报告摘要：RecentworkinthestudyofdynamicsystemshasfocussedondatadrivendecompositiontechniquesthatapproximatetheactionoftheKoopmanoperatoronobservablefunctionsoftheunderlyingphenomena.Inparticular,thedatadrivenmethodofdynamicmodedecomposition(DMD)hasbeenexplored,withmultiplevariantsofthealgorithminexistence,includingextendedDMD,DMDinreproducingkernelHilbertspaces,aBayesianframework,avariantforstochasticdynamicalsystems,andavariantthatusesdeepneuralnetworks.Inthistalk,IshallbrieflysummarizethelargeexistingworkondatadrivenlearningofKoopmanoperatormodels,andthendescribenewsamplingbasedsketchingapproachesSketchyCoreSVD,SketchyCoreTucker)togetherwithmatrix-valuedKernels,toachieveadeeplearningarchitectureforacceleratedKoopmanoperatorapproximationsofynamicobservabledata.Examplesaredrawnfromremotesensing,bio-medicalcardiacmagneticresonancevideo,andtimeseriesreactiveflowsimulationsofasinglejectorcombustionprocess.报告人简介：ChandrajitBajajisthedirectoroftheCenterforComputationalVisualization,intheOdenInstituteforComputationalandEngineeringSciencesandaProfessorofComputerSciencesattheUniversityofTexasatAustin.BajajholdstheComputationalAppliedMathematicsChairinVisualization.HeisalsoanaffiliatefacultymemberofMathematics,ComputationalNeuroscienceandElectricalEngineering.HeiscurrentlyontheeditorialboardsfortheInternationalJournalofComputationalGeometryandApplications,andtheACMComputingSurveys,andpasteditorialmemberoftheSIAMJournalonImagingSciences.HewasawardedadistinguishedalumnusawardfromtheIndianInstituteofTechnology,Delhi,(IIT,Delhi).HeisalsoaFellowofTheAmericanAssociationfortheAdvancementofScience(AAAS),FellowoftheAssociationforComputingMachinery(ACM),FellowoftheInstituteofElectricalandElectronicEngineers(IEEE),andFellowoftheSocietyofIndustrialandAppliedMathematics(SIAM).Homepage:http://www.cs.utexas.edu/~bajaj