Parameter Estimation and Inverse Problems

Language of Instruction

English if English-speaking students attend the seminars, otherwise Norwegian

Learning Outcomes

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.

Course offered (semester)

Irregular

Language of Instruction

English if English-speaking students attend the seminars, otherwise Norwegian

Aim 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.)

Learning Outcomes

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

MAT121 Linear Algebra, MAT160 Scientific Computing 1, MAT212 Functions of Several Variables, and STAT101 Elementary Statistics or STAT110 Basic Course in Statistics

Grading Scale

The grading scale used is A to F. Grade A is the highest passing grade in the grading scale, grade F is a fail.