Model order reduction techniques for efficient numerical simulations

Data is displayed for the academic year: 2025./2026.

Lecturers

Asst. Prof.
Ana Žgaljić Keko
PhD

Course Description

Numerical solving of practical-sized mathematical models is often limited by their sizes and complexity. Among key solving techniques are the tractably solvable reduced-size models. The original model is replaced by a reduced one, and the original model characteristics are kept. In this course, modern techniques of dynamical systems model order reduction will be covered, e.g. the SVD decomposition methods, balanced truncation, Hankel approximation, and interpolation-based model reduction for linear dynamical systems. Proper orthogonal decomposition (POD) and discrete empirical interpolation (DEIM) methods will be explained, as well as techniques based on convolutional autoencoders. Krylov's methods for large-scale dynamical systems, as well as combinations of the mentioned methods, will be considered. The course pays specific attention to building skills to apply the above techniques in practical problems, so combinations of the above will be considered as well.

Study Programmes

Postgraduate doctoral study programme

Literature

Athanasios C. Antoulas (2009.), Approximation of Large-Scale Dynamical Systems, SIAM
Peter Benner, Albert Cohen, Mario Ohlberger, Karen Willcox (2017.), Model Reduction and Approximation, SIAM
Peter Benner, et al. (2021.), System- and Data-Driven Methods and Algorithms, De Gruyter

General

ID 271543
  Winter semester
6 ECTS