Large-Scale Inverse Problems and Quantification of Uncertainty

Thisbookfocusesoncomputationalmethodsforlarge-scalestatisticalinverseproblemsandprovidesanintroductiontostatisticalBayesianandfrequentistmethodologies.Recentresearchadvancesforapproximationmethodsarediscussed,alongwithKalmanfilteringmethodsandoptimization-basedapproachestosolvinginverseproblems.Theaimistocross-fertilizetheperspectivesofresearchersintheareasofdataassimilation,statistics,large-scaleoptimization,appliedandcomputationalmathematics,highperformancecomputing,andcutting-edgeapplications.Thesolutiontolarge-scaleinverseproblemscriticallydependsonmethodstoreducecomputationalcost.Recentresearchapproachestacklethischallengeinavarietyofdifferentways.Manyofthecomputationalframeworkshighlightedinthisbookbuilduponstate-of-the-artmethodsforsimulationoftheforwardproblem,suchas,fastPartialDifferentialEquation(PDE)solvers,reduced-ordermodelsandemulatorsoftheforwardproblem,stochasticspectralapproximations,andensemble-basedapproximations,aswellasexploitingthemachineryforlarge-scaledeterministicoptimizationthroughadjointandothersensitivityanalysismethods.KeyFeatures:•Bringstogethertheperspectivesofresearchersinareasofinverseproblemsanddataassimilation.•Assessesthecurrentstate-of-the-artandidentifyneedsandopportunitiesforfutureresearch.•Focusesonthecomputationalmethodsusedtoanalyzeandsimulateinverseproblems.•Writtenbyleadingexpertsofinverseproblemsanduncertaintyquantification.Graduatestudentsandresearchersworkinginstatistics,mathematicsandengineeringwillbenefitfromthisbook.