Large-Scale Inverse Problems and Quantification of Uncertainty

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Large-Scale Inverse Problems and Quantification of Uncertainty

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This book focuses on computational methods for large-scalestatistical inverse problems and provides an introduction tostatistical Bayesian and frequentist methodologies. Recent researchadvances for approximation methods are discussed, along with Kalmanfiltering methods and optimization-based approaches to solvinginverse problems. The aim is to cross-fertilize the perspectives ofresearchers 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 dependson methods to reduce computational cost. Recent research approachestackle this challenge in a variety of different ways. Many of thecomputational frameworks highlighted in this book build uponstate-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-basedapproximations, as well as exploiting the machinery for large-scaledeterministic optimization through adjoint and other sensitivityanalysis methods.

Key Features:
- Brings together the perspectives of researchers in areasof inverse problems and data assimilation.
- Assesses the current state-of-the-art and identify needsand opportunities for future research.
- Focuses on the computational methods used to analyze andsimulate inverse problems.
- Written by leading experts of inverse problems anduncertainty quantification.

Graduate students and researchers working in statistics,mathematics and engineering will benefit from this book.