Inverse Problems

Course content

The objective of the course is to provide theory and methods for solving and analyzing inverse problems in physics and geosciences. Inverse problem theory will be formulated as a probabilistic data integration problem, and a number of analytical/numerical methods for solution of linear and nonlinear inverse problems will be presented. The role and interplay between uncertainties in data, model and prior knowledge is an important theme in the course.

A significant part of the course involves work with projects where inverse problems from physics and geosciences will be analyzed,for example analysis of seismic data or climate data.


M.Sc. Physics

Learning outcome

This course aims to provide the student with skills to

  • Describe and quantify data uncertainties and modeling errors.

  • Describe available prior (external) information using probabilistic/statistical models and methods

  • Solve inverse problems

    • Linear and weakly non-linear Gaussian inverse problems

      • Probabilistic least squares inversion

      • Classical parameter estimation methods and regularization

    • Non-linear non-Gaussian inverse problem

      • Importance sampling (rejection, Metropolis, extended Metropolis)

  • Analyze and validate solutions to inverse problems

This course will give the student a mathematical description of inverse problems as they appear in connection with measurements and experiments in physics and geosciences. It teaches them to solve linear inverse problems with analytical and numerical methods and non-linear problems with Monte Carlo methods. The students will study the propagation of noise in data to uncertainty in the solutions.

Through the course the student will be able to identify inverse problems in various fields of physics and geosciences, classify them, and choose appropriate solution methods. The student will be able to treat data uncertainties and to evaluate the accuracy and resolution of the inverse solution.



Lectures, exercises (using Matlab), and projects.

Tarantola (2005) Inverse Problem Theory, and Lecture notes.

Throughout the course Matlab will be used extensively, and therefore Dat F (NFYA06018U) or equivalent will be useful.
Linear Algebra corresponding to the course LinAlgNat or equivalent.

7,5 ECTS
Type of assessment
Continuous assessment
Oral examination, 20 minutes
3 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 pased separately.
Marking scale
7-point grading scale
Censorship form
No external censorship
Several internal examiners
Criteria for exam assessment

see "skills"

Part time Master and Diploma courses

  • Category
  • Hours
  • Lectures
  • 27
  • Practical exercises
  • 16
  • Project work
  • 90
  • Preparation
  • 73
  • English
  • 206