Odjel za matematiku

Workshop on Model Reduction Methods and Optimization

20-21 September 2016, in Opatija, Croatia.


The goal of this workshop 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 optimization and model reduction methods for large-scale systems.




  • Zlatko Drmač, Department of Mathematics, University of Zagreb, Croatia

Numerical linear algebra for model reduction

The demand for accuracy in applications in engineering and applied sciences leads to numerical tasks of increasingly large dimensions. To make simulations and modeling in such large-scale settings computationally feasible, one uses model reduction methods to create approximations to a complex dynamical system by one of much lower order, that still sufficiently accurately reproduces the input-output relations. At the core of all those methods are the algorithms of numerical linear algebra. In this talk, we focus on two themes: (i) rational matrix valued least squares fitting (e.g. least squares fit to frequency response measurements of an LTI system) and model order reduction in H_2 setting, and (ii) nonlinear dimension reduction and the Discrete Empirical Interpolation Method (DEIM). We show how to properly identify relevant condition numbers, and how to implement the algorithms in a robust numerical software.
  • Serkan GugercinDepartment of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg,  USA

What to interpolate for optimal model reduction: Moving from linear to nonlinear dynamics

For linear dynamical systems, model reduction has achieved great success. In the case of linear dynamics, we know how to construct, at a modest cost, (locally) optimal, input-independent reduced models; that is, reduced models that are uniformly good over all inputs having bounded energy. In addition, in some cases we can achieve this goal using only input/output data without a priori knowledge of internal dynamics. Even though model reduction has been successfully and effectively applied to nonlinear dynamical systems as well, in this setting, both the reduction process and the reduced models are input dependent and the high fidelity of the resulting approximation is generically restricted to the training input/data. In this talk, we will offer remedies to this situation.
First, we will review model reduction for linear systems by using rational interpolation as the underlying framework. The concept of transfer function will prove fundamental in this setting. Then, we will show how rational interpolation and transfer function concepts can be extended to nonlinear dynamics, specifically to bilinear systems and quadratic-in-state systems, allowing us to construct input-independent reduced models in this setting as well. Several numerical examples will be illustrated to support the discussion.
  • Karl Meerbergen, KU Leuven Department of Computer Science, Leuven, Belgium

Progress in model reduction for systems with nonlinear frequency dependency

Classical models in mechanical and civil engineering are second order finite element systems, usually represented by three matrices: mass, stiffness and damping. For new materials, the damping matrix is often frequency dependent. The dependency can be rather complex, but is usually nonlinear. In this talk, we show how techniques inititally developed for nonlinear eigenvalue problems can be used for model order reduction of such problems. We present the Compact Rational Krylov method (CORK) as the computational work horse. Then, we illustrate how it can be used to build a linear reduced model of a nonlinear model in the Laplace or frequency variable. The idea is to reduce a large linear model obtained from interpolating the nonlinear model. Finally, we will also show how two-sided models can be built in a dynamic way.
Joint work with Roel Van Beeumen, Wim Michiels and Pieter Lietaert

Control and model reduction for reactive flows

We discuss the optimal control of reactive flows arising e.g. in the construction of modern pulse detonation engines. Several major challenges have to be dealt with. Due to the nonlinear transport phenomenon and the occurence of fast moving shocks, classical model reduction techniques typically do not lead to a sufficient reduction of the model. Furthermore, typically the shock front is not resolved anymore in the reduced model. We discuss two new approaches, the new shifted POD technique and the use of innovative interpolation techniques for the treatment of fast moving sharp fronts in reactive flows.
Many challenges remain and we will discuss several open problems that arise in this context.
Joint work with Julius Reiss, Philipp Schulze, and Jörn Sesterhenn.
  • Tim Mitchell, Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany

Solving problems in reduced order modeling via nonsmooth constrained optimization and fast approximation

The optimal H-infinity norm model reduction problem for linear dynamical systems can be stated as a nonsmooth, nonconvex optimization problem subject to a stability constraint, typically non-locally Lipschitz. As the objective and constraint functions are often prohibitively expensive to compute and historically, there has only been limited availability of software applicable to such difficult optimization problems, techniques developed for model order reduction have typically been motivated by the intractability of direct approaches. However, recent advances in both fast algorithms for approximating the H-infinity norm and new efficient and reliable methods for highly nonlinear nonsmooth constrained optimization now make more direct and/or hybrid methods for reduced order modeling a real possibility. In this talk, we give an overview of many of these newly developed tools and then show how they can be effectively applied to problems in reduced order modeling.
Joint work with Peter Benner.



Contributed talks:

  • Olena Burkovska, Calibration to American options with the reduced basis method, abstract.pdf

  • Alessandro Castagnotto, How to split optimization and reduction cost in H2-optimal model order reduction, abstract.pdf

  • Manuela Hund, A Connection between Time Domain Model Order Reduction and Moment Matching, abstract.pdf

  • Petar Mlinarić, Almost almost-equitableness and clustering-based error bounds, abstract.pdf

  • Maria Cruz Varona, Krylov subspace model reduction for bilinear and MIMO quadratic-bilinear systems, abstract.pdf



  • registration until 10 July 2016 10 August 2016




  Tuesday, 20 September 2016 Wednesday, 21 September 2016
 9:00-10:00  Drmač  Mehrmann
 10:00-10:30  Mlinarić  Burkovska
 10:30-11:00  coffee break  coffee break
 11:00-12:00  Gugercin  Mitchell
 12:00-12:30  Castagnotto
 12:30-15:00  break  
 15:00-16:00  Meerbergen  
 16:00-16:30  Hund  
 16:30-17:00  coffee break  
 17:00-17:30  Cruz Varona   




  • Workshop is supported by European Model Reduction Network (EU-MORNET). 


  • Registration

    • To register please send an email to Ova e-mail adresa je zaštićena od spambota. Potrebno je omogućiti JavaScript da je vidite. containing the following information:

      Position (student,...)
      University (with address)
      Email Address

    • Participants who would like to give contributed talk should also send title and abstract of a talk.

      The accommodation:

      • in single room is approx. 120 eur per person for a day (full board)

      • in double room 

        is approx. 90 eur per person for a day (full board) 
      • The accommodation has to be paid on arrival.

    • Participants with or without talk should register until  10 July 2016  extended to 10 August 2016.
    • Notification of acceptance will be sent until 20 July 2016.
  • Venue

    The Grand Hotel 4 Opatijska Cvijeta is located in the very centre of Opatija:


  • Location

Address: Ul. Viktora Cara Emina 6, Opatija, Croatia

How to reach Opatija?  The nearest international airport is Rijeka airport which is located on the island of Krk in Omišalj and it is located approximately 40 kilometers from Opatija.  Web address of the airport Rijeka www.rijeka-airport.hr. Another options will be airport at Trieste or Zagreb. From Rijeka or Trieste airport to Opatija you can come by bus, using a taxi or hiring transfer vehicles. From Zagreb airport one can take bus to Opatija where bus lines can be found here.




Workshop will be held in Opatija. Opatija is located 90 km from Trieste by rail and 82 km from Pula by road. The city is geographically on the Istrian peninsula, though it is not in Istria County, but Primorje-Gorski Kotar County.

It is a popular summer and winter resort, with average temperatures of 10 °C in winter, and 25 °C in summer. Opatija is surrounded by beautiful woods of bay laurel. The whole sea-coast to the north and south of Opatija is rocky and picturesque, and contains several smaller winter resorts.

  Opatija - ´Djevojka s galebom´