Model Order Reduction: Techniques and Tools

@article{Benner2015ModelOR,
title={Model Order Reduction: Techniques and Tools},
author={Peter Benner and Heike Fa{\ss}bender},
journal={Encyclopedia of Systems and Control},
year={2015}
}
• Published 2015
• Computer Science
• Encyclopedia of Systems and Control
Model order reduction (MOR) is here understood as a computational technique to reduce the order of a dynamical system described by a set of ordinary or differential-algebraic equations (ODEs or DAEs) to facilitate or enable its simulation, the design of a controller, or optimization and design of the physical system modeled. It focuses on representing the map from inputs into the system to its outputs, while its dynamics are treated as a blackbox so that the large-scale set of describing ODEs…
6 Citations

Reduced Order Controller Design for Robust Output Regulation

• Mathematics
IEEE Transactions on Automatic Control
• 2020
It is shown that robust output tracking and disturbance rejection for this class of systems can be achieved using a finite-dimensional controller and algorithms for construction of two different internal model based robust controllers are presented.

A Fully Bayesian Gradient-Free Supervised Dimension Reduction Method using Gaussian Processes

• Computer Science
International Journal for Uncertainty Quantification
• 2021
The comparison shows that the proposed method improves the active subspace recovery and predictive accuracy, in both the deterministic and probabilistic sense, when only few model observations are available for training, at the cost of increased training time.

A brief note on the generalized singular perturbation approximation

• H. Shaker
• Mathematics
2015 6th International Conference on Modeling, Simulation, and Applied Optimization (ICMSAO)
• 2015
The generalized singular perturbation approximation is a method for approximation of dynamical systems which has been presented in the literature on model reduction over the past two decades. In this

Clustering as Approximation Method to Optimize Hydrological Simulations

• Computer Science
Euro-Par
• 2019
This paper extends this approach by applying machine learning methods to cluster functionally similar model units and by running the model only on a small yet representative subset of each cluster, which achieves the best trade-off between decreasing computation time and increasing simulation uncertainty.

On Using Clustering for the Optimization of Hydrological Simulations

• E. Azmi
• Computer Science
2018 IEEE International Conference on Data Mining Workshops (ICDMW)
• 2018
This work shows an ongoing project that applies existing clustering methods to identify functionally similar model units and runs the model only on representative model units, to reduce model redundancies and computation complexities.

References

SHOWING 1-10 OF 24 REFERENCES

Model order reduction of large-scale dynamical systems with Jacobi-Davidson style eigensolvers

• Computer Science
2011 International Conference on Communications, Computing and Control Applications (CCCA)
• 2011
This paper focuses on a model order reduction method for linear time in-variant (LTI) systems based on modal approximation via dominant poles based on Jacobi-Davidson method, which has proven to be a suitable and competitive candidate for the solution of various eigenvalue problems.

H2 Model Reduction for Large-Scale Linear Dynamical Systems

• Computer Science, Mathematics
SIAM J. Matrix Anal. Appl.
• 2008
A new unifying framework for the optimal $\mathcal{H}_2$ approximation problem is developed using best approximation properties in the underlying Hilbert space and leads to a new set of local optimality conditions taking the form of a structured orthogonality condition.

Numerical Linear Algebra for Model Reduction in Control and Simulation

Some of the most prominent methods used for linear systems, compare their properties and highlight similarities are discussed, and the role of recent developments in numerical linear algebra in the different approaches is emphasized.

All optimal Hankel-norm approximations of linear multivariable systems and their L, ∞ -error bounds†

The problem of approximating a multivariable transfer function G(s) of McMillan degree n, by Ĝ(s) of McMillan degree k is considered. A complete characterization of all approximations that minimize

Dimension Reduction of Large-Scale Systems

• Materials Science
• 2005
The aim of this book is to survey some of the most successful model reduction methods in tutorial style articles and to present benchmark problems from several application areas for testing and comparing existing and new algorithms.

Model Order Reduction: Theory, Research Aspects and Applications

• Engineering, Mathematics
• 2014
Basic Concepts.- to Model Order Reduction.- Linear Systems, Eigenvalues, and Projection.- Theory.- Structure-Preserving Model Order Reduction of RCL Circuit Equations.- A Unified Krylov Projection

Balanced Truncation Model Reduction of Large-Scale Dense Systems on Parallel Computers

• Computer Science
• 2000
This paper analyzes the use of parallel computing in model reduction methods based on balanced truncation of large-scale dense systems and uses a sign function-based solver for computing full-rank factors of the Gramians.

Model reduction methods based on Krylov subspaces

The main ideas of reduction-order modelling techniques based on Krylov subspaces are reviewed and some applications of reduced- order modelling in circuit simulation are described.

Approximation of Large-Scale Dynamical Systems

• A. Antoulas
• Computer Science