Abstract
Discrete-time systems are a common tool in the modeling of processes in many application areas such as digital signal processing and population dynamics. Model reduction is an essential remedy to handle high-fidelity systems in practice. To benefit from the performance gained by using reduced-order models, the computation of these models itself must be done with a reasonable use of resources. In this paper, we consider the case of medium-scale dense discrete-time systems and compare the performance of different numerical methods for the implementation of two basic model reduction techniques. Therefore, we give an overview of the considered model reduction methods and of the techniques used in underlying implementations. The outlined methods are then compared with established implementations in several numerical examples in terms of accuracy and performance.
Zusammenfassung
Zeitdiskrete Systeme sind ein typisches Werkzeug zur Modellierung von Prozessen in vielen Anwendungsbereichen wie z.B. in der digitalen Signalverarbeitung oder in Populationsdynamiken. Modellreduktion ist ein wesentliches Mittel zur Handhabung von hochgenauen Systemen in der praktischen Anwendung. Um aber von der zusätzlichen Performance durch die Nutzung von reduzierten Modellen zu profitieren, ist es nötig diese unter sinnvollem Einsatz von Ressourcen zu berechnen. In diesem Beitrag betrachten wir den Fall von mittelgroßen, dichtbesetzten, zeitdiskreten Systemen und vergleichen die Performance von verschiedenen, numerischen Methoden für die Implementierung zweier grundlegender Modellreduktionsverfahren. Dafür geben wir einen Überblick zu den betrachteten Modellreduktionsmethoden und den Techniken für die darunterliegenden Implementierungen. Die dargestellten Methoden werden dann mit etablierten Implementierungen in mehreren numerischen Beispielen in Bezug auf Genauigkeit und Performance verglichen.
Funding source: Deutsche Forschungsgemeinschaft
Award Identifier / Grant number: 314838170
Funding statement: The work of Steffen W. R. Werner was supported by the German Research Foundation (DFG) Research Training Group 2297 “MathCoRe”, Magdeburg (Grant No. 314838170).
About the authors
Robert Jendersie is a student of computer science at the Otto von Guericke University Magdeburg. He finished his bachelor degree in 2019 working on model order reduction during an internship at the Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg. Currently, he is exploring the stability of neural networks in the context of physical simulations.
Steffen W. R. Werner finished his master studies in mathematics at the Otto von Guericke University Magdeburg in 2016. Thereafter, he joined the Max Planck Institute for Dynamics of Complex Technical Systems, where he is working on the application of structure-preserving model order reduction methods for mechanical systems.
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