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

Study level:
Pass - fail
Language:
English
Responsible organisation:
Faculty of Information Technology
Coordinating organisation:
Faculty of Mathematics and Science
Curriculum periods:
2020-2021, 2021-2022

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Machine learning in inverse and ill-posed problems

## Description

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

Course literature: L. Beilina, M. Klibanov, Approximate global convergence and adaptivity for coefficient inverse problems. Book, available at https://www.springer.com/gp/book/9781441978042

## Completion methods

### Method 1

Select all marked parts
Parts of the completion methods
x

### Participation in teaching (2 cr)

Type:
Participation in teaching