Inverse modeling :an introduction to the theory and methods of inverse problems and data assimilation /

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"Version: 20151201"--Title page verso.Includes bibliographical references.Preface -- 1. Introduction -- 1.1. A tour through theory and applications -- 1.2. Types of inverse problems2. Functional analytic tools -- 2.1. Normed spaces, elementary topology and compactness -- 2.2. Hilbert spaces, orthogonal systems and Fourier expansion -- 2.3. Bounded operators, Neumann series and compactness -- 2.4. Adjoint operators, eigenvalues and singular values -- 2.5. Lax-Milgram and weak solutions to boundary value problems -- 2.6. The Fr?echet derivative and calculus in normed spaces3. Approaches to regularization -- 3.1. Classical regularization methods -- 3.2. The Moore-Penrose pseudo-inverse and Tikhonov regularization -- 3.3. Iterative approaches to inverse problems4. A stochastic view of inverse problems -- 4.1. Stochastic estimators based on ensembles and particles -- 4.2. Bayesian methods -- 4.3. Markov chain Monte Carlo methods -- 4.4. Metropolis-Hastings and Gibbs sampler -- 4.5. Basic stochastic concepts5. Dynamical systems inversion and data assimilation -- 5.1. Set-up for data assimilation -- 5.2. Three-dimensional variational data assimilation (3D-VAR) -- 5.3. Four-dimensional variational data assimilation (4D-VAR) -- 5.4. The Kalman filter and Kalman smoother -- 5.5. Ensemble Kalman filters (EnKFs) -- 5.6. Particle filters and nonlinear Bayesian data assimilation6. Programming of numerical algorithms and useful tools -- 6.1. MATLAB or OCTAVE programming : the butterfly -- 6.2. Data assimilation made simple -- 6.3. Ensemble data assimilation in a nutshell -- 6.4. An integral equation of the first kind, regularization and atmospheric radiance retrievals -- 6.5. Integro-differential equations and neural fields -- 6.6. Image processing operators7. Neural field inversion and kernel reconstruction -- 7.1. Simulating neural fields -- 7.2. Integral kernel reconstruction -- 7.3. A collocation method for kernel reconstruction -- 7.4. Traveling neural pulses and homogeneous kernels -- 7.5. Bi-orthogonal basis functions and integral operator inversion -- 7.6. Dimensional reduction and localization8. Simulation of waves and fields -- 8.1. Potentials and potential operators -- 8.2. Simulation of wave scattering -- 8.3. The far field and the far field operator -- 8.4. Reciprocity relations -- 8.5. The Lax-Phillips method to calculate scattered waves9. Nonlinear operators -- 9.1. Domain derivatives for boundary integral operators -- 9.2. Domain derivatives for boundary value problems -- 9.3. Alternative approaches to domain derivatives -- 9.4. Gradient and Newton methods for inverse scattering -- 9.5. Differentiating dynamical systems : tangent linear models10. Analysis : uniqueness, stability and convergence questions -- 10.1. Uniqueness of inverse problems -- 10.2. Uniqueness and stability for inverse obstacle scattering -- 10.3. Discrete versus continuous problems -- 10.4. Relation between inverse scattering and inverse boundary value problems -- 10.5. Stability of cycled data assimilation -- 10.6. Review of convergence concepts for inverse problems11. Source reconstruction and magnetic tomography -- 11.1. Current simulation -- 11.2. The Biot-Savart operator and magnetic tomography -- 11.3. Parameter estimation in dynamic magnetic tomography -- 11.4. Classification methods for inverse problems12. Field reconstruction techniques -- 12.1. Series expansion methods -- 12.2. Fourier plane-wave methods -- 12.3. The potential or Kirsch-Kress method -- 12.4. The point source method -- 12.5. Duality and equivalence for the potential method and the point source method13. Sampling methods -- 13.1. Orthogonality or direct sampling -- 13.2. The linear sampling method of Colton and Kirsch -- 13.3. Kirsch's factorization method14. Probe methods -- 14.1. The SSM -- 14.2. The probing method for near field data by Ikehata -- 14.3. The multi-wave no-response and range test of Schulz and Potthast -- 14.4. Equivalence results -- 14.5. The multi-wave enclosure method of Ikehata15. Analytic continuation tests -- 15.1. The range test -- 15.2. The no-response test of Luke-Potthast -- 15.3. Duality and equivalence for the range test and no-response test -- 15.4. Ikehata's enclosure method16. Dynamical sampling and probe methods -- 16.1. Linear sampling method for identifying cavities in a heat conductor -- 16.2. Nakamura's dynamical probe method -- 16.3. The time-domain probe method -- 16.4. The BC method of Belishev for the wave equation17. Targeted observations and meta-inverse problems -- 17.1. A framework for meta-inverse problems -- 17.2. Framework adaption or zoom -- 17.3. Inverse source problems -- Appendix A.This book provides a comprehensive introduction to the techniques, tools and methods for inverse problems and data assimilation, and is written at the interface between mathematics and applications for students, researchers and developers in mathematics, physics, engineering, acoustics, electromagnetics, meteorology, biology, environmental and other applied sciences. Basic analytic questions and tools are introduced, as well as a wide variety of concepts, methods and approaches to formulate and solve inverse problems. OCTAVE /MATLAB codes are included, which serve as a first step towards simulations and more sophisticated inversion or data assimilation algorithms.Students (advanced undergraduate to young researchers).Also available in print.Mode of access: World Wide Web.System requirements: Adobe Acrobat Reader.Gen Nakamura received his Bachelor's Degree 1971 from International Christian University, his Master's Degree 1974 from the Graduate School of Tokyo Metropolitan University and Doctor of Science Degree 1977 from the Graduate School of Tokyo Metropolitan University. He worked as Assistant Professor 1977-1991 at Josai University, 1981-1982 Lecturer of MIT, 1982-1983 Japan-US Exchange Fellow, 1989 Visiting Scientist of Brown University, 1991-1994 Professor of Josai University, 1994-1997 Professor of Science University of Tokyo, 1997-2001 Professor of Gunma University, 2001-2012 Professor of the Graduate School of Science, Hokkaido University, 2012-2013 Specially appointed Professor of the Graduate School of Science, Hokkaido University, 2013-2015 Professor of Inha University, since 2015 Harim Professor (special professor) Inha University, 2001--Visiting Professor of South East University. Professor Nakamura has served 2006-2009 as Program Officer of Japan Science for the Promotion of Science, 2009-2013 Board Member of Mathematical Society of Japan, 2011-2015 Expert Committee Member of Research Institute of Mathematical Science, Kyoto University and since 2011 Committee Member Based on the Fields of Specialties of Science Council of Japan. He received several prizes, for example the Autumn Prize of Mathematical Society of Japan, 2000 and the Prize for Science and Technology by the Minister of Education, Culture, Sports, Science and Technology of Japan, 2009. He is Editor of Eurasian Journal of Mathematical and Computer Applications and Member of the steering committee of Eurasian Association for Inverse Problems. Professor Nakamura has published 170 publications recorded in the MathScinet data base. Roland Potthast received his Diplom 1993, a PhD in Mathematics 1994 and a Habilitation Degree in Mathematics 1999 at the University of G?ottingen, Germany. Postdoctoral positions led him 1996-1998 to the University of Delaware, USA. After the Habilitation, Roland worked in a Consultancy Company in Cologne, Germany, 1999-2000, and at the Brunel University in London 2000-2001. From 2001 to 2006 he was leader of a Young Researcher Group on Inverse Problems in G?ottingen, funded by the Volkswagen Foundation. He received an extraordinary professorship at the University of G?ottingen in 2004. As a part-time activity, he was Owner and CEO of an IT-company based in G?ottingen for seven years 2005-2012, providing internet-based services to large-scale European companies. Roland moved to the UK in 2006, with a lectureship at the University of Reading 2006, with promotions to Reader (Associate Professor) 2008 and Full Professor in 2010. Roland has been visiting professor at the University of Rennes, France, 2007-2009 and at the Research Center J?ulich, Germany, 2009 and had a call to a W3 professorship in Munich 2010. Since 2010 he holds a post as 'Director and Professor' (B1) at the German Federal Ministry of Transport and digital Infrastructure (BMVI), leading the Data Assimilation Department of the German Weather Service (DWD) in Frankfurt/Offenbach, with a part-time involvement as full professor at the University of Reading, UK. He is supervising a group of about 25 scientists and coordinates a network of about 45 researchers in data assimilation and inverse problems working in collaboration with DWD. Roland received several prizes and awards, among them 1994 the best PhD award of the German Mathematical Society, four years of full-time funding by the German Science foundation DFG and five years by the Volkswagen Foundation; in the UK an EPSRC Springboard fellowship in 2007 and a Leverhulme research fellowship in 2008, a 'Bridging-the-Gaps Award' by EPSRC in 2009-12; and the Pichorides Distinguished Lectureship of the University of Crete, Greece, in 2015. Professor Potthast has published more than 65 mathematical research papers, which received more than 1000 citations, a book on inverse scattering theory 2001 and a book on neural field theory 2014.Title from PDF title page (viewed on January 10, 2016).

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: .,

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1 online resource (various pagings) :illustrations (some color).

Language

English

ISBN/ISSN

9780750312189

Classification

511/.8

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Subject(s)

Inverse problems (Differential equations)
Stochastic processes.
MATHEMATICS / Applied.
Applied mathematics.

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Gen Nakamura and Roland Potthast.

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