Large-Scale Inverse Problems and Quantification of Uncertainty

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Publisher : John Wiley & Sons
ISBN 13 : 1119957583
Total Pages : 403 pages
Book Rating : 4.1/5 (199 download)

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Book Synopsis Large-Scale Inverse Problems and Quantification of Uncertainty by : Lorenz Biegler

Download or read book Large-Scale Inverse Problems and Quantification of Uncertainty written by Lorenz Biegler and published by John Wiley & Sons. This book was released on 2011-06-24 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Optimal Design of Experiments

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Publisher : SIAM
ISBN 13 : 0898716047
Total Pages : 527 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Optimal Design of Experiments by : Friedrich Pukelsheim

Download or read book Optimal Design of Experiments written by Friedrich Pukelsheim and published by SIAM. This book was released on 2006-04-01 with total page 527 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimal Design of Experiments offers a rare blend of linear algebra, convex analysis, and statistics. The optimal design for statistical experiments is first formulated as a concave matrix optimization problem. Using tools from convex analysis, the problem is solved generally for a wide class of optimality criteria such as D-, A-, or E-optimality. The book then offers a complementary approach that calls for the study of the symmetry properties of the design problem, exploiting such notions as matrix majorization and the Kiefer matrix ordering. The results are illustrated with optimal designs for polynomial fit models, Bayes designs, balanced incomplete block designs, exchangeable designs on the cube, rotatable designs on the sphere, and many other examples.

Bayesian Approach to Inverse Problems

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Publisher : John Wiley & Sons
ISBN 13 : 111862369X
Total Pages : 322 pages
Book Rating : 4.1/5 (186 download)

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Book Synopsis Bayesian Approach to Inverse Problems by : Jérôme Idier

Download or read book Bayesian Approach to Inverse Problems written by Jérôme Idier and published by John Wiley & Sons. This book was released on 2013-03-01 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many scientific, medical or engineering problems raise the issue of recovering some physical quantities from indirect measurements; for instance, detecting or quantifying flaws or cracks within a material from acoustic or electromagnetic measurements at its surface is an essential problem of non-destructive evaluation. The concept of inverse problems precisely originates from the idea of inverting the laws of physics to recover a quantity of interest from measurable data. Unfortunately, most inverse problems are ill-posed, which means that precise and stable solutions are not easy to devise. Regularization is the key concept to solve inverse problems. The goal of this book is to deal with inverse problems and regularized solutions using the Bayesian statistical tools, with a particular view to signal and image estimation. The first three chapters bring the theoretical notions that make it possible to cast inverse problems within a mathematical framework. The next three chapters address the fundamental inverse problem of deconvolution in a comprehensive manner. Chapters 7 and 8 deal with advanced statistical questions linked to image estimation. In the last five chapters, the main tools introduced in the previous chapters are put into a practical context in important applicative areas, such as astronomy or medical imaging.

Computational Methods for Inverse Problems

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Publisher : SIAM
ISBN 13 : 0898717574
Total Pages : 195 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Computational Methods for Inverse Problems by : Curtis R. Vogel

Download or read book Computational Methods for Inverse Problems written by Curtis R. Vogel and published by SIAM. This book was released on 2002-01-01 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a basic understanding of both the underlying mathematics and the computational methods used to solve inverse problems.

Foundations of Optimum Experimental Design

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Publisher : Springer
ISBN 13 :
Total Pages : 256 pages
Book Rating : 4.:/5 (44 download)

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Book Synopsis Foundations of Optimum Experimental Design by : Andrej Pázman

Download or read book Foundations of Optimum Experimental Design written by Andrej Pázman and published by Springer. This book was released on 1986-01-31 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introductory remarks about the experiment and its disign. The regression model and methods of estimation. The ordering of designs and the properties of variaces of estimates. Optimality critaria in the regression model. Iterative computation of optimum desings Design of experiments in particular cases. The functional model and measurements of physical fields.

Simulation and Optimization in Process Engineering

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Publisher : Elsevier
ISBN 13 : 0323850448
Total Pages : 428 pages
Book Rating : 4.3/5 (238 download)

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Book Synopsis Simulation and Optimization in Process Engineering by : Michael Bortz

Download or read book Simulation and Optimization in Process Engineering written by Michael Bortz and published by Elsevier. This book was released on 2022-04-16 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: Simulation and Optimization in Process Engineering: The Benefit of Mathematical Methods in Applications of the Process Industry brings together examples where the successful transfer of progress made in mathematical simulation and optimization has led to innovations in an industrial context that created substantial benefit. Containing introductory accounts on scientific progress in the most relevant topics of process engineering (substance properties, simulation, optimization, optimal control and real time optimization), the examples included illustrate how such scientific progress has been transferred to innovations that delivered a measurable impact, covering details of the methods used, and more. With each chapter bringing together expertise from academia and industry, this book is the first of its kind, providing demonstratable insights. - Recent mathematical methods are transformed into industrially relevant innovations. - Covers recent progress in mathematical simulation and optimization in a process engineering context with chapters written by experts from both academia and industry - Provides insight into challenges in industry aiming for a digitized world.

Numerical Analysis and Optimization

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Publisher : Springer
ISBN 13 : 3319176897
Total Pages : 351 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Numerical Analysis and Optimization by : Mehiddin Al-Baali

Download or read book Numerical Analysis and Optimization written by Mehiddin Al-Baali and published by Springer. This book was released on 2015-07-16 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting the latest findings in the field of numerical analysis and optimization, this volume balances pure research with practical applications of the subject. Accompanied by detailed tables, figures, and examinations of useful software tools, this volume will equip the reader to perform detailed and layered analysis of complex datasets. Many real-world complex problems can be formulated as optimization tasks. Such problems can be characterized as large scale, unconstrained, constrained, non-convex, non-differentiable, and discontinuous, and therefore require adequate computational methods, algorithms, and software tools. These same tools are often employed by researchers working in current IT hot topics such as big data, optimization and other complex numerical algorithms on the cloud, devising special techniques for supercomputing systems. The list of topics covered include, but are not limited to: numerical analysis, numerical optimization, numerical linear algebra, numerical differential equations, optimal control, approximation theory, applied mathematics, algorithms and software developments, derivative free optimization methods and programming models. The volume also examines challenging applications to various types of computational optimization methods which usually occur in statistics, econometrics, finance, physics, medicine, biology, engineering and industrial sciences.

Advances in Geophysics

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Publisher : Academic Press
ISBN 13 : 0128124148
Total Pages : 106 pages
Book Rating : 4.1/5 (281 download)

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Book Synopsis Advances in Geophysics by :

Download or read book Advances in Geophysics written by and published by Academic Press. This book was released on 2017-12-15 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advances in Geophysics, Volume 58, the latest in this critically acclaimed serialized review journal that has published for over 50 years, contains the latest information available in the field. Users will find valuable chapters highlighting the Novel use of geodynamics in plate tectonic reconstruction, and on Optimized experimental design in the context of seismic full waveform inversion and seismic imaging. Since 1952, each volume in this series has been eagerly awaited, frequently consulted, and praised by researchers and reviewers alike. Now in its 58th volume, it is truly an essential publication for researchers in all fields of geophysics. - Provides high-level reviews of the latest innovations in geophysics - Written by recognized experts in the field - Essential publication for researchers in all fields of geophysics

High Performance Computing for Computational Science – VECPAR 2016

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Publisher : Springer
ISBN 13 : 3319619829
Total Pages : 277 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis High Performance Computing for Computational Science – VECPAR 2016 by : Inês Dutra

Download or read book High Performance Computing for Computational Science – VECPAR 2016 written by Inês Dutra and published by Springer. This book was released on 2017-07-13 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed post-conference proceedings of the 12fth International Conference on High Performance Computing in Computational Science, VECPAR 2016, held in Porto, Portugal, in June 2016. The 20 full papers presented were carefully reviewed and selected from 36 submissions. The papers are organized in topical sections on applications; performance modeling and analysis; low level support; environments/libraries to support parallelization.

The Design and Analysis of Computer Experiments

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Publisher : Springer
ISBN 13 : 1493988476
Total Pages : 446 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis The Design and Analysis of Computer Experiments by : Thomas J. Santner

Download or read book The Design and Analysis of Computer Experiments written by Thomas J. Santner and published by Springer. This book was released on 2019-01-08 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes methods for designing and analyzing experiments that are conducted using a computer code, a computer experiment, and, when possible, a physical experiment. Computer experiments continue to increase in popularity as surrogates for and adjuncts to physical experiments. Since the publication of the first edition, there have been many methodological advances and software developments to implement these new methodologies. The computer experiments literature has emphasized the construction of algorithms for various data analysis tasks (design construction, prediction, sensitivity analysis, calibration among others), and the development of web-based repositories of designs for immediate application. While it is written at a level that is accessible to readers with Masters-level training in Statistics, the book is written in sufficient detail to be useful for practitioners and researchers. New to this revised and expanded edition: • An expanded presentation of basic material on computer experiments and Gaussian processes with additional simulations and examples • A new comparison of plug-in prediction methodologies for real-valued simulator output • An enlarged discussion of space-filling designs including Latin Hypercube designs (LHDs), near-orthogonal designs, and nonrectangular regions • A chapter length description of process-based designs for optimization, to improve good overall fit, quantile estimation, and Pareto optimization • A new chapter describing graphical and numerical sensitivity analysis tools • Substantial new material on calibration-based prediction and inference for calibration parameters • Lists of software that can be used to fit models discussed in the book to aid practitioners

Computational Challenges in the Geosciences

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Publisher : Springer Science & Business Media
ISBN 13 : 1461474345
Total Pages : 176 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Computational Challenges in the Geosciences by : Clint Dawson

Download or read book Computational Challenges in the Geosciences written by Clint Dawson and published by Springer Science & Business Media. This book was released on 2013-09-17 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational Challenges in the Geosciences addresses a cross-section of grand challenge problems arising in geoscience applications, including groundwater and petroleum reservoir simulation, hurricane storm surge, oceanography, volcanic eruptions and landslides, and tsunamis. Each of these applications gives rise to complex physical and mathematical models spanning multiple space-time scales, which can only be studied through computer simulation. The data required by the models is often highly uncertain, and the numerical solution of the models requires sophisticated algorithms which are mathematically accurate, computationally efficient and yet must preserve basic physical properties of the models. This volume summarizes current methodologies and future research challenges in this broad and important field.

An Introduction to Data Analysis and Uncertainty Quantification for Inverse Problems

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Author :
Publisher : SIAM
ISBN 13 : 1611974917
Total Pages : 275 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis An Introduction to Data Analysis and Uncertainty Quantification for Inverse Problems by : Luis Tenorio

Download or read book An Introduction to Data Analysis and Uncertainty Quantification for Inverse Problems written by Luis Tenorio and published by SIAM. This book was released on 2017-07-06 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse problems are found in many applications, such as medical imaging, engineering, astronomy, and geophysics, among others. To solve an inverse problem is to recover an object from noisy, usually indirect observations. Solutions to inverse problems are subject to many potential sources of error introduced by approximate mathematical models, regularization methods, numerical approximations for efficient computations, noisy data, and limitations in the number of observations; thus it is important to include an assessment of the uncertainties as part of the solution. Such assessment is interdisciplinary by nature, as it requires, in addition to knowledge of the particular application, methods from applied mathematics, probability, and statistics. This book bridges applied mathematics and statistics by providing a basic introduction to probability and statistics for uncertainty quantification in the context of inverse problems, as well as an introduction to statistical regularization of inverse problems. The author covers basic statistical inference, introduces the framework of ill-posed inverse problems, and explains statistical questions that arise in their applications. An Introduction to Data Analysis and Uncertainty Quantification for Inverse Problems?includes many examples that explain techniques which are useful to address general problems arising in uncertainty quantification, Bayesian and non-Bayesian statistical methods and discussions of their complementary roles, and analysis of a real data set to illustrate the methodology covered throughout the book.

Bayesian Data Analysis, Third Edition

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Publisher : CRC Press
ISBN 13 : 1439840954
Total Pages : 677 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis Bayesian Data Analysis, Third Edition by : Andrew Gelman

Download or read book Bayesian Data Analysis, Third Edition written by Andrew Gelman and published by CRC Press. This book was released on 2013-11-01 with total page 677 pages. Available in PDF, EPUB and Kindle. Book excerpt: Now in its third edition, this classic book is widely considered the leading text on Bayesian methods, lauded for its accessible, practical approach to analyzing data and solving research problems. Bayesian Data Analysis, Third Edition continues to take an applied approach to analysis using up-to-date Bayesian methods. The authors—all leaders in the statistics community—introduce basic concepts from a data-analytic perspective before presenting advanced methods. Throughout the text, numerous worked examples drawn from real applications and research emphasize the use of Bayesian inference in practice. New to the Third Edition Four new chapters on nonparametric modeling Coverage of weakly informative priors and boundary-avoiding priors Updated discussion of cross-validation and predictive information criteria Improved convergence monitoring and effective sample size calculations for iterative simulation Presentations of Hamiltonian Monte Carlo, variational Bayes, and expectation propagation New and revised software code The book can be used in three different ways. For undergraduate students, it introduces Bayesian inference starting from first principles. For graduate students, the text presents effective current approaches to Bayesian modeling and computation in statistics and related fields. For researchers, it provides an assortment of Bayesian methods in applied statistics. Additional materials, including data sets used in the examples, solutions to selected exercises, and software instructions, are available on the book’s web page.

Optimal Measurement Methods for Distributed Parameter System Identification

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Publisher : CRC Press
ISBN 13 : 0203026780
Total Pages : 390 pages
Book Rating : 4.2/5 (3 download)

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Book Synopsis Optimal Measurement Methods for Distributed Parameter System Identification by : Dariusz Ucinski

Download or read book Optimal Measurement Methods for Distributed Parameter System Identification written by Dariusz Ucinski and published by CRC Press. This book was released on 2004-08-27 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: For dynamic distributed systems modeled by partial differential equations, existing methods of sensor location in parameter estimation experiments are either limited to one-dimensional spatial domains or require large investments in software systems. With the expense of scanning and moving sensors, optimal placement presents a critical problem.

Large Scale Inverse Problems

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Publisher : Walter de Gruyter
ISBN 13 : 3110282267
Total Pages : 216 pages
Book Rating : 4.1/5 (12 download)

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Book Synopsis Large Scale Inverse Problems by : Mike Cullen

Download or read book Large Scale Inverse Problems written by Mike Cullen and published by Walter de Gruyter. This book was released on 2013-08-29 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Variational Methods

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Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110430398
Total Pages : 540 pages
Book Rating : 4.1/5 (14 download)

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Book Synopsis Variational Methods by : Maïtine Bergounioux

Download or read book Variational Methods written by Maïtine Bergounioux and published by Walter de Gruyter GmbH & Co KG. This book was released on 2017-01-11 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: With a focus on the interplay between mathematics and applications of imaging, the first part covers topics from optimization, inverse problems and shape spaces to computer vision and computational anatomy. The second part is geared towards geometric control and related topics, including Riemannian geometry, celestial mechanics and quantum control. Contents: Part I Second-order decomposition model for image processing: numerical experimentation Optimizing spatial and tonal data for PDE-based inpainting Image registration using phase・amplitude separation Rotation invariance in exemplar-based image inpainting Convective regularization for optical flow A variational method for quantitative photoacoustic tomography with piecewise constant coefficients On optical flow models for variational motion estimation Bilevel approaches for learning of variational imaging models Part II Non-degenerate forms of the generalized Euler・Lagrange condition for state-constrained optimal control problems The Purcell three-link swimmer: some geometric and numerical aspects related to periodic optimal controls Controllability of Keplerian motion with low-thrust control systems Higher variational equation techniques for the integrability of homogeneous potentials Introduction to KAM theory with a view to celestial mechanics Invariants of contact sub-pseudo-Riemannian structures and Einstein・Weyl geometry Time-optimal control for a perturbed Brockett integrator Twist maps and Arnold diffusion for diffeomorphisms A Hamiltonian approach to sufficiency in optimal control with minimal regularity conditions: Part I Index

Sequential Analysis and Optimal Design

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Publisher : SIAM
ISBN 13 : 9781611970593
Total Pages : 124 pages
Book Rating : 4.9/5 (75 download)

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Book Synopsis Sequential Analysis and Optimal Design by : Herman Chernoff

Download or read book Sequential Analysis and Optimal Design written by Herman Chernoff and published by SIAM. This book was released on 1972-01-01 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: An exploration of the interrelated fields of design of experiments and sequential analysis with emphasis on the nature of theoretical statistics and how this relates to the philosophy and practice of statistics.