{"product_id":"large-scale-inverse-problems-and-quantification-of-uncertainty-isbn-9780470697436","title":"Large-Scale Inverse Problems and Quantification of Uncertainty","description":"This book focuses on computational methods for large-scale statistical inverse problems and provides an introduction to statistical Bayesian and frequentist methodologies. Recent research advances for approximation methods are discussed, along with Kalman filtering methods and optimization-based approaches to solving inverse problems. The aim is to cross-fertilize the perspectives of researchers in the areas of data assimilation, statistics, large-scale optimization, applied and computational mathematics, high performance computing, and cutting-edge applications. \u003cp\u003eThe solution to large-scale inverse problems critically depends on methods to reduce computational cost. Recent research approaches tackle this challenge in a variety of different ways. Many of the computational frameworks highlighted in this book build upon state-of-the-art methods for simulation of the forward problem, such as, fast Partial Differential Equation (PDE) solvers, reduced-order models and emulators of the forward problem, stochastic spectral approximations, and ensemble-based approximations, as well as exploiting the machinery for large-scale deterministic optimization through adjoint and other sensitivity analysis methods.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eKey Features:\u003c\/b\u003e\u003c\/p\u003e \u003cul\u003e \u003cli\u003eBrings together the perspectives of researchers in areas of inverse problems and data assimilation.\u003c\/li\u003e \u003cli\u003eAssesses the current state-of-the-art and identify needs and opportunities for future research.\u003c\/li\u003e \u003cli\u003eFocuses on the computational methods used to analyze and simulate inverse problems.\u003c\/li\u003e \u003cli\u003eWritten by leading experts of inverse problems and uncertainty quantification.\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003eGraduate students and researchers working in statistics, mathematics and engineering will benefit from this book.\u003c\/p\u003e  1 Introduction\u003cbr\u003e 1.1 Introduction\u003cbr\u003e 1.2 Statistical Methods\u003cbr\u003e 1.3 Approximation Methods\u003cbr\u003e 1.4 Kalman Filtering\u003cbr\u003e 1.5 Optimization  \u003cp\u003e\u003cbr\u003e 2 A Primer of Frequentist and Bayesian Inference in Inverse Problems\u003cbr\u003e 2.1 Introduction\u003cbr\u003e 2.2 Prior Information and Parameters: What do you know, and what do you want to know?\u003cbr\u003e 2.3 Estimators: What can you do with what you measure?\u003cbr\u003e 2.4 Performance of estimators: How well can you do?\u003cbr\u003e 2.5 Frequentist performance of Bayes estimators for a BNM\u003cbr\u003e 2.6 Summary\u003cbr\u003e Bibliography\u003c\/p\u003e \u003cp\u003e\u003cbr\u003e 3 Subjective Knowledge or Objective Belief? An Oblique Look to Bayesian Methods\u003cbr\u003e 3.1 Introduction\u003cbr\u003e 3.2 Belief, information and probability\u003cbr\u003e 3.3 Bayes' formula and updating probabilities\u003cbr\u003e 3.4 Computed examples involving hypermodels\u003cbr\u003e 3.5 Dynamic updating of beliefs\u003cbr\u003e 3.6 Discussion\u003cbr\u003e Bibliography\u003c\/p\u003e \u003cp\u003e\u003cbr\u003e 4 Bayesian and Geostatistical Approaches to Inverse Problems\u003cbr\u003e 4.1 Introduction\u003cbr\u003e 4.2 The Bayesian and Frequentist Approaches\u003cbr\u003e 4.3 Prior Distribution\u003cbr\u003e 4.4 A Geostatistical Approach\u003cbr\u003e 4.5 Concluding\u003cbr\u003e Bibliography\u003c\/p\u003e \u003cp\u003e\u003cbr\u003e 5 Using the Bayesian Framework to Combine Simulations and Physical Observations\u003cbr\u003e for Statistical Inference\u003cbr\u003e 5.1 Introduction\u003cbr\u003e 5.2 Bayesian Model Formulation \u003cbr\u003e 5.3 Application: Cosmic Microwave Background\u003cbr\u003e 5.4 Discussion\u003cbr\u003e Bibliography\u003c\/p\u003e \u003cp\u003e\u003cbr\u003e 6 Bayesian Partition Models for Subsurface Characterization\u003cbr\u003e 6.1 Introduction\u003cbr\u003e 6.2 Model equations and problem setting\u003cbr\u003e 6.3 Approximation of the response surface using the Bayesian Partition Model and two-stage\u003cbr\u003e MCMC\u003cbr\u003e 6.4 Numerical results\u003cbr\u003e 6.5 Conclusions\u003cbr\u003e Bibliography\u003c\/p\u003e \u003cp\u003e\u003cbr\u003e 7 Surrogate and reduced-order modeling: a comparison of approaches for large-scale\u003cbr\u003e statistical inverse problems\u003cbr\u003e 7.1 Introduction\u003cbr\u003e 7.2 Reducing the computational cost of solving statistical inverse problems\u003cbr\u003e 7.3 General formulation\u003cbr\u003e 7.4 Model reduction\u003cbr\u003e 7.5 Stochastic spectral methods\u003cbr\u003e 7.6 Illustrative example\u003cbr\u003e 7.7 Conclusions\u003cbr\u003e Bibliography\u003c\/p\u003e \u003cp\u003e8 Reduced basis approximation and a posteriori error estimation for parametrized\u003cbr\u003e parabolic PDEs; Application to real-time Bayesian parameter estimation\u003cbr\u003e 8.1 Introduction\u003cbr\u003e 8.2 Linear Parabolic Equations\u003cbr\u003e 8.3 Bayesian Parameter Estimation\u003cbr\u003e 8.4 Concluding Remarks\u003cbr\u003e Bibliography\u003c\/p\u003e \u003cp\u003e\u003cbr\u003e 9 Calibration and Uncertainty Analysis for Computer Simulations with Multivariate\u003cbr\u003e Output\u003cbr\u003e 9.1 Introduction\u003cbr\u003e 9.2 Gaussian Process Models\u003cbr\u003e 9.3 Bayesian Model Calibration\u003cbr\u003e 9.4 Case Study: Thermal Simulation of Decomposing Foam\u003cbr\u003e 9.5 Conclusions\u003cbr\u003e Bibliography\u003c\/p\u003e \u003cp\u003e\u003cbr\u003e 10 Bayesian Calibration of Expensive Multivariate Computer Experiments\u003cbr\u003e 10.1 Calibration of computer experiments\u003cbr\u003e 10.2 Principal component emulation \u003cbr\u003e 10.3 Multivariate calibration\u003cbr\u003e 10.4 Summary\u003cbr\u003e Bibliography\u003c\/p\u003e \u003cp\u003e\u003cbr\u003e 11 The Ensemble Kalman Filter and Related Filters\u003cbr\u003e 11.1 Introduction\u003cbr\u003e 11.2 Model Assumptions\u003cbr\u003e 11.3 The Traditional Kalman Filter (KF)\u003cbr\u003e 11.4 The Ensemble Kalman Filter (EnKF)\u003cbr\u003e 11.5 The Randomized Maximum Likelihood Filter (RMLF)\u003cbr\u003e 11.6 The Particle Filter (PF)\u003cbr\u003e 11.7 Closing Remarks\u003cbr\u003e 11.8 Appendix A: Properties of the EnKF Algorithm\u003cbr\u003e 11.9 Appendix B: Properties of the RMLF Algorithm\u003cbr\u003e Bibliography\u003c\/p\u003e \u003cp\u003e\u003cbr\u003e 12 Using the ensemble Kalman Filter for history matching and uncertainty quantification\u003cbr\u003e of complex reservoir models\u003cbr\u003e 12.1 Introduction\u003cbr\u003e 12.2 Formulation and solution of the inverse problem\u003cbr\u003e 12.3 EnKF history matching workflow\u003cbr\u003e 12.4 Field Case\u003cbr\u003e 12.5 Conclusion\u003cbr\u003e Bibliography\u003c\/p\u003e \u003cp\u003e13 Optimal Experimental Design for the Large-Scale Nonlinear Ill-posed Problem of\u003cbr\u003e Impedance Imaging\u003cbr\u003e 13.1 Introduction\u003cbr\u003e 13.2 Impedance Tomography\u003cbr\u003e 13.3 Optimal Experimental Design - Background\u003cbr\u003e 13.4 Optimal Experimental Design for Nonlinear Ill-Posed Problems\u003cbr\u003e 13.5 Optimization Framework\u003cbr\u003e 13.6 Numerical Results\u003cbr\u003e 13.7 Discussion and Conclusions\u003cbr\u003e Bibliography\u003c\/p\u003e \u003cp\u003e\u003cbr\u003e 14 Solving Stochastic Inverse Problems: A Sparse Grid Collocation Approach\u003cbr\u003e 14.1 Introduction\u003cbr\u003e 14.2 Mathematical developments\u003cbr\u003e 14.3 Numerical Examples\u003cbr\u003e 14.4 Summary\u003cbr\u003e Bibliography\u003c\/p\u003e \u003cp\u003e\u003cbr\u003e 15 Uncertainty analysis for seismic inverse problems: two practical examples\u003cbr\u003e 15.1 Introduction\u003cbr\u003e 15.2 Traveltime inversion for velocity determination.\u003cbr\u003e 15.3 Prestack stratigraphic inversion\u003cbr\u003e 15.4 Conclusions\u003c\/p\u003e \u003cp\u003e\u003cbr\u003e Bibliography\u003cbr\u003e 16 Solution of inverse problems using discrete ODE adjoints\u003cbr\u003e 16.1 Introduction\u003cbr\u003e 16.2 Runge-Kutta Methods\u003cbr\u003e 16.3 Adaptive Steps\u003cbr\u003e 16.4 Linear Multistep Methods\u003cbr\u003e 16.5 Numerical Results\u003cbr\u003e 16.6 Application to Data Assimilation\u003cbr\u003e 16.7 Conclusions\u003cbr\u003e Bibliography\u003cbr\u003e TBD\u003cbr\u003e \u003c\/p\u003e \u003cp\u003e\u003cb\u003eLorenz Biegler,\u003c\/b\u003e Carnegie Mellon University, USA.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eGeorge Biros,\u003c\/b\u003e Georgia Institute of Technology, USA.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eOmar Ghattas\u003c\/b\u003e, University of Texas at Austin, USA.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eMatthias Heinkenschloss\u003c\/b\u003e, Rice University, USA.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eDavid Keyes\u003c\/b\u003e, KAUST and Columbia University, USA.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eBani Mallick\u003c\/b\u003e, Texas A\u0026amp;M University, USA.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eLuis Tenorio\u003c\/b\u003e, Colorado School of Mines, USA.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eBart van Bloemen Waanders\u003c\/b\u003e, Sandia National Laboratories, USA.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eKaren Wilcox,\u003c\/b\u003e Massachusetts Institute of Technology, USA.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eYoussef Marzouk\u003c\/b\u003e, Massachusetts Institute of Technology, USA.\u003c\/p\u003e \u003cp\u003eThis book focuses on computational methods for large-scale statistical inverse problems and provides an introduction to statistical Bayesian and frequentist methodologies. Recent research advances for approximation methods are discussed, along with Kalman filtering methods and optimization-based approaches to solving inverse problems. The aim is to cross-fertilize the perspectives of researchers in the areas of data assimilation, statistics, large-scale optimization, applied and computational mathematics, high performance computing, and cutting-edge applications.\u003c\/p\u003e \u003cp\u003eThe solution to large-scale inverse problems critically depends on methods to reduce computational cost. Recent research approaches tackle this challenge in a variety of different ways. Many of the computational frameworks highlighted in this book build upon state-of-the-art methods for simulation of the forward problem, such as, fast Partial Differential Equation (PDE) solvers, reduced-order models and emulators of the forward problem, stochastic spectral approximations, and ensemble-based approximations, as well as exploiting the machinery for large-scale deterministic optimization through adjoint and other sensitivity analysis methods.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eKey Features:\u003c\/b\u003e\u003c\/p\u003e \u003cul\u003e \u003cli\u003eBrings together the perspectives of researchers in areas of inverse problems and data assimilation.\u003c\/li\u003e \u003cli\u003eAssesses the current state-of-the-art and identify needs and opportunities for future research.\u003c\/li\u003e \u003cli\u003eFocuses on the computational methods used to analyze and simulate inverse problems.\u003c\/li\u003e \u003cli\u003eWritten by leading experts of inverse problems and uncertainty quantification.\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003eGraduate students and researchers working in statistics, mathematics and engineering will benefit from this book.\u003c\/p\u003e  ","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989510045925,"sku":"NP9780470697436","price":174.95,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9780470697436.jpg?v=1761784397","url":"https:\/\/k12savings.com\/products\/large-scale-inverse-problems-and-quantification-of-uncertainty-isbn-9780470697436","provider":"K12savings","version":"1.0","type":"link"}