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Optimization based model order reduction for stochastic systems

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  • Redmann, Martin
  • Freitag, Melina A.

Abstract

In this paper, we bring together the worlds of model order reduction for stochastic linear systems and H2-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 H2-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.

Suggested Citation

  • Redmann, Martin & Freitag, Melina A., 2021. "Optimization based model order reduction for stochastic systems," Applied Mathematics and Computation, Elsevier, vol. 398(C).
    • Handle: RePEc:eee:apmaco:v:398:y:2021:i:c:s0096300320307360
    DOI: 10.1016/j.amc.2020.125783
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    References listed on IDEAS

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    1. Carsten Hartmann, 2011. "Balanced model reduction of partially observed Langevin equations: an averaging principle," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 17(5), pages 463-490, March.
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    Cited by:

    1. Redmann, Martin & Duff, Igor Pontes, 2022. "Full state approximation by Galerkin projection reduced order models for stochastic and bilinear systems," Applied Mathematics and Computation, Elsevier, vol. 420(C).

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