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Inverse Theory II: Applications
Last Updated: 2026-06-03 00:13:58
Abstract
This second part of the course on Inverse Theory provides an introduction to the numerical solution of (non-)linear inverse problems including uncertainty quantification. Specific examples are drawn from different areas of geophysics and image processing. Students solve various model problems using Jupyter notebooks (in Julia), and familiarize themselves with relevant open-source libraries.
Objective
This course provides numerical tools and recipes to solve (non)-linear inverse problems arising in nearly all fields of science and engineering. After successful completion of the class, the students will have a thorough understanding of suitable solution algorithms, common challenges and possible mitigations to infer parameters that govern large-scale physical systems from sparse data measurements. Prerequisites for this course are (i) 651-4096-00L Inverse Theory: Basics, (ii) basic programming skills.
Content
The class discusses several important concepts to solve (non)-linear inverse problems and demonstrates how to apply them to real-world data applications. All sessions are split into a lecture part in the first half, followed by tutorials using Jupyter notebooks in the second. The range of covered topics include: 1. Regularization filters and image deblurring 2. Link between regularization, deterministic and probabilistic approaches for the solution of linear inverse problems. 3. Optimization for nonlinear inverse problems (line-search methods). 4. Adjoint methods and time reversal, computing gradients for large-scale inverse problems. 5. Full-waveform inversion. 6. Machine learning basics (artificial neural networks) and links to inverse problems. 6. Uncertainty quantification and (Hamiltonian) Monte Carlo method
Resources
Lecture Notes
Presentation slides and some background material will be provided.
Literature
Nocedal, J. and Wright, S.J. (2006) Numerical Optimization, 2nd Edition, Springer. Tarantola, A. (2005) Inverse Problem Theory and Methods for Model Parameter Estimation. SIAM: Society for Industrial and Applied Mathematics.
General Information
- Language
- English
- Levels
- BSC , MSC
- Frequency
- Yearly recurring
Examination
- Type
- graded semester performance
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture with exercise | Inverse Theory II: Applications |
|
28 h semesterly |
Offered In
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Geophysics (Recommended combinations: Subject 1 + Subject 2 Subject 1 + Subject 3 Subject 2 + Subject 3 Subject 3 + Subject 4 Subject 5 + Subject 6 + Subject 8 Subject 4 + Subject 5 Subject 7 + Subject 8)
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Geophysics (Recommended combinations: Subject 2 + Subject 5 + Subject 6 + Subject 7 Subject 2 + Subject 4 + Subject 5 + Subject 6 + Subject 8 Subject 2 + Subject 5 + Subject 6 + (Subject 1 or Subject 3))
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Electives (Courses can be chosen from the complete offerings of the ETH Zurich and University of Zurich (according to prior agreement with the MSc Committee).)
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General Electives (Students may choose General Electives from the entire course programme of ETH Zurich - with the following restrictions: courses that belong to the first or second year of a Bachelor curriculum at ETH Zurich as well as courses from GESS "Science in Perspective" are not eligible here. The following courses are explicitly recommended to physics students by their lecturers. (Courses in this list may be assigned to the category "General Electives" directly in myStudies. For the category assignment of other eligible courses keep the choice "no category" and take contact with the Study Administration ( ) after having received the credits.))
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