Fakultet primijenjene matematike i informatike

Mat-Dyn-Net Winter School  on

Model Reduction for Optimization and Control

The winter school 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
  • Melina Freitag, Institute of Mathematics, University of Potsdam, Potsdam, 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 30 September 2023.

SCHEDULE

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

Program

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

Melina Freitag: Data Assimilation using variational methods and the Kalman filter - with some insight into dimension reduction
 Data assimilation is a method that combines observations (ie, real world data) of a state of a system with model output for that system in order to improve the estimate of the state of the system and thereby the model output. The model is usually represented by a discretized partial differential equation. The data assimilation problem can be formulated as a large scale Bayesian inverse problem. Based on this interpretation we will derive the most important variational and sequential data assimilation approaches, in particular three-dimensional and four-dimensional variational data assimilation (3D-Var and 4D-Var) and the Kalman filter. One challenge in data assimilation is, that the discretized model is usually very high dimensional, and we will introduce model reduction approaches for this problem.
 
 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

  • Registration

    • The eligible participants will be covered within the COST action (CA18232): Mathematical models for interacting dynamics on networks (Mat-Dyn-Net). The support includes daily allowance, accommodation, coffee break and travel is supported (up to 350 eur).
    • 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:

     

caas    caas

 

matdynnet  eu flag
Official COST Logo
mathos logotype

 

 

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).

Dubrovnik1