Inverse Problems On Large Scales
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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 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 Convex Optimization
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Author : Ernest K. Ryu
language : en
Publisher: Cambridge University Press
Release Date : 2022-12-01
Large Scale Convex Optimization written by Ernest K. Ryu and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-01 with Mathematics categories.
Starting from where a first course in convex optimization leaves off, this text presents a unified analysis of first-order optimization methods – including parallel-distributed algorithms – through the abstraction of monotone operators. With the increased computational power and availability of big data over the past decade, applied disciplines have demanded that larger and larger optimization problems be solved. This text covers the first-order convex optimization methods that are uniquely effective at solving these large-scale optimization problems. Readers will have the opportunity to construct and analyze many well-known classical and modern algorithms using monotone operators, and walk away with a solid understanding of the diverse optimization algorithms. Graduate students and researchers in mathematical optimization, operations research, electrical engineering, statistics, and computer science will appreciate this concise introduction to the theory of convex optimization algorithms.
Inverse Problem Theory And Methods For Model Parameter Estimation
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Author : Albert Tarantola
language : en
Publisher: SIAM
Release Date : 2005-01-01
Inverse Problem Theory And Methods For Model Parameter Estimation written by Albert Tarantola and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-01-01 with Mathematics categories.
While the prediction of observations is a forward problem, the use of actual observations to infer the properties of a model is an inverse problem. Inverse problems are difficult because they may not have a unique solution. The description of uncertainties plays a central role in the theory, which is based on probability theory. This book proposes a general approach that is valid for linear as well as for nonlinear problems. The philosophy is essentially probabilistic and allows the reader to understand the basic difficulties appearing in the resolution of inverse problems. The book attempts to explain how a method of acquisition of information can be applied to actual real-world problems, and many of the arguments are heuristic.
Handbook Of Large Scale Random Networks
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Author : Bela Bollobas
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-05-17
Handbook Of Large Scale Random Networks written by Bela Bollobas 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 2010-05-17 with Mathematics categories.
With the advent of digital computers more than half a century ago, - searchers working in a wide range of scienti?c disciplines have obtained an extremely powerful tool to pursue deep understanding of natural processes in physical, chemical, and biological systems. Computers pose a great ch- lenge to mathematical sciences, as the range of phenomena available for rigorous mathematical analysis has been enormously expanded, demanding the development of a new generation of mathematical tools. There is an explosive growth of new mathematical disciplines to satisfy this demand, in particular related to discrete mathematics. However, it can be argued that at large mathematics is yet to provide the essential breakthrough to meet the challenge. The required paradigm shift in our view should be compa- ble to the shift in scienti?c thinking provided by the Newtonian revolution over 300 years ago. Studies of large-scale random graphs and networks are critical for the progress, using methods of discrete mathematics, probabil- tic combinatorics, graph theory, and statistical physics. Recent advances in large scale random network studies are described in this handbook, which provides a signi?cant update and extension - yond the materials presented in the “Handbook of Graphs and Networks” published in 2003 by Wiley. The present volume puts special emphasis on large-scale networks and random processes, which deemed as crucial for - tureprogressinthe?eld. Theissuesrelatedtorandomgraphsandnetworks pose very di?cult mathematical questions.
Inverse Problems
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Author : Mathias Richter
language : en
Publisher: Birkhäuser
Release Date : 2016-11-24
Inverse Problems written by Mathias Richter and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-24 with Mathematics categories.
The overall goal of the book is to provide access to the regularized solution of inverse problems relevant in geophysics without requiring more mathematical knowledge than is taught in undergraduate math courses for scientists and engineers. From abstract analysis only the concept of functions as vectors is needed. Function spaces are introduced informally in the course of the text, when needed. Additionally, a more detailed, but still condensed introduction is given in Appendix B. A second goal is to elaborate the single steps to be taken when solving an inverse problem: discretization, regularization and practical solution of the regularized optimization problem. These steps are shown in detail for model problems from the fields of inverse gravimetry and seismic tomography. The intended audience is mathematicians, physicists and engineers having a good working knowledge of linear algebra and analysis at the upper undergraduate level.
Computational Methods For Inverse Problems
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Author : Curtis R. Vogel
language : en
Publisher: SIAM
Release Date : 2002-01-01
Computational Methods For Inverse Problems written by Curtis R. Vogel and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-01-01 with Mathematics categories.
Provides a basic understanding of both the underlying mathematics and the computational methods used to solve inverse problems.
Large Scale Scientific Computing
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Author : Deuflhard
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Large Scale Scientific Computing written by Deuflhard 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.
In this book, the new and rapidly expanding field of scientific computing is understood in a double sense: as computing for scientific and engineering problems and as the science of doing such computations. Thus scientific computing touches at one side mathematical modelling (in the various fields of applications) and at the other side computer science. As soon as the mathematical models de scribe the features of real life processes in sufficient detail, the associated computations tend to be large scale. As a consequence, interest more and more focusses on such numerical methods that can be expected to cope with large scale computational problems. Moreover, given the algorithms which are known to be efficient on a tradi tional computer, the question of implementation on modern supercomputers may get crucial. The present book is the proceedings of a meeting on "Large Scale Scientific Computing" , that was held a t the Oberwolfach Mathematical Institute (July 14-19, 1985) under the auspices of the Sonderforschungsbereich 123 of the University of Heidelberg. Participants included applied scientists with computational interests, numerical analysts, and experts on modern parallel computers. 'l'he purpose of the meeting was to establish a common under standing of recent issues in scientific computing, especially in view of large scale problems. Fields of applications, which have been covered, included semi-conductor design, chemical combustion, flow through porous media, climatology, seismology, fluid dynami. cs, tomography, rheology, hydro power plant optimization, subwil. y control, space technology.
Extraction Of Quantifiable Information From Complex Systems
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Author : Stephan Dahlke
language : en
Publisher: Springer
Release Date : 2014-11-13
Extraction Of Quantifiable Information From Complex Systems written by Stephan Dahlke and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-13 with Mathematics categories.
In April 2007, the Deutsche Forschungsgemeinschaft (DFG) approved the Priority Program 1324 “Mathematical Methods for Extracting Quantifiable Information from Complex Systems.” This volume presents a comprehensive overview of the most important results obtained over the course of the program. Mathematical models of complex systems provide the foundation for further technological developments in science, engineering and computational finance. Motivated by the trend toward steadily increasing computer power, ever more realistic models have been developed in recent years. These models have also become increasingly complex, and their numerical treatment poses serious challenges. Recent developments in mathematics suggest that, in the long run, much more powerful numerical solution strategies could be derived if the interconnections between the different fields of research were systematically exploited at a conceptual level. Accordingly, a deeper understanding of the mathematical foundations as well as the development of new and efficient numerical algorithms were among the main goals of this Priority Program. The treatment of high-dimensional systems is clearly one of the most challenging tasks in applied mathematics today. Since the problem of high-dimensionality appears in many fields of application, the above-mentioned synergy and cross-fertilization effects were expected to make a great impact. To be truly successful, the following issues had to be kept in mind: theoretical research and practical applications had to be developed hand in hand; moreover, it has proven necessary to combine different fields of mathematics, such as numerical analysis and computational stochastics. To keep the whole program sufficiently focused, we concentrated on specific but related fields of application that share common characteristics and as such, they allowed us to use closely related approaches.
Fast Processes In Large Scale Atmospheric Models
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Author : Yangang Liu
language : en
Publisher: John Wiley & Sons
Release Date : 2023-12-11
Fast Processes In Large Scale Atmospheric Models written by Yangang Liu 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 2023-12-11 with Science categories.
Improving weather and climate prediction with better representation of fast processes in atmospheric models Many atmospheric processes that influence Earth’s weather and climate occur at spatiotemporal scales that are too small to be resolved in large scale models. They must be parameterized, which means approximately representing them by variables that can be resolved by model grids. Fast Processes in Large-Scale Atmospheric Models: Progress, Challenges and Opportunities explores ways to better investigate and represent multiple parameterized processes in models and thus improve their ability to make accurate climate and weather predictions. Volume highlights include: Historical development of the parameterization of fast processes in numerical models Different types of major sub-grid processes and their parameterizations Efforts to unify the treatment of individual processes and their interactions Top-down versus bottom-up approaches across multiple scales Measurement techniques, observational studies, and frameworks for model evaluation Emerging challenges, new opportunities, and future research directions The American Geophysical Union promotes discovery in Earth and space science for the benefit of humanity. Its publications disseminate scientific knowledge and provide resources for researchers, students, and professionals.