Parameter Estimation and Inverse Problems
Objectives and Content
The subject is concerned with theory and methods of solution for linear and nonlinear inverse problems with emphasis on regularization techniques and parameter estimation. The more well-known regularization techniques are lectured. Both the classical and the Bayesian ways to formulate the inverse problem are lectured, in addition to sequential techniques (data assimilation).
On completion of the course the students are expected to:
- Demonstrate understanding of important properties of ill-posed problems.
- Be familiar with different methods for solving linear and nonlinear regression problems, and be able to discuss the impact of measurement errors.
- Discuss methods for discretization of integral equations.
- Demonstrate understanding of properties of rank deficient linear problems.
- Master lectured regularization techniques and methods for selecting the regularization parameter.
- Demonstrate understanding of the principles underlying Bayesian methods for inverse problems and be able to discuss relations between classical and Bayesian methods.
- Be able to discuss the relation between data assimilation and the Bayesian formulation of the inverse problem.
- Explain the principles underlying, and discuss use of, the ensemble Kalman Filter as solution method for data assimilation problems.
Recommended Previous Knowledge
Forms of Assessment
The grading scale used is A to F. Grade A is the highest passing grade in the grading scale, grade F is a fail.