapproximatingdesignobjectivesPolynomialofdegree814ASE6002:SystemsDesignandAnalysis2008-2012Copyright©GeorgiaTech.AllRightsReserved.PolynomialFit—LinearRegression
Fitbecomesincreasingoscillatoryasdegreeincreases
Forlargedegrees,averylargenumberofpointsareneeded
Goodformodelinggeneraltrendsinnoisydata
NOTGOODforapproximatingdesignobjectives051015051015xy=f(x)polynomialfitofdegree9Polynomialofdegree915ASE6002:SystemsDesignandAnalysis2008-2012Copyright©GeorgiaTech.AllRightsReserved.KindsofSurrogateModels
Fitting:surrogateisappr