Single-Course English 5 ECTS

Inverse Problems and Machine Learning in Earth and Space Physics

Overall Course Objectives

This course covers advanced methods for inversion of geophysical and astrophysical data, including machine learning techniques. Case studies from a wide range of inverse problems in Earth and Space physics (e.g. seismic tomography, geomagnetism, exoplanets, ground penetrating radar, galactic emission spectra, gravity) are presented and solved. The emphasis in this course is on inversion methods that handle non-Gaussian noise and use of suitable a priori information to get the most out of the observed data.

Python will be used as a tool throughout the course.

Learning Objectives

  • formulate and solve practical inverse problems with incomplete, noisy data
  • use robust statistical methods to derive models from data, handling non-Gaussian noise
  • use model regularization and a priori information during the inversion procedure
  • explain how to select level of model regularization
  • use of sparsity regularization methods
  • explain the use of Bayesian methods for inversion of geophysical and astrophysical data
  • use Markov-Chain Monte Carlo (MCMC) techniques to find probabilistic solutions to inverse problems.
  • explain relevance of machine learning techniques to problems in Earth and Space physics
  • use backpropagation methods to train feed-forward neural networks for solving inverse problems

Course Content

Statistical data description, Maximum likelihood, Model non-uniqueness, null space and resolution, Bayes Theorem, Probabilistic Inversion, Supervised and Unsupervised Machine Learning

Robust statistics for non-Gaussian errors, Annihilators, Model regularization, Trade-off curves, Generalized cross validation, Resolution matrix, Markov-Chain-Monte-Carlo (MCMC) methods, Sequential Gibbs sampling, Feed-forward neural networks, Training by Back-propagation, Stochastic gradient descent

Recommended prerequisites


Teaching Method

Lectures, exercises, projects.



The course is aimed at students who want competence in advanced inversion methods and machine learning for use in Earth and Space Physics.

See course in the course database.





13 weeks




DTU Lyngby Campus

Course code 30760
Course type Candidate
Semester start Week 5
Semester end Week 19
Days Thurs 13-17

7.500,00 DKK