Computational Methods for Inverse Problems

This book presents methods for the computational solution of some important problems of linear algebra: linear systems, linear least squares problems, eigenvalue problems, and linear programming probl

Observations of ocean circulation have increased as a result of international field programmes and of remote sensing systems on artificial earth satellites. Oceanographers are increasingly turning to inverse methods for combining these observations with numerical models of ocean circulation. Professor Bennett's work explores the potential for inverse theory, emphasizing possibilities rather than expedient or rudimentary applications. In addition to interpolating the data and adding realism to the model solutions, the methods can yield estimates for unobserved flow variables, forcing fields, and model parameters. Inverse formulations can resolve ill-posed modelling problems, lead to design criteria for oceanic observing systems, and enable the testing of models as scientific hypothesis. Exercises of varying difficulty rehearse technical skills and supplement the central theoretical development. Thus this book will be invaluable for environmental scientists and engineers, advanced underg

Inverse problems are immensely important in modern science and technology. However, the broad mathematical issues raised by inverse problems receive scant attention in the university curriculum. This

This book describes mathematical formulations and computational methods for solving two-phase flow problems with a computer code that calculates thermal hydraulic problems related to light water and f

The second edition of Computational Fluid Dynamics represents a significant improvement from the first edition. However, the original idea of including all computational fluid dynamics methods (FDM, FEM, FVM); all mesh generation schemes; and physical applications to turbulence, combustion, acoustics, radiative heat transfer, multiphase flow, electromagnetic flow, and general relativity is still maintained. The second edition includes a new section on preconditioning for EBE-GMRES and a complete revision of the section on flowfield-dependent variation methods, which demonstrates more detailed computational processes and includes additional example problems. For those instructors desiring a textbook that contains homework assignments, a variety of problems for FDM, FEM and FVM are included in an appendix. To facilitate students and practitioners intending to develop a large-scale computer code, an example of FORTRAN code capable of solving compressible, incompressible, viscous, inviscid

The development of effective methods for the prediction of ontological annotations is an important goal in computational biology, yet evaluating their performance is difficult due to problems caused b

This book introduces the reader to the area of inverse problems. The study of inverse problems is of vital interest to many areas of science and technology such as geophysical exploration, system iden

The problems of making inferences about the natural world from noisy observations and imperfect theories occur in almost all scientific disciplines. This 2006 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

Computational synthetic geometry deals with methods for realizing abstract geometric objects in concrete vector spaces. This research monograph considers a large class of problems from convexity and d

Bringing together idiomatic Python programming, foundational numerical methods, and physics applications, this is an ideal standalone textbook for courses on computational physics. All the frequently used numerical methods in physics are explained, including foundational techniques and hidden gems on topics such as linear algebra, differential equations, root-finding, interpolation, and integration. Accompanying the mathematical derivations are full implementations of dozens of numerical methods in Python, as well as more than 250 end-of-chapter problems. Numerical methods and physics examples are clearly separated, allowing this introductory book to be later used as a reference; the penultimate section in each chapter is an in depth project, tackling physics problems which cannot be solved without the use of a computer. Written primarily for students studying computational physics, this textbook brings the non-specialist quickly up to speed with Python before looking in detail at the

Parameter Estimation and Inverse Problems, Third Edition, is structured around a course at New Mexico Tech and is designed to be accessible to typical graduate students in the physical sciences who do

Parameter Estimation and Inverse Problems, 2e provides geoscience students and professionals with answers to common questions like how one can derive a physical model from a finite set of observations

The advent of supercomputers has brought computational fluid dynamics (CFD) to the forefront as a tool to analyze increasingly complex simulation scenarios in many fields. Computational aerodynamics problems are also increasingly moving towards being coupled, multi-physics and multi-scale with complex, moving geometries. The latter presents severe geometry handling and meshing challenges. Simulations also frequently use formal design optimization processes. This book explains the evolution of CFD and provides a comprehensive overview of the plethora of tools and methods available for solving complex scenarios while exploring the future directions and possible outcomes. Using numerous examples, illustrations and computational methods the author discusses turbulence modeling, pre and post processing, coupled solutions, the importance of design optimization, multiphysics problems, reduced order models, and large scale computations and the future of CFD. Advanced Computational Fluid and Ae

This volume presents a mathematical development of a recent approach to the modeling and simulation of turbulent flows based on methods for the approximate solution of inverse problems. The resulting

This book is devoted to an introduction of elliptic and parabolic inverse problems. Our goal is to present some recent methods for establishing uniqueness and stability results. We study some classica

With contributions from some of the leading authorities in the field, the work in Differential Equations: Inverse and Direct Problems stimulates the preparation of new research results and offers exci

This book presents a variety of computational methods used to solve dynamic problems in economics and finance. It emphasizes practical numerical methods rather than mathematical proofs and focuses on

Computational techniques have become indispensable tools in solving complex problems in transport phenomena. This book, first published in 1997, provides a clear, user-oriented introduction to the subject. Each self-contained chapter includes a detailed worked example and a discussion of the problem system equations. Also included are the numerical methods used; computer code for the solution of the problem system equations; discussion of the numerical solution with emphasis on physical interpretation; and when appropriate, a comparison of the numerical solution with an analytical solution or a discussion of how the numerical solution goes beyond what can be done analytically, especially for nonlinear problems. Intended for students and a broad range of scientists and engineers, the book includes computer code written in transportable Fortran so that readers can produce the numerical solutions and then extend them to other cases. The programs are also available on the author's web site

This book introduces the fundamental concepts of inverse heat transfer problems. It presents in detail the basic steps of four techniques of inverse heat transfer protocol, as a parameter estimation

This monograph is a compilation of research on the inverse Gaussian distribution. It emphasizes the presentation of the statistical properties, methods, and applications of the two-parameter inverse G

Learn how to apply cognitive principles to the problems of computer vision Computational Models for Cognitive Vision formulates the computational models for the cognitive principles found in bio

Computational Non-coding RNA Biology is a resource for the computation of non-coding RNAs. The book covers computational methods for the identification and quantification of non-coding RNAs, including

Free-Surface Flow: Computational Methods presents a detailed analysis of numerical schemes for shallow-water waves. It includes practical applications for the numerical simulation of flow and transpor

Fluid mechanics is a branch of classical physics that has a rich tradition in applied mathematics and numerical methods. It is at work virtually everywhere, from nature to technology. This broad and fundamental coverage of computational fluid dynamics (CFD) begins with a presentation of basic numerical methods and flows into a rigorous introduction to the subject. A heavy emphasis is placed on the exploration of fluid mechanical physics through CFD, making this book an ideal text for any new course that simultaneously covers intermediate fluid mechanics and computation. Ample examples, problems and computer exercises are provided to allow students to test their understanding of a variety of numerical methods for solving flow physics problems, including the point-vortex method, numerical methods for hydrodynamic stability analysis, spectral methods and traditional CFD topics.

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 m

This manuscript is devoted to a rigorous and detailed exposition of the spectral theory and associated forward and inverse scattering problems for the Laplace-Beltrami operators on asymptotically hype

This book is intended to provide the reader with a firm conceptual and empirical understanding of basic information-theoretic econometric models and methods. Because most data are observational, practitioners work with indirect noisy observations and ill-posed econometric models in the form of stochastic inverse problems. Consequently, traditional econometric methods in many cases are not applicable for answering many of the quantitative questions that analysts wish to ask. After initial chapters deal with parametric and semiparametric linear probability models, the focus turns to solving nonparametric stochastic inverse problems. In succeeding chapters, a family of power divergence measure-likelihood functions are introduced for a range of traditional and nontraditional econometric-model problems. Finally, within either an empirical maximum likelihood or loss context, Ron C. Mittelhammer and George G. Judge suggest a basis for choosing a member of the divergence family.

This book constitutes the thoroughly refereed post-proceedings of the 7th International Meeting on Computational Intelligence Methods for Bioinformatics and Biostatistics, CIBB 2010, held in Palermo,

This volume contains the results of the workshop on Parameter Identification and Inverse Problems in Hydrology, Geology and Ecology, held in Karlsruhe, Germany, and represents a balanced selection o

Inverse problems arise in practical situations such as medical imaging, geophysical exploration, and non-destructive evaluation where measurements made on the exterior of a body are used to determine properties of the inaccessible interior. There have been substantial developments in the mathematical theory of inverse problems, and applications have expanded greatly. In this volume, leading experts in the theoretical and applied aspects of inverse problems offer extended surveys on several important topics in modern inverse problems, such as microlocal analysis, reflection seismology, tomography, inverse scattering, and X-ray transforms. Each article covers a particular topic or topics with an emphasis on accessibility and integration with the whole volume. Thus the collection can be at the same time stimulating to researchers and accessible to graduate students.

The critical role of trace gases in global atmospheric change makes an improved understanding of these gases imperative. Measurements of the distributions of these gases in space and time provide important information, but the interpretation of this information often involves ill-conditioned model inversions. A variety of techniques have therefore been developed to analyze these problems. Inverse Problems in Atmospheric Constituent Transport is the first book to give comprehensive coverage of work on this topic. The trace gas inversion problem is presented in general terms and the various different approaches are unified by treating the inversion problem as one of statistical estimation. Later chapters demonstrate the application of these methods to studies of carbon dioxide, methane, halocarbons and other gases implicated in global climate change. This book is aimed at graduate students and researchers embarking upon studies of global atmospheric change, biogeochemical cycles and Eart

Low-speed aerodynamics is important in the design and operation of aircraft flying at low Mach number, and ground and marine vehicles. This 2001 book offers a modern treatment of the subject, both the theory of inviscid, incompressible, and irrotational aerodynamics and the computational techniques now available to solve complex problems. A unique feature of the text is that the computational approach (from a single vortex element to a three-dimensional panel formulation) is interwoven throughout. Thus, the reader can learn about classical methods of the past, while also learning how to use numerical methods to solve real-world aerodynamic problems. This second edition has a new chapter on the laminar boundary layer (emphasis on the viscous-inviscid coupling), the latest versions of computational techniques, and additional coverage of interaction problems. It includes a systematic treatment of two-dimensional panel methods and a detailed presentation of computational techniques for thr

Computational thinking is increasingly gaining importance in modern biology, due to the unprecedented scale at which data is nowadays produced. Bridging the cultural gap between the biological and computational sciences, this book serves as an accessible introduction to computational concepts for students in the life sciences. It focuses on teaching algorithmic and logical thinking, rather than just the use of existing bioinformatics tools or programming. Topics are presented from a biological point of view, to demonstrate how computational approaches can be used to solve problems in biology such as biological image processing, regulatory networks, and sequence analysis. The book contains a range of pedagogical features to aid understanding, including real-world examples, in-text exercises, end-of-chapter problems, colour-coded Python code, and 'code explained' boxes. User-friendly throughout, Computational Thinking for Life Scientists promotes the thinking skills and self-efficacy req

The area of computational cryptography is dedicated to the development of effective methods in algorithmic number theory that improve implementation of cryptosystems or further their cryptanalysis. This book is a tribute to Arjen K. Lenstra, one of the key contributors to the field, on the occasion of his 65th birthday, covering his best-known scientific achievements in the field. Students and security engineers will appreciate this no-nonsense introduction to the hard mathematical problems used in cryptography and on which cybersecurity is built, as well as the overview of recent advances on how to solve these problems from both theoretical and practical applied perspectives. Beginning with polynomials, the book moves on to the celebrated Lenstra–Lenstra–Lovász lattice reduction algorithm, and then progresses to integer factorization and the impact of these methods to the selection of strong cryptographic keys for usage in widely used standards.

Meaningful use of advanced Bayesian methods requires a good understanding of the fundamentals. This engaging book explains the ideas that underpin the construction and analysis of Bayesian models, with particular focus on computational methods and schemes. The unique features of the text are the extensive discussion of available software packages combined with a brief but complete and mathematically rigorous introduction to Bayesian inference. The text introduces Monte Carlo methods, Markov chain Monte Carlo methods, and Bayesian software, with additional material on model validation and comparison, transdimensional MCMC, and conditionally Gaussian models. The inclusion of problems makes the book suitable as a textbook for a first graduate-level course in Bayesian computation with a focus on Monte Carlo methods. The extensive discussion of Bayesian software - R/R-INLA, OpenBUGS, JAGS, STAN, and BayesX - makes it useful also for researchers and graduate students from beyond statistics.

This book is a guide to numerical methods for solving fluid dynamics problems. The most widely used discretization and solution methods, which are also found in most commercial CFD-programs, are descr

Algebraic and Combinatorial Computational Biology introduces students and researchers to a panorama of powerful and current methods for mathematical problem-solving in modern computational biology. Pr

This book presents computational and statistical methods used by intelligent systems within the concept of Industry 4.0. The methods include among others evolution-based and swarm intelligence-based m

This book is a guide to the use of inverse theory for estimation and conditional simulation of flow and transport parameters in porous media. It describes the theory and practice of estimating properties of underground petroleum reservoirs from measurements of flow in wells, and it explains how to characterize the uncertainty in such estimates. Early chapters present the reader with the necessary background in inverse theory, probability and spatial statistics. The book demonstrates how to calculate sensitivity coefficients and the linearized relationship between models and production data. It also shows how to develop iterative methods for generating estimates and conditional realizations. The text is written for researchers and graduates in petroleum engineering and groundwater hydrology, and can be used as a textbook for advanced courses on inverse theory in petroleum engineering. It includes many worked examples to demonstrate the methodologies and a selection of exercises.