NFYA04034U Inverse Problems
MSc Programme in Physics
MSc Programme in Physics with a minor subject
The objective of the course is to provide theory and methods for solving and analyzing inverse problems in physical sciences. Inverse problem theory will be formulated as a probabilistic data integration problem, and a number of analytical/numerical methods for solution of inverse problems will be presented. The role and interplay between problem formulation, uncertainties in data and model parameters, and prior knowledge are important themes in the course. A significant part of the course involves work with projects where inverse problems from physics, astrophysics, geoscience or engineering will be analyzed.
This course aims to provide the student with skills to
- Formulate a complex data analysis problem as an inverse problem
- Describe and quantify data uncertainties and modeling errors
- Describe available prior (external) information using probabilistic models and methods
- Find probabilistic solutions to
- Linear and weakly non-linear, Gaussian inverse problems
- General (non-linear, non-Gaussian) inverse problems
- Analyze and validate solutions to inverse problems
This course will give the students a mathematical description of inverse problems as they
appear in connection with measurements and experiments in physical sciences. It teaches them to solve inverse problems with analytical and numerical methods. The students will study illposedness, numerical instability, non-uniqueness of solutions, and how noise propagates into uncertainty of the solutions.
Through the course the students will be able to identify inverse problems in various fields of physical sciences, classify them, and choose appropriate solution methods. The students will be able to find appropriate parameterizations, treat data uncertainties, and to evaluate the accuracy and resolution of the inverse solution.
See Absalon for final course material.
Knowledge of linear algebra, mathematical analysis, and differential equations (ordinary and partial) corresponding to a B.Sc. in physics or mathematics is expected.
In general, academic qualifications equivalent to a BSc degree is recommended.
- Practical exercises
- Project work
- 7,5 ECTS
- Type of assessment
- Continuous assessmentOral examination, 20 minutes3 projects (group or individual) [weighed by 12.5%, 12.5% and 25%] followed by 1 individual oral examination [weighed by 50%]. Both the continuous evaluation and the oral examintation should be passed separately.
- Marking scale
- 7-point grading scale
- Censorship form
- No external censorship
Several internal examiners
Same as ordinary exam. The student can choose to re-use points from projects handed in during the course, or make new projects, which must be handed in no later than 2 weeks before the oral re-exam.
Criteria for exam assesment
see "learning outcome"
- Course code
- 7,5 ECTS
- Full Degree Master
- 1 block
- Block 2
- Course capacity
- No restriction
- Course is also available as continuing and professional education
- Study board
- Study Board of Physics, Chemistry and Nanoscience
- The Niels Bohr Institute
- Faculty of Science
- Klaus Mosegaard (9-74767a6c6e6868796b4775697035727c356b72)