Large Scale Inverse Problems

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Large Scale Inverse Problems

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Author : Mike Cullen
language : en
Publisher: Walter de Gruyter
Release Date : 2013-08-29

Large Scale Inverse Problems written by Mike Cullen and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-29 with Mathematics categories.

This book is thesecond volume of a three volume series recording the "Radon Special Semester 2011 on Multiscale Simulation & Analysis in Energy and the Environment" that took placein Linz, Austria, October 3-7, 2011. This volume addresses the common ground in the mathematical and computational procedures required for large-scale inverse problems and data assimilation in forefront applications. The solution of inverse problems is fundamental to a wide variety of applications such as weather forecasting, medical tomography, and oil exploration. Regularisation techniques are needed to ensure solutions of sufficient quality to be useful, and soundly theoretically based. This book addresses the common techniques required for all the applications, and is thus truly interdisciplinary. Thiscollection of surveyarticlesfocusses onthe large inverse problems commonly arising in simulation and forecasting in the earth sciences. For example, operational weather forecasting models have between 107 and 108 degrees of freedom. Even so, these degrees of freedom represent grossly space-time averaged properties of the atmosphere. Accurate forecasts require accurate initial conditions. With recent developments in satellite data, there are between 106 and 107 observations each day. However, while these also represent space-time averaged properties, the averaging implicit in the measurements is quite different from that used in the models. In atmosphere and ocean applications, there is a physically-based model available which can be used to regularise the problem. We assume that there is a set of observations with known error characteristics available over a period of time. The basic deterministic technique is to fit a model trajectory to the observations over a period of time to within the observation error. Since the model is not perfect the model trajectory has to be corrected, which defines the data assimilation problem. The stochastic view can be expressed by using an ensemble of model trajectories, and calculating corrections to both the mean value and the spread which allow the observations to be fitted by each ensemble member. In other areas of earth science, only the structure of the model formulation itself is known and the aim is to use the past observation history to determine the unknown model parameters. The book records the achievements of Workshop2 "Large-Scale Inverse Problems and Applications in the Earth Sciences". Itinvolves experts in the theory of inverse problems together with experts working on both theoretical and practical aspects of the techniques by which large inverse problems arise in the earth sciences.

Large Scale Inverse Problems And Quantification Of Uncertainty

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Author : Lorenz Biegler
language : en
Publisher: John Wiley & Sons
Release Date : 2011-06-24

Large Scale Inverse Problems And Quantification Of Uncertainty written by Lorenz Biegler and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-24 with Mathematics categories.

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.

Inverse Problems And Large Scale Computations

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Author : Larisa Beilina
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-10-01

Inverse Problems And Large Scale Computations written by Larisa Beilina and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-01 with Computers categories.

This volume is a result of two international workshops, namely the Second Annual Workshop on Inverse Problems and the Workshop on Large-Scale Modeling, held jointly in Sunne, Sweden from May 1-6 2012. The subject of the inverse problems workshop was to present new analytical developments and new numerical methods for solutions of inverse problems. The objective of the large-scale modeling workshop was to identify large-scale problems arising in various fields of science and technology and covering all possible applications, with a particular focus on urgent problems in theoretical and applied electromagnetics. The workshops brought together scholars, professionals, mathematicians, and programmers and specialists working in large-scale modeling problems. The contributions in this volume are reflective of these themes and will be beneficial to researchers in this area.

Solving Large Scale Inverse Problems Via Approximate Message Passing And Optimization

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Author : Yanting Ma
language : en
Publisher:
Release Date : 2017

Solving Large Scale Inverse Problems Via Approximate Message Passing And Optimization written by Yanting Ma and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with categories.

Inverse Problems On Large Scales

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Author : Bochra Mejri
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2024-12-30

Inverse Problems On Large Scales written by Bochra Mejri and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-30 with Mathematics categories.

This book presents new contributions and substantial advancements in the field of inverse imaging problems. Several chapters are driven by novel applications, which leads to novel mathematical formulations. The book contains mathematical and modeling techniques studying inverse and ill-posed problems with theoretical, numerical, and practical aspects arising in science and engineering.

Large Scale Optimization With Applications Optimization In Inverse Problems And Design

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Author :
language : en
Publisher:
Release Date : 1997

Large Scale Optimization With Applications Optimization In Inverse Problems And Design written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Engineering design categories.

Optimal Input Design For Large Scale Inverse Problems Using Pde Constrained Optimization

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Author : Andrea Petrocchi
language : en
Publisher:
Release Date : 2024

Optimal Input Design For Large Scale Inverse Problems Using Pde Constrained Optimization written by Andrea Petrocchi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024 with categories.

Computational Optimization Methods For Large Scale Inverse Problems

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Author : Kati Niinimaki
language : en
Publisher:
Release Date : 2013

Computational Optimization Methods For Large Scale Inverse Problems written by Kati Niinimaki and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Image reconstruction categories.

Large Scale Optimization With Applications

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Author : Lorenz T. Biegler
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Large Scale Optimization With Applications written by Lorenz T. Biegler and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Inverse problems and optimal design have come of age as a consequence of the availability of better, more accurate, and more efficient simulation packages. Many of these simulators, which can run on small workstations, can capture the complicated behavior of the physical systems they are modeling, and have become commonplace tools in engineering and science. There is a great desire to use them as part of a process by which measured field data are analyzed or by which design of a product is automated. A major obstacle in doing precisely this is that one is ultimately confronted with a large-scale optimization problem. This volume contains expository articles on both inverse problems and design problems formulated as optimization. Each paper describes the physical problem in some detail and is meant to be accessible to researchers in optimization as well as those who work in applied areas where optimization is a key tool. What emerges in the presentations is that there are features about the problem that must be taken into account in posing the objective function, and in choosing an optimization strategy. In particular there are certain structures peculiar to the problems that deserve special treatment, and there is ample opportunity for parallel computation. THIS IS BACK COVER TEXT!!! Inverse problems and optimal design have come of age as a consequence of the availability of better, more accurate, and more efficient, simulation packages. The problem of determining the parameters of a physical system from

Large Scale Inverse Problems

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Author :
language : en
Publisher:
Release Date : 2013

Large Scale Inverse Problems written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Inverse problems (Differential equations) categories.