Norsk
Course MAT265

# Parameter Estimation and Inverse Problems

## Course offered:

### Course offered by

 Number of credits 10 Course offered (semester) Irregular Subject overlap MATINV: 10 SP Schedule Schedule Reading list Reading list

### 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.

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