Parameter estimation and inverse problems pdf

Although it contains a lot of mathematics, it is not intended as a mathematical book, but rather tries to explain how a method of acquisition of information can be applied to the actual world. The book provides a comprehensive, up-to-date description of the methods to be used for fitting experimental data, or to estimate model parameters, and to unify these methods into the Inverse Problem Theory.

The first part of the book deals with discrete problems and describes Maximum likelihood, Monte Carlo, Least squares, and Least absolute values methods. The second part deals with inverse problems involving functions. The book is almost completely self-contained, with all important concepts carefully introduced. Although theoretical concepts are strongly emphasized, the author has ensured that all the useful formulas are listed, with many special cases included.

The book will thus serve equally well as a reference manual for researchers needing to refresh their memories on a given algorithm, or as a textbook in a course for undergraduate or graduate students. This publication is designed to provide a practical understanding of methods of parameter estimation and uncertainty analysis.

The practical problems covered range from simple processing of time- and space-series data to inversion of potential field, seismic, electrical, and electromagnetic data.

The various formulations are reconciled with field data in the numerous examples provided in the book; well-documented computer programmes are also given to show how easy it is to implement inversion algorithms.

The problems of making inferences about the natural world from noisy observations and imperfect theories occur in almost all scientific disciplines. This book addresses these problems using examples taken from geophysical fluid dynamics. It focuses on discrete formulations, both static and time-varying, known variously as inverse, state estimation or data assimilation problems.

Starting with fundamental algebraic and statistical ideas, the book guides the reader through a range of inference tools including the singular value decomposition, Gauss-Markov and minimum variance estimates, Kalman filters and related smoothers, and adjoint Lagrange multiplier methods. The final chapters discuss a variety of practical applications to geophysical flow problems.

Discrete Inverse and State Estimation Problems is an ideal introduction to the topic for graduate students and researchers in oceanography, meteorology, climate dynamics, and geophysical fluid dynamics. It is also accessible to a wider scientific audience; the only prerequisite is an understanding of linear algebra. A diskette with the updated programme of Appendix C and examples is available through the author at a small fee.

This book systematically discusses basic concepts, theory, solution methods and applications of inverse problems in groundwater modeling. It is the first book devoted to this subject. The inverse problem is defined and solved in both deterministic and statistic frameworks. Various direct and indirect methods are discussed and compared.

As a useful tool, the adjoint state method and its applications are given in detail. For a stochastic field, the maximum likelihood estimation and co-kriging techniques are used to estimate unknown parameters. The ill-posed problem of inverse solution is highlighted through the whole book.

The importance of data collection strategy is specially emphasized. Besides the classical design criteria, the relationships between decision making, prediction, parameter identification and experimental design are considered from the point of view of extended identifiabilities. The problem of model structure identification is also considered. This book can be used as a textbook for graduate students majoring in hydrogeology or related subjects.

It is also a reference book for hydrogeologists, petroleum engineers, environmental engineers, mining engineers and applied mathematicians. 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. This three-part book provides a comprehensive and systematic introduction to these challenging topics such as model calibration, parameter estimation, reliability assessment, and data collection design.

Part 1 covers the classical inverse problem for parameter estimation in both deterministic and statistical frameworks, Part 2 is dedicated to system identification, hyperparameter estimation, and model dimension reduction, and Part 3 considers how to collect data and construct reliable models for prediction and decision-making.

For the first time, topics such as multiscale inversion, stochastic field parameterization, level set method, machine learning, global sensitivity analysis, data assimilation, model uncertainty quantification, robust design, and goal-oriented modeling, are systematically described and summarized in a single book from the perspective of model inversion, and elucidated with numerical examples from environmental and water resources modeling.

Readers of this book will not only learn basic concepts and methods for simple parameter estimation, but also get familiar with advanced methods for modeling complex systems.

Translate PDF. The audience for the course has included a broad range of first— or second—year graduate stu- dents and occasionally advanced undergraduates from geophysics, hydrology, mathematics, astronomy, and other disciplines.

Cliff Thurber joined this col- laboration during the past three years and has taught a similar course at the University of Wisconsin. Our principal goal for this text is to promote fundamental understanding of parameter estimation and inverse problem philosophy and methodology, specifi- cally regarding such key issues as uncertainty, ill—posedness, regularization, bias, and resolution.

Throughout the examples and exercises, a CD icon indicates that there is additional material on the CD. Exercises include a mix of programming and theoretical problems.

This book has necessarily had to distill a tremendous body of mathematics and science going back to at least Newton and Gauss. We hope that it will find a broad audience of students and professionals interested in the general problem of estimating physical models from data. Because this is an introductory text surveying a very broad field, we have not been able to go into great depth.

Where appropriate, we have also directly referenced research contributions to the field. For example, read- ers with a strong mathematical background may be surprised that we consider only inverse problems with discrete data and discretized models.

By doing this we avoid the much of the technical complexity of functional analysis. Some advanced applications and topics that we have omitted include inverse scatter- ing problems, seismic diffraction tomography, wavelets, data assimilation, and expectation maximization EM methods. In our experience, many students are in need of at least a review of these topics, and we typically spend the first two to three weeks of the course reviewing this material from Appendices A, B, and C.

View 13 excerpts, cites methods and background. Outlier-insensitive Bayesian inference for linear inverse problems OutIBI with applications to space geodetic data. Data kit inversion and uncertainty analysis. Journal of Applied Geophysics. Mathematical Geosciences. A Bayesian linear inversion methodology based on Gaussian mixture models and its application to geophysical inverse problems are presented in this paper. The proposed inverse method is based on a … Expand. Inverse problems are typically ill-posed or ill-conditioned and require regularization.

Tikhonov regularization is a popular approach and it requires an additional parameter called the regularization … Expand. View 10 excerpts, cites methods and background. Trans-dimensional inverse problems, model comparison and the evidence. In some cases arguments can be used to bound the maximum number of … Expand. View 2 excerpts, cites methods. Uncertainty quantification in Bayesian inverse problems with model and data dimension reduction.

Computationally efficient Bayesian inference for inverse problems. Bayesian statistics provides a foundation for inference from noisy and incomplete data, a natural mechanism for regularization in the form of prior information, and a quantitative assessment of … Expand.

Technical Note: Improving computational efficiency in large linear inverse problems: an example from carbon dioxide flux estimation. View 1 excerpt. A review of Markov Chain Monte Carlo and information theory tools for inverse problems in subsurface flow.

Computational Geosciences. Parameter identification is one of the key elements in the construction of models in geosciences. However, inherent difficulties such as the instability of ill-posed problems or the presence of … Expand. View 1 excerpt, cites background. Computational Methods for Inverse Problems. In verse problems arise in a number of important practical applications, ranging from biomedical imaging to seismic prospecting.

This book provides the reader with a basic understanding of both the … Expand.