Model Reduction for Optimization and Control

Mat-Dyn-Net Winter School on Model Reduction for Optimization and Control is held on 19 – 23 February 2024 in Dubrovnik, Croatia

The school aims to provide a coherent set of lectures that will elucidate the mathematical foundations of the control of dynamical systems, with particular emphasis on optimization and computational methods for large-scale systems based on model reduction. It is particularly aimed at PhD students, but not limited to.

Lecturers

• Tobias Breiten, Institute of Mathematics, TU Berlin, Berlin, Germany
• Serkan Gugercin, Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, USA
• Olga Mula, TU Eindhoven, Eindhoven, The Netherlands
• Martin Stoll, Department of Mathematics, TU Chemnitz, Chemnitz, Germany

Lectures will be held at Centre for Advanced Academic Studies.

Deadlines:

• Registration until 20 October 2023.

Schedule

The school will begin on Monday lunchtime, February 19th, 2024, and end by lunchtime on Friday, February 23rd, 2024.

	Monday	Tuesday	Wednesday	Thursday	Friday
8:30-10:00		Olga Mula	Martin Stoll	Tobias Breiten	Tobias Breiten
10:00-10:30		coffee break	coffee break	coffee break	coffee break
10:30-12:00		Martin Stoll	Tobias Breiten	Serkan Gugercin	Serkan Gugercin
12:00-14:00		lunch break	lunch break	lunch break
14:00-15:30	Olga Mula	Martin Stoll	Serkan Gugercin
15:30-16:00	coffee break	coffee break	coffee break
16:00-17:30	Olga Mula

Abstracts

Tobias Breiten and Serkan Gugercin: System Theoretic Methods

Part I (Tobias Breiten) Control systems Transfer functions System norms Bode plots Linear balanced truncation Part II (Serkan Gugercin) Rational interpolation Projection The Loewner framework Optimal interpolation H2, IRKA Part III (Tobias Breiten) Bilinear control theory Algebraic Gramians Volterra series interpolation Optimal interpolation Part IV (Serkan Gugercin) Data-driven barycentric interpolants Least squares rational fitting, AAA (Parametric) extensions

Olga Mula: Nonlinear, Geometric Reduced Models for Forward and Inverse Problems

This course will discuss the role of nonlinear approximation and geometry to address bottlenecks in reduced order modelling when applied to forward and inverse problems.

Martin Stoll: Low-rank methods for PDE-constrained optimization

Solving PDE-constrained optimization problems leads to very large linear systems in structured form. In my talk I will first explain how to discretize these problems and arrive at the large linear systems and how to solve them efficiently using preconditioned Krylov solvers. We then illustrate that the systems can be written in very structured form and we can utilize this structure for developing low-rank methods that approximate the solution in space and time.

Organization and registration

• The school is organised by COST and the School of Applied Mathematics and Informatics, Josip Juraj Strossmayer University of Osijek,  Croatia, within the COST action Mathematical models for interacting dynamics on networks (Mat-Dyn-Net), CA18232.
• Mathematical models for interacting dynamics on networks (Mat-Dyn-Net), CA18232.

Registration

• The eligible participants will be covered within the COST action (CA18232): Mathematical models for interacting dynamics on networks (Mat-Dyn-Net). The cap for the travel is up to 450 eur and the daily allowance for the trainees 90 EUR per day, for further information please contact GH Manager Mojca Premuš (Mojca.Premus@fgg.uni-lj.si).
• In order to register for the school, interested students should apply on email: mrcschool2024@mathos.hr
  • with the following data: first name, last name, affiliation, city, country, e-mail address, letter of motivation (max one A4 page).
• Participants should register until 20 October 2023.
• Due to the fact that the number of participants is limited, notification of acceptance will be sent to each registered student by 5 November 2023.

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
  Croatia

Local organizers

• Petra Csomós, Department of Applied Analysis and Computational Mathematics, Eötvös Loránd University, Budapest, Hungary
• Zlatko Drmač, Department of Mathematics, University of Zagreb, Faculty of Science, Zagreb, Croatia
• Jan Giesselman, Department of Mathematics, Numerical Analysis and Scientific Computing, Technical University of Darmstadt, Darmstadt, Germany
• Zoran Tomljanović, School of Applied Mathematics and Informatics, Josip Juraj Strossmayer University of Osijek, Osijek, Croatia

Supported by

• COST action Mathematical models for interacting dynamics on networks (CA18232)
• School of Applied Mathematics and Informatics, Josip Juraj Strossmayer University of Osijek, Croatia

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 famous tourist destinations in the Croatia and the centre of Dubrovnik-Neretva County (about Dubrovnik).