Inverse Problems and Machine Learning in Earth and Space Physics

• 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

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


Methods:
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

30230/02631/02632/02633/02686/01418

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.