Inverse modeling: an introduction to the theory and methods of inverse problems and data assimilation
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| Main Authors: | , |
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| Format: | Electronic eBook |
| Language: | English |
| Published: |
Bristol
IOP Publishing
[2015]
|
| Edition: | Version: 20151201 |
| Series: | IOP expanding physics
|
| Subjects: | |
| Online Access: | UBM01 Volltext Inhaltsverzeichnis |
| Physical Description: | 1 Online-Ressource |
| ISBN: | 9780750312189 9780750312202 |
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Record in the Search Index
| _version_ | 1804175885765443584 |
|---|---|
| adam_text | Titel: Inverse modeling
Autor: Nakamura, Gen
Jahr: 2015
Contents
Preface xiii
Acknowledgements xv
Author biographies xvi
1 Introduction 1-1
1.1 A tour through theory and applications 1-2
1.2 Types of inverse problems 1-14
1.2.1 The general inverse problem 1-15
1.2.2 Source problems 1-16
1.2.3 Scattering from obstacles 1-17
1.2.4 Dynamical systems inversion 1-19
1.2.5 Spectral inverse problems 1-21
Bibliography 1-22
2 Functional analytic tools 2-1
2.1 Normed spaces, elementary topology and compactness 2-1
2.1.1 Norms, convergence and the equivalence of norms 2-1
2.1.2 Open and closed sets, Cauchy sequences and completeness 2-5
2.1.3 Compact and relatively compact sets 2-7
2.2 Hilbert spaces, orthogonal systems and Fourier expansion 2-10
2.2.1 Scalar products and orthonormal systems 2-10
2.2.2 Best approximations and Fourier expansion 2-13
2.3 Bounded operators, Neumann series and compactness 2-19
2.3.1 Bounded and linear operators 2-19
2.3.2 The solution of equations of the second kind and the 2-25
Neumann series
2.3.3 Compact operators and integral operators 2-27
2.3.4 The solution of equations of the second kind and Riesz theory 2-32
2.4 Adjoint operators, eigenvalues and singular values 2-33
2.4.1 Riesz representation theorem and adjoint operators 2-33
2.4.2 Weak compactness of Hilbert spaces 2-36
2.4.3 Eigenvalues, spectrum and the spectral radius of an operator 2-38
2.4.4 Spectral theorem for compact self-adjoint operators 2-40
2.4.5 Singular value decomposition 2-46
2.5 Lax-Milgram and weak solutions to boundary value problems 2-48
2.6 The Frechet derivative and calculus in normed spaces 2-50
Bibliography 2-55
3 Approaches to regularization 3-1
3.1 Classical regularization methods 3-1
3.1.1 Ill-posed problems 3 -1
3.1.2 Regularization schemes 3-2
3.1.3 Spectral damping 3 -4
3.1.4 Tikhonov regularization and spectral cut-off 3-7
3.1.5 The minimum norm solution and its properties 3-10
3.1.6 Methods for choosing the regularization parameter 3-14
3.2 The Moore-Penrose pseudo-inverse and Tikhonov regularization 3-20
3.3 Iterative approaches to inverse problems 3-22
3.3.1 Newton and quasi-Newton methods 3-23
3.3.2 The gradient or Landweber method 3-25
3.3.3 Stopping rules and convergence order 3-31
Bibliography 3-34
4 A stochastic view of inverse problems 4-1
4.1 Stochastic estimators based on ensembles and particles 4-1
4.2 Bayesian methods 4-4
4.3 Markov chain Monte Carlo methods 4-6
4.4 Metropolis-Hastings and Gibbs sampler 4-11
4.5 Basic stochastic concepts 4-14
Bibliography 4-19
5 Dynamical systems inversion and data assimilation 5-1
5.1 Set-up for data assimilation 5.3
5.2 Three-dimensional variational data assimilation (3D-VAR) 5-5
5.3 Four-dimensional variational data assimilation (4D-VAR) 5-8
5.3.1 Classical 4D-VAR 5-8
5.3.2 Ensemble-Based 4D-VAR 5.13
5.4 The Kalman filter and Kalman smoother 5_16
5.5 Ensemble Kalman filters (EnKFs) 5_22
5.6 Particle filters and nonlinear Bayesian data assimilation 5-29
Bibliography 5-33
6 Programming of numerical algorithms and useful tools 6-1
6.1 MATLAB or OCTAVE programming: the butterfly 6-1
6.2 Data assimilation made simple 6-4
6.3 Ensemble data assimilation in a nutshell 6-8
6.4 An integral equation of the first kind, regularization and 6-9
atmospheric radiance retrievals
6.5 Integro-differential equations and neural fields 6-12
6.6 Image processing operators 6-15
Bibliography 6-18
7 Neural field inversion and kernel reconstruction 7-1
7.1 Simulating neural fields 7-4
7.2 Integral kernel reconstruction 7-8
7.3 A collocation method for kernel reconstruction 7-17
7.4 Traveling neural pulses and homogeneous kernels 7-20
7.5 Bi-orthogonal basis functions and integral operator inversion 7-23
7.6 Dimensional reduction and localization 7-26
Bibliography 7-30
8 Simulation of waves and fields 8-1
8.1 Potentials and potential operators 8-1
8.2 Simulation of wave scattering 8-11
8.3 The far field and the far field operator 8-15
8.4 Reciprocity relations 8-21
8.5 The Lax-Phillips method to calculate scattered waves 8-23
Bibliography 8-26
9 Nonlinear operators 9-1
9.1 Domain derivatives for boundary integral operators 9-1
9.2 Domain derivatives for boundary value problems 9-8
9.3 Alternative approaches to domain derivatives 9-11
9.3.1 The variational approach 9-11
9.3.2 Implicit function theorem approach 9-18
9.4 Gradient and Newton methods for inverse scattering 9-21
9.5 Differentiating dynamical systems: tangent linear models 9-27
Bibliography 9-30
10 Analysis: uniqueness, stability and convergence questions 10-1
10.1 Uniqueness of inverse problems 10~3
10.2 Uniqueness and stability for inverse obstacle scattering 10-4
10.3 Discrete versus continuous problems 10 7
10.4 Relation between inverse scattering and inverse boundary value 10-9
problems
10.5 Stability of cycled data assimilation 10-14
10.6 Review of convergence concepts for inverse problems 10-18
10.6.1 Convergence concepts in stochastics and in data 10-19
assimilation
10.6.2 Convergence concepts for reconstruction methods in inverse 10-21
scattering
Bibliography 10-24
11 Source reconstruction and magnetic tomography 11-1
11.1 Current simulation 11 -2
11.1.1 Currents based on the conductivity problem 11 -2
11.1.2 Simulation via the finite integration technique 11-4
11.2 The Biot-Savart operator and magnetic tomography 11 -8
11.2.1 Uniqueness and non-uniqueness results 11-12
11.2.2 Reducing the ill-posedness of the reconstruction by 11-16
using appropriate subspaces
11.3 Parameter estimation in dynamic magnetic tomography 11-25
11.4 Classification methods for inverse problems 11-28
Bibliography 11-32
12 Field reconstruction techniques 12-1
12.1 Series expansion methods 12-2
12.1.1 Fourier-Hankel series for field representation 12-2
12.1.2 Field reconstruction via exponential functions with an 12-6
imaginary argument
12.2 Fourier plane-wave methods 12-10
12.3 The potential or Kirsch-Kress method 12-12
12.4 The point source method 12-20
12.5 Duality and equivalence for the potential method and the 12-27
point source method
Bibliography 12-29
13 Sampling methods 13-1
13.1 Orthogonality or direct sampling 13-2
13.2 The linear sampling method of Colton and Kirsch 13-4
13.3 Kirsch s factorization method 13-10
Bibliography 13-17
14 Probe methods 14-1
14.1 The SSM 14-2
14.1.1 Basic ideas and principles 14-2
14.1.2 The needle scheme for probe methods 14-7
14.1.3 Domain sampling for probe methods 14-9
14.1.4 The contraction scheme for probe methods 14-10
14.1.5 Convergence analysis for the SSM 14-13
14.2 The probing method for near field data by Ikehata 14-16
14.2.1 Basic idea and principles 14-17
14.2.2 Convergence and equivalence of the probe and SSM 14-20
14.3 The multi-wave no-response and range test of Schulz and Potthast 14-21
14.4 Equivalence results 14-26
14.4.1 Equivalence of SSM and the no-response test 14-27
14.4.2 Equivalence of the no-response test and the range test 14-29
14.5 The multi-wave enclosure method of Ikehata 14-31
Bibliography 14-38
15 Analytic continuation tests 15-1
15.1 The range test 15-1
15.2 The no-response test of Luke-Potthast 15-6
15.3 Duality and equivalence for the range test and no-response test 15-10
15.4 Ikehata s enclosure method 15-11
15.4.1 Oscillating-decaying solutions 15-13
15.4.2 Identification of the singular points 15-18
Bibliography 15-20
16 Dynamical sampling and probe methods 16-1
16.1 Linear sampling method for identifying cavities in a heat conductor 16-2
16.1.1 Tools and theoretical foundation 16-4
16.1.2 Property of potential 16-14
16.1.3 The j ump relations of K* 16-16
16.2 Nakamura s dynamical probe method 16-17
16.2.1 Inverse boundary value problem for heat conductors with 16-17
inclusions
16.2.2 Tools and theoretical foundation 16-18
16.2.3 Proof of theorem 16.2.6 16-20
16.2.4 Existence of Runge s approximation functions 16-24
16.3 The time-domain probe method 16-26
16.4 The BC method of Belishev for the wave equation 16-29
Bibliography 16-35
17 Targeted observations and meta-inverse problems 17-1
17.1 A framework for meta-inverse problems 17-1
17.2 Framework adaption or zoom 17-7
17.3 Inverse source problems 17-8
Bibliography 17-13
Appendix A
|
| any_adam_object | 1 |
| author | Nakamura, Gen Potthast, Roland 1967- |
| author_GND | (DE-588)17287856X |
| author_facet | Nakamura, Gen Potthast, Roland 1967- |
| author_role | aut aut |
| author_sort | Nakamura, Gen |
| author_variant | g n gn r p rp |
| building | Verbundindex |
| bvnumber | BV043337015 |
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| dewey-full | 511.8 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.8 |
| dewey-search | 511.8 |
| dewey-sort | 3511.8 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | Version: 20151201 |
| format | Electronic eBook |
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| spelling | Nakamura, Gen Verfasser aut Inverse modeling an introduction to the theory and methods of inverse problems and data assimilation Gen Nakamura and Roland Potthast Hokkaido University, Japan Inha University, Korea University of Reading, United Kingdom German Meteorological Service (DWD) Version: 20151201 Bristol IOP Publishing [2015] © 2015 1 Online-Ressource txt rdacontent c rdamedia cr rdacarrier IOP expanding physics Inverses Problem (DE-588)4125161-1 gnd rswk-swf Datenassimilation (DE-588)4803260-8 gnd rswk-swf Inverses Problem (DE-588)4125161-1 s Datenassimilation (DE-588)4803260-8 s DE-604 Potthast, Roland 1967- Verfasser (DE-588)17287856X aut Erscheint auch als Druckausgabe 978-0-7503-1219-6 http://iopscience.iop.org/book/978-0-7503-1218-9 Verlag URL des Erstveröffentlichers Volltext HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028757017&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Nakamura, Gen Potthast, Roland 1967- Inverse modeling an introduction to the theory and methods of inverse problems and data assimilation Inverses Problem (DE-588)4125161-1 gnd Datenassimilation (DE-588)4803260-8 gnd |
| subject_GND | (DE-588)4125161-1 (DE-588)4803260-8 |
| title | Inverse modeling an introduction to the theory and methods of inverse problems and data assimilation |
| title_auth | Inverse modeling an introduction to the theory and methods of inverse problems and data assimilation |
| title_exact_search | Inverse modeling an introduction to the theory and methods of inverse problems and data assimilation |
| title_full | Inverse modeling an introduction to the theory and methods of inverse problems and data assimilation Gen Nakamura and Roland Potthast Hokkaido University, Japan Inha University, Korea University of Reading, United Kingdom German Meteorological Service (DWD) |
| title_fullStr | Inverse modeling an introduction to the theory and methods of inverse problems and data assimilation Gen Nakamura and Roland Potthast Hokkaido University, Japan Inha University, Korea University of Reading, United Kingdom German Meteorological Service (DWD) |
| title_full_unstemmed | Inverse modeling an introduction to the theory and methods of inverse problems and data assimilation Gen Nakamura and Roland Potthast Hokkaido University, Japan Inha University, Korea University of Reading, United Kingdom German Meteorological Service (DWD) |
| title_short | Inverse modeling |
| title_sort | inverse modeling an introduction to the theory and methods of inverse problems and data assimilation |
| title_sub | an introduction to the theory and methods of inverse problems and data assimilation |
| topic | Inverses Problem (DE-588)4125161-1 gnd Datenassimilation (DE-588)4803260-8 gnd |
| topic_facet | Inverses Problem Datenassimilation |
| url | http://iopscience.iop.org/book/978-0-7503-1218-9 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028757017&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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