Odjel za matematiku

The third International School on

Model Reduction for Dynamical Control Systems

The summer school is held on 5 - 10 October 2015, in Dubrovnik, Croatia.


The goal of the school is to provide a coherent set of lectures that will adequately clarify the mathematical aspects of the (optimal) control of dynamical systems, with special emphasis on recent developments and computational methods for large-scale systems,which are based on model reduction.




  • Peter Benner, Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany 

  • Albert Cohen, Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC), Paris,   France

  • Danny C. Sorensen, Noah Harding Professor of Computational and Applied Mathematics at Rice University in Houston, Texas, USA

Lectures will be held in lecture room 5.


  • registration until June 15, 2015.



9:00-10:30 Prof Cohen Prof Cohen Prof Benner Prof Sorensen Prof Sorensen
10:30-11:00 Coffee break
11:00-12:30 Prof Cohen Prof Cohen Prof Benner Prof Sorensen Prof Sorensen
12:30-15:00 Lunch
15:00-18:00 Prof Cohen Prof Benner Prof Benner Dubrovnik sightseeing Prof Sorensen



 Peter Benner: Model order reduction via system balancing

 We will investigate model order reduction method based on truncating balanced realizations.  This class of model reduction techniques originates in systems and control theory.  We will therefore provide a brief introduction into necessary properties of linear time-invariant systems.  Then we will introduce the basic concept of system balancing, and show how this principle can be used to define a whole family of model reduction methods.  We will discuss how to apply these techniques to really large-scale systems, making use of efficient tools from linear algebra in order to exploit sparsity and low-rank structures. We will also briefly discuss the extension of this approach to nonlinear systems.

Materials: lectures-Benner-Dubrovnik-2015.pdf

beam.zip, exercises.pdf, solutions.pdf

 Albert Cohen: High dimensional approximation of parametric PDE's - theory and algorithms

 Various mathematical problems are challenged by the fact they involve functions of a very large number of variables. Such problems arise naturally in learning theory, partial differential equations or numerical models depending on parametric or stochastic variables. They typically result in numerical difficulties due to the so-called ''curse of dimensionality''. We shall discuss how these difficulties may be handled in the context of stochastic-parametric PDE’s. The lectures will both investigate the theoretical analysis of several high dimensional approximation methods and concrete algorithms for implementing them.

Materials: slides.pdf

 Danny C. Sorensen: Model Order Reduction for Linear and Non-Linear Dynamical Systems

   I will discuss two related aspects of model order reduction (MOR). The rst involves projection methods derived from Krylov and Rational Krylov theory. These methods are moment matching or interpolatory methods that are closely related to the standard Krylov based iterative methods for linear algebraic systems. Nonlinear model reduction has seen a number of advances over the past decade. For quite some time, the only reasonable projection method has been Proper Orthogonal Decomposition (POD). This is an orthogonal projection of the dynamical system onto a dominant subspace associated with
its trajectories. Although signi cant dimension reduction can be achieved through this approach, there remains a serious complexity issue associated with evaluation of the projected nonlinear terms. The Discrete Empirical Interpolation Method (DEIM) is one approach to overcoming this de ciency. This approach will be developed and analyzed during this tutorial.
The following is a brief outline of topics that shall be covered.




  • School is organized by European Model Reduction Network (EU-MORNET), project within: Training Schools (TS).
  • Registration

    • The cost for participants will be covered within the COST action (TD1307): European Model Reduction Network (EU-MORNET).  The support includes travel expenses, accommodation and coffee break for eligible participants coming from universities that are project participants from COST countries. The list of cost countries that participate in this project can be found on this link.
    • In order to register, interested students should apply on:
        • email: mrcschool2015 @ mathos.hr
        • with the following data: first name, last name, affiliation, city, country, e-mail address, short CV (max one A4 page).
    • Participants should register until June 15, 2015.
    • Due to the fact that the number of participants is limited, notification of acceptance will be sent to each registered student.
  • Venue

    • Lectures will be held at Centre for Advanced Academic Studies 
    • Accommodation for participants will be organized at Centre for Advanced Academic Studies Dubrovnik, Croatia

    Centre for Advanced Academic Studies:


  • address: 

    University of Zagreb
    Centre for Advanced Academic Studies
    Don Frana Bulica 4
    20000 Dubrovnik

  • Local organizers

  • Supported by


  • History

The planned school will be third school, succeeds the first two schools:


School will be held in Dubrovnik. Dubrovnik is the city on the Adriatic Sea in the region of Dalmatia.  It is one of the most respectable tourist destinations in the Croatia and the centre of Dubrovnik-Neretva County (about Dubrovnik).