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Large-Scale Inverse Problems and Quantification of Uncertainty


Large-Scale Inverse Problems and Quantification of Uncertainty


Wiley Series in Computational Statistics, Band 708 1. Aufl.

von: Lorenz Biegler, George Biros, Omar Ghattas, Matthias Heinkenschloss, David Keyes, Bani Mallick, Luis Tenorio, Bart van Bloemen Waanders, Karen Willcox, Youssef Marzouk

114,99 €

Verlag: Wiley
Format: PDF
Veröffentl.: 17.09.2010
ISBN/EAN: 9780470685860
Sprache: englisch
Anzahl Seiten: 400

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Beschreibungen

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. <p>The 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.</p> <p><b>Key Features:</b></p> <ul> <li>Brings together the perspectives of researchers in areas of inverse problems and data assimilation.</li> <li>Assesses the current state-of-the-art and identify needs and opportunities for future research.</li> <li>Focuses on the computational methods used to analyze and simulate inverse problems.</li> <li>Written by leading experts of inverse problems and uncertainty quantification.</li> </ul> <p>Graduate students and researchers working in statistics, mathematics and engineering will benefit from this book.</p>
1 Introduction<br /> 1.1 Introduction<br /> 1.2 Statistical Methods<br /> 1.3 Approximation Methods<br /> 1.4 Kalman Filtering<br /> 1.5 Optimization <p><br /> 2 A Primer of Frequentist and Bayesian Inference in Inverse Problems<br /> 2.1 Introduction<br /> 2.2 Prior Information and Parameters: What do you know, and what do you want to know?<br /> 2.3 Estimators: What can you do with what you measure?<br /> 2.4 Performance of estimators: How well can you do?<br /> 2.5 Frequentist performance of Bayes estimators for a BNM<br /> 2.6 Summary<br /> Bibliography</p> <p><br /> 3 Subjective Knowledge or Objective Belief? An Oblique Look to Bayesian Methods<br /> 3.1 Introduction<br /> 3.2 Belief, information and probability<br /> 3.3 Bayes' formula and updating probabilities<br /> 3.4 Computed examples involving hypermodels<br /> 3.5 Dynamic updating of beliefs<br /> 3.6 Discussion<br /> Bibliography</p> <p><br /> 4 Bayesian and Geostatistical Approaches to Inverse Problems<br /> 4.1 Introduction<br /> 4.2 The Bayesian and Frequentist Approaches<br /> 4.3 Prior Distribution<br /> 4.4 A Geostatistical Approach<br /> 4.5 Concluding<br /> Bibliography</p> <p><br /> 5 Using the Bayesian Framework to Combine Simulations and Physical Observations<br /> for Statistical Inference<br /> 5.1 Introduction<br /> 5.2 Bayesian Model Formulation <br /> 5.3 Application: Cosmic Microwave Background<br /> 5.4 Discussion<br /> Bibliography</p> <p><br /> 6 Bayesian Partition Models for Subsurface Characterization<br /> 6.1 Introduction<br /> 6.2 Model equations and problem setting<br /> 6.3 Approximation of the response surface using the Bayesian Partition Model and two-stage<br /> MCMC<br /> 6.4 Numerical results<br /> 6.5 Conclusions<br /> Bibliography</p> <p><br /> 7 Surrogate and reduced-order modeling: a comparison of approaches for large-scale<br /> statistical inverse problems<br /> 7.1 Introduction<br /> 7.2 Reducing the computational cost of solving statistical inverse problems<br /> 7.3 General formulation<br /> 7.4 Model reduction<br /> 7.5 Stochastic spectral methods<br /> 7.6 Illustrative example<br /> 7.7 Conclusions<br /> Bibliography</p> <p>8 Reduced basis approximation and a posteriori error estimation for parametrized<br /> parabolic PDEs; Application to real-time Bayesian parameter estimation<br /> 8.1 Introduction<br /> 8.2 Linear Parabolic Equations<br /> 8.3 Bayesian Parameter Estimation<br /> 8.4 Concluding Remarks<br /> Bibliography</p> <p><br /> 9 Calibration and Uncertainty Analysis for Computer Simulations with Multivariate<br /> Output<br /> 9.1 Introduction<br /> 9.2 Gaussian Process Models<br /> 9.3 Bayesian Model Calibration<br /> 9.4 Case Study: Thermal Simulation of Decomposing Foam<br /> 9.5 Conclusions<br /> Bibliography</p> <p><br /> 10 Bayesian Calibration of Expensive Multivariate Computer Experiments<br /> 10.1 Calibration of computer experiments<br /> 10.2 Principal component emulation <br /> 10.3 Multivariate calibration<br /> 10.4 Summary<br /> Bibliography</p> <p><br /> 11 The Ensemble Kalman Filter and Related Filters<br /> 11.1 Introduction<br /> 11.2 Model Assumptions<br /> 11.3 The Traditional Kalman Filter (KF)<br /> 11.4 The Ensemble Kalman Filter (EnKF)<br /> 11.5 The Randomized Maximum Likelihood Filter (RMLF)<br /> 11.6 The Particle Filter (PF)<br /> 11.7 Closing Remarks<br /> 11.8 Appendix A: Properties of the EnKF Algorithm<br /> 11.9 Appendix B: Properties of the RMLF Algorithm<br /> Bibliography</p> <p><br /> 12 Using the ensemble Kalman Filter for history matching and uncertainty quantification<br /> of complex reservoir models<br /> 12.1 Introduction<br /> 12.2 Formulation and solution of the inverse problem<br /> 12.3 EnKF history matching workflow<br /> 12.4 Field Case<br /> 12.5 Conclusion<br /> Bibliography</p> <p>13 Optimal Experimental Design for the Large-Scale Nonlinear Ill-posed Problem of<br /> Impedance Imaging<br /> 13.1 Introduction<br /> 13.2 Impedance Tomography<br /> 13.3 Optimal Experimental Design - Background<br /> 13.4 Optimal Experimental Design for Nonlinear Ill-Posed Problems<br /> 13.5 Optimization Framework<br /> 13.6 Numerical Results<br /> 13.7 Discussion and Conclusions<br /> Bibliography</p> <p><br /> 14 Solving Stochastic Inverse Problems: A Sparse Grid Collocation Approach<br /> 14.1 Introduction<br /> 14.2 Mathematical developments<br /> 14.3 Numerical Examples<br /> 14.4 Summary<br /> Bibliography</p> <p><br /> 15 Uncertainty analysis for seismic inverse problems: two practical examples<br /> 15.1 Introduction<br /> 15.2 Traveltime inversion for velocity determination.<br /> 15.3 Prestack stratigraphic inversion<br /> 15.4 Conclusions</p> <p><br /> Bibliography<br /> 16 Solution of inverse problems using discrete ODE adjoints<br /> 16.1 Introduction<br /> 16.2 Runge-Kutta Methods<br /> 16.3 Adaptive Steps<br /> 16.4 Linear Multistep Methods<br /> 16.5 Numerical Results<br /> 16.6 Application to Data Assimilation<br /> 16.7 Conclusions<br /> Bibliography<br /> TBD<br /> </p>
<p><b>Lorenz Biegler,</b> Carnegie Mellon University, USA.</p> <p><b>George Biros,</b> Georgia Institute of Technology, USA.</p> <p><b>Omar Ghattas</b>, University of Texas at Austin, USA.</p> <p><b>Matthias Heinkenschloss</b>, Rice University, USA.</p> <p><b>David Keyes</b>, KAUST and Columbia University, USA.</p> <p><b>Bani Mallick</b>, Texas A&M University, USA.</p> <p><b>Luis Tenorio</b>, Colorado School of Mines, USA.</p> <p><b>Bart van Bloemen Waanders</b>, Sandia National Laboratories, USA.</p> <p><b>Karen Wilcox,</b> Massachusetts Institute of Technology, USA.</p> <p><b>Youssef Marzouk</b>, Massachusetts Institute of Technology, USA.</p>

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