Optimization based model order reduction for stochastic systems

  • In this paper, we bring together the worlds of model order reduction for stochastic linear systems and H-2-optimal model order reduction for deterministic systems. In particular, we supplement and complete the theory of error bounds for model order reduction of stochastic differential equations. With these error bounds, we establish a link between the output error for stochastic systems (with additive and multiplicative noise) and modified versions of the H-2-norm for both linear and bilinear deterministic systems. When deriving the respective optimality conditions for minimizing the error bounds, we see that model order reduction techniques related to iterative rational Krylov algorithms (IRKA) are very natural and effective methods for reducing the dimension of large-scale stochastic systems with additive and/or multiplicative noise. We apply modified versions of (linear and bilinear) IRKA to stochastic linear systems and show their efficiency in numerical experiments.

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Author details:Martin RedmannORCiDGND, Melina A. FreitagORCiDGND
Title of parent work (English):Applied mathematics and computation
Place of publishing:New York
Publication type:Article
Date of first publication:2021/06/01
Publication year:2021
Release date:2023/09/06
Tag:Levy process; Model order reduction; Optimality conditions; Stochastic systems; Sylvester equations
Article number:125783
Number of pages:18
Funding institution:[SFB1294/1-318763901]
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
DDC classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Peer review:Referiert
Publishing method:Open Access / Green Open-Access
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