Model Order Reduction

Definition : (Parameterized) Model Order Reduction (MOR/PMOR)

MOR

Model Order Reduction (MOR) is a branch of system and control theory, which reduces the complexity of large-scale dynamical systems, while preserving (to the possible extent) their input-output behavior.

Reduced (parameterized) models mimic the complex behavior of large-scale dynamical systems, and can be efficiently used for design automation, optimization and sensitivity analysis.

Background

Dynamical systems are a principal tool in modeling and control of many physical phenomena, such as heat transfer and temperature control in various media, signal propagation and interference in electric circuits, wave propagation and vibration suppression in large structures, and behavior of micro-electro-mechanical systems (MEMS).

Direct numerical simulation of the associated models has been one of the few available means for studying the complex underlying physical phenomena. However, the ever increasing need for improved accuracy requires the inclusion of ever more detail in the modeling stage, leading inevitably to ever larger-scale, ever more complex dynamical systems. Simulations in such large-scale settings lead in turn to unmanageably large demands on computational resources, which is the main motivation for system approximation (model reduction).

The goal is to produce a low dimensional system that has the same response characteristics as the original system. Low dimensionality means far less storage and far less evaluation time. The resulting reduced order model can be used to replace the original system as a component in a larger simulation or it might be used to develop a simpler and faster controller suitable for real time applications. [ref]

Research goals

We study and develop efficient, numerically stable, fully automated Model Order Reduction (MOR) and Parameterized Model Order Reduction (PMOR) techniques, which ensure good approximation of the original system, and preserve as much as possible the physical properties of the underlying system (such as causality, stability and passivity).

This research is based on, or linked with:
  • System and Control theory
    [Linear Systems, System Identification, State-space realization]

  • Numerical techniques
    [Krylov-subspace methods (moment matching), Balanced-truncation methods, Proper Orthogonal Decomposition (POD) Projection-based methods, Rational approximation, Orthonormal bases, Data-driven modelling]