Biegler L., Biros G., Ghattas O., Heinkenschloss M., Keyes D., Mallick B., Tenorio L., van Bloemen Waanders B., Willcox K., Marzouk Y. (eds.) Large-Scale Inverse Problems and Quantification of Uncertainty

N.-Y.: Wiley, 2011. — 388 p.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.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.Key Features: Brings together the perspectives of researchers in areas of inverse problems and data assimilation. Assesses the current state-of-the-art and identify needs and opportunities for future research. Focuses on the computational methods used to analyze and simulate inverse problems. Written by leading experts of inverse problems and uncertainty quantification.Graduate students and researchers working in statistics, mathematics and engineering will benefit from this book.A Primer of Frequentist and Bayesian Inference in Inverse Problems
Subjective Knowledge or Objective Belief? An Oblique Look to Bayesian Methods
Bayesian and Geostatistical Approaches to Inverse Problems
Using the Bayesian Framework to Combine Simulations and Physical Observations for Statistical Inference
Bayesian Partition Models for Subsurface Characterization
Surrogate and reduced-order modeling: a comparison of approaches for large-scale statistical inverse problems
Reduced basis approximation and a posteriori error estimation for parametrized parabolic PDEs; Application to real-time Bayesian parameter estimation
Calibration and Uncertainty Analysis for Computer Simulations with Multivariate
Output
Bayesian Calibration of Expensive Multivariate Computer Experiments
The Ensemble Kalman Filter and Related Filters
Using the ensemble Kalman Filter for history matching and uncertainty quantification of complex reservoir models
Optimal Experimental Design for the Large-Scale Nonlinear Ill-posed Problem of
Impedance Imaging
Solving Stochastic Inverse Problems: A Sparse Grid Collocation Approach
Uncertainty analysis for seismic inverse problems: two practical examples
Solution of inverse problems using discrete ODE adjoints