Parametric Model Order Reduction of Dynamical Systems: Survey and Recent Advances

  • Peter Benner (Max-Planck-Institut für Dynamik komplexer technischer Systeme, Magdeburg)
A3 01 (Sophus-Lie room)


Model reduction has become an ubiquitous tool in simulation and control for dynamical systems arising in various engineering disciplines. Often, models of physical processes contain parameters describing material properties and geometry variations, or arising from changing boundary conditions. These parameters may vary with time or be stochastic when modeling the uncertain knowledge about them. For purposes of design, optimization, and uncertainty quantification, it is often desirable to preserve these parameters as symbolic quantities in the reduced-order model (ROM). This allows the re-use of the ROM after changing the parameter so that the repeated computation of reduced-order models can be avoided. Significant savings in simulation times for full parameter sweeps, within optimization algorithms and Monte Carlo simulations can be achieved this way.

In this talk, we survey several approaches for computing ROMs for linear and nonlinear parametric systems. Parameter dependencies can be linear, polynomial, or nonlinear in general. The considered methods construct the ROMs in different way, using system theoretic concepts, rational interpolation, and/or greedy-type sampling approaches. We discuss the state-of-the-art of these methods and present recent advances. We illustrate the performance of the available methods using numerical examples, often in the context of industrially relevant applications.

Katja Heid

MPI for Mathematics in the Sciences Contact via Mail

Upcoming Events of This Seminar

  • Mar 12, 2024 tba with Theresa Simon
  • Mar 26, 2024 tba with Phan Thành Nam
  • Mar 26, 2024 tba with Dominik Schmid
  • May 7, 2024 tba with Manuel Gnann
  • May 14, 2024 tba with Barbara Verfürth
  • May 14, 2024 tba with Lisa Hartung
  • Jun 25, 2024 tba with Paul Dario
  • Jul 16, 2024 tba with Michael Loss