# TIES6830 COM5: Machine learning in inverse and ill-posed problems (2 cr)

**Study level:**

**Grading scale:**

**Language:**

**Responsible organisation:**

**Coordinating organisation:**

**Curriculum periods:**

## Tweet text

## Description

The information about the course will be here: http://waves24.com/download/

Course plan:

- Physical formulations leading to ill- and well-posed problems

- Methods of regularization of inverse problems (Morozov’s discrepancy, balancing principle, iterative regularization)

- Numerical methods for solution of inverse and ill-posed problems: Lagrangian approach and adaptive optimization, a posteriori error estimation, methods of analytical reconstruction and layer-stripping algorithms, solution of MRI problem.

- Machine learning algorithms in inverse problems: solution of linear and non-linear least-squares problems, classification algorithms, non-regularized and regularized neural networks.

## Learning outcomes

After a successful completion of the course the students will be able to:

Knowledge and understanding:

- have basic understanding of the notion of inverse problems
- understand main machine learning algorithms for classiﬁcation (least squares and perceptron, SVM and Kernel Methods)
- understand basic numerical methods for solution of inverse and ill-posed problems.
- derive and use the numerical techniques needed for a professional solution of a given ill-posed or classiﬁcation problem.

Skills and abilities:

- use computer algorithms, programs and software packages to compute solutions of ill-posed or classiﬁcation problem.
- critically analyze and give advice regarding diﬀerent choices of regularization techniques, algorithms, and mathematical methods for solution of ill-posed or classiﬁcation problem with respect to eﬃciency and reliability.
- critically analyze the accuracy of the obtained numerical result and present it in a visualized way.
- write a scientiﬁc report and make a scientiﬁc presentation summarizing obtained results.

## Description of prerequisites

Numerical analysis, partial diﬀerential equations, programming in Matlab.

## Study materials

*Approximate global convergence and adaptivity for coefficient inverse problems*. Book, available at https://www.springer.com/gp/book/9781441978042

Projects together with examples of Matlab and C++ programs are available for download at www.waves24.com/download

## Completion methods

### Method 1

**Parts of the completion methods**

### Participation in teaching (2 cr)

**Type:**

**Grading scale:**

**Language:**