Computational and Bayesian Inverse Problems, 5.0 credits

Entry requirements

Basic knowledge of:

• Mathematical analysis
• Linear algebra
• Programming (any language is okay)

Learning outcomes

After completing the course, students will be able to:

• Formulate, analyze, and solve inverse problems
• Apply regularization techniques using prior knowledge to address ill-posedness
• Formulate inverse problems in a Bayesian/statistical framework
• Critically assess modeling assumptions and data-related uncertainties
• Apply computational inference methods for Bayesian inverse problems
• Quantify uncertainty in estimated parameters

Contents

The course introduces the foundations and computational aspects of inverse problems, with a focus on Bayesian approaches. It covers:

• Basic theory of inverse problems
• Ill-posedness and regularization techniques
• Fundamentals of probability theory and Bayes’ rule
• Bayesian formulation of inverse problems
• Bayesian inference methods and uncertainty quantification

Educational methods

The course consists of:

• One week of on-campus lectures and activities at Linköping University
• Remote project work in teams (~80h) over around four weeks
• One final day for project presentations

Compulsory components include:

• Participation in group project work
• Final project presentation

Examination

Assessment is based on:

• Written reports from project work
• Oral presentation of project results

Active participation in all course components is required.

Grading

Course literature

Combination of lecture notes, books, and selected research articles in inverse problems, Bayesian inference, and uncertainty quantification. Examples include:

• Calvetti D, Somersalo E. Bayesian scientific computing. New York: Springer; 2023 Mar 9.
• Sanz-Alonso D, Stuart A, Taeb A. Inverse problems and data assimilation. Cambridge University Press; 2023 Aug 10.