English | 2022 | ISBN: 0367506300 | 394 pages | True EPUB | 8.24 MB
Inverse problems of identifying parameters and initial/boundary conditions in deterministic and stochastic partial differential equations constitute a vibrant and emerging research area that has found numerous applications. A related problem of paramount importance is the optimal control problem for stochastic differential equations. This edited volume comprises invited contributions from world-renowned researchers in the subject of control and inverse problems. There are several contributions on optimal control and inverse problems covering different aspects of the theory, numerical methods, and applications. Besides a unified presentation of the most recent and relevant developments, this volume also presents some survey articles to make the material self-contained. To maintain the highest level of scientific quality, all manuscripts have been thoroughly reviewed. This edited volume comprises invited contributions from world-renowned researchers in the subject of stochastic control and inverse problems. There are several contributions on stochastic optimal control and stochastic inverse problems covering different aspects of the theory, numerical methods, and applications.

Inverse Optimal Control and Inverse Noncooperative Dynamic Game Theory: A Minimum-Principle Approach by Timothy L. Molloy
English | EPUB | 2022 | 278 Pages | ISBN : 3030933164 | 20.6 MB
This book presents a novel unified treatment of inverse problems in optimal control and noncooperative dynamic game theory. It provides readers with fundamental tools for the development of practical algorithms to solve inverse problems in control, robotics, biology, and economics.

English | 2021 | ISBN: 1786349817 | 247 pages | True PDF EPUB | 38.98 MB
Currently, solving problems based on designing and calculating complex structures with significant nonlinearity usually require:Semi-inverse Method in Nonlinear Problems of Axisymmetric Shells Forming provides an alternative method for solving problems with deep geometric and physical nonlinearity. Easily implemented on normal PCs, this method is fast and creative. The reader can use integrated packages of the MathCad variety that implement 'live mathematics'. Such packages give the reader the freedom to create programs for themselves.In the proposed method, a function for molding pressure is constructed, which is output to a stationary value by varying the shape parameters and edge reactions. The final shape of the shell is given using analytical approximations. Applications of the method are applied to real shell structures. Forming spherical and ellipsoidal shells (flapping membranes), correcting the shape of the bottom of a container for liquid cargo, modeling the operation of a flat jack, and converting a cylindrical shell into a barrel-shape are also considered.

English | 2021 | ISBN: 0367001985 | 359 pages | pdf | 8.75 MB
Driven the advancement of industrial mathematics and the need for impact case studies,Inverse Problems with Applications in Science and Engineeringthoroughly examines the state-of-the-art of some representative classes of inverse and ill-posed problems for partial differential equations (PDEs). The natural practical applications of this examination arise in heat transfer, electrostatics, porous media, acoustics, fluid and solid mechanics - all of which are addressed in this text.

English | 2021 | ISBN: 0367470055 | 358 pages | True PDF | 14.84 MB
Fully updated throughout, with several new chapters, this second edition of Introduction to Inverse Problems in Imaging guides advanced undergraduate and graduate students in physics, computer science, mathematics and engineering through the principles of linear inverse problems, in addition to methods of their approximate solution and their practical applications in imaging. The level of mathematical treatment is kept as low as possible to make the book suitable for a wide range of readers from different backgrounds, with readers needing just a rudimentary understanding of analysis, geometry, linear algebra, probability theory, and Fourier analysis. This second edition contains new chapters on quadratic, iterative, and sparsity-enforcing tikhonov regularizations in addition to maximum likelihood methods and bayesian regularization. The authors concentrate on presenting easily implementable and fast solution algorithms. With examples and exercised throughout, the book will provide the reader with the appropriate background for a clear understanding of the essence of inverse problems (ill-posedness and its cure) and, consequently, for an intelligent assessment of the rapidly growing literature on these problems.

English | 2021 | ISBN: 0367506300 , 978-0367506308 | 395 pages | True PDF | 12.44 MB
Inverse problems of identifying random parameters and random initial/boundary conditions in stochastic partial differential equations constitute a vibrant and emerging research area that has found numerous applications. A related problem of paramount importance is the optimal control problem for stochastic differential equations.

English | 2020 | ISBN: 9811221669 | 387 pages | True PDF | 7.17 MB
This book is a compilation of different methods of formulating and solving inverse problems in physics from classical mechanics to the potentials and nucleus-nucleus scattering. Mathematical proofs are omitted since excellent monographs already exist dealing with these aspects of the inverse problems.The emphasis here is on finding numerical solutions to complicated equations. A detailed discussion is presented on the use of continued fractional expansion, its power and its limitation as applied to various physical problems. In particular, the inverse problem for discrete form of the wave equation is given a detailed exposition and applied to atomic and nuclear scattering, in the latter for elastic as well as inelastic collision. This technique is also used for inverse problem of geomagnetic induction and one-dimensional electrical conductivity. Among other topics covered are the inverse problem of torsional vibration, and also a chapter on the determination of the motion of a body with reflecting surface from its reflection coefficient.

English | 2021 | ISBN: 3110745410 | 344 pages | pdf | 6.3 MB
This book summarizes the main analytical and numerical results of Carleman estimates. In the analytical part, Carleman estimates for three main types of Partial Differential Equations (PDEs) are derived. In the numerical part, first numerical methods are proposed to solve ill-posed Cauchy problems for both linear and quasilinear PDEs. Next, various versions of the convexification method are developed for a number of Coefficient Inverse Problems.

Inverse Magnetometry: Mollifier Magnetization Distribution from Geomagnetic Field Data by Christian Blick
English | PDF,EPUB | 2021 | 121 Pages | ISBN : 3030795071 | 17.9 MB
This monograph presents the geoscientific context arising in decorrelative geomagnetic exploration. First, an insight into the current state of research is given by reducing magnetometry to mathematically accessible, and thus calculable, decorrelated models. In this way, various questions and problems of magnetometry are made available to a broad scientific audience and the exploration industry. New stimuli are given, and innovative ways of modeling geologic strata by mollifier magnetometric techniques are shown.

English | 2021 | ISBN: 1774077078 | 346 pages | True PDF | 32.18 MB
The book Numerical Methods for Inverse Problems consists of contemporaneouss articles featuring not only several well-known inverse problems used in the inference of many physical and engineering systems such as that of the partial differential equations but also the statistical and imaging inverse problems. It includes a variety of numerical methods for solving inverse problems such as that of the Tikhonov regularization; finite differences; and orthogonal decomposition; as well as those based on Bayesian inference, artificial neural networks, and quantum annealing.
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