651-4096-00L Inverse Theory I: Basics
Semester | Spring Semester 2021 |
Lecturers | A. Fichtner |
Periodicity | yearly recurring course |
Language of instruction | English |
Courses
Number | Title | Hours | Lecturers | |||||||
---|---|---|---|---|---|---|---|---|---|---|
651-4096-00 V | Inverse Theory I: Basics For students attending Geothermal Energy: Note that Geothermal Energy starts at 12:30 | 28s hrs |
| A. Fichtner |
Catalogue data
Abstract | Inverse theory is the art of inferring properties of a physical system from noisy and sparse observations. It is used to transform observations of waves into 3D images of a medium seismic tomography, medical imaging and material science; to constrain density in the Earth from gravity; to obtain probabilities of life on exoplanets ... . Inverse theory is at the heart of many natural sciences. |
Objective | The goal of this course is to enable students to develop a mathematical formulation of specific inference (inverse) problems that may arise anywhere in the physical sciences, and to implement suitable solution methods. Furthermore, students should become aware that nearly all relevant inverse problems are ill-posed, and that their meaningful solution requires the addition of prior knowledge in the form of expertise and physical intuition. This is what makes inverse theory an art. |
Content | This first of two courses covers the basics needed to address (and hopefully solve) any kind of inverse problem. Starting from the description of information in terms of probabilities, we will derive Bayes' Theorem, which forms the mathematical foundation of modern scientific inference. This will allow us to formalise the process of gaining information about a physical system using new observations. Following the conceptual part of the course, we will focus on practical solutions of inverse problems, which will lead us to study Monte Carlo methods and the special case of least-squares inversion. In more detail, we aim to cover the following main topics: 1. The nature of observations and physical model parameters 2. Representing information by probabilities 3. Bayes' theorem and mathematical scientific inference 4. Random walks and Monte Carlo Methods 5. The Metropolis-Hastings algorithm 6. Simulated Annealing 7. Linear inverse problems and the least-squares method 8. Resolution and the nullspace 9. Basic concepts of iterative nonlinear inversion methods While the concepts introduced in this course are universal, they will be illustrated with numerous simple and intuitive examples. These will be complemented with a collection of computer and programming exercises. Prerequisites for this course include (i) basic knowledge of analysis and linear algebra, (ii) basic programming skills, for instance in Matlab or Python, and (iii) scientific curiosity. |
Lecture notes | Presentation slides and detailed lecture notes will be provided. |
Prerequisites / Notice | This course is offered as a half-semester course during the first part of the semester |
Performance assessment
Performance assessment information (valid until the course unit is held again) | |
Performance assessment as a semester course | |
ECTS credits | 3 credits |
Examiners | A. Fichtner |
Type | graded semester performance |
Language of examination | English |
Repetition | Repetition possible without re-enrolling for the course unit. |
Additional information on mode of examination | Written Exams and Exercises |
Learning materials
No public learning materials available. | |
Only public learning materials are listed. |
Groups
No information on groups available. |
Restrictions
There are no additional restrictions for the registration. |