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

Study level:
Postgraduate studies
Grading scale:
Pass - fail
Responsible organisation:
Faculty of Information Technology
Coordinating organisation:
Faculty of Mathematics and Science
Curriculum periods:
2020-2021, 2021-2022

Tweet text

Machine learning in inverse and ill-posed problems


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

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

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

Completion methods

Method 1

Select all marked parts
Parts of the completion methods

Participation in teaching (2 cr)

Participation in teaching
Grading scale:
Pass - fail