Optimization based model order reduction for stochastic systems

• Published in: Applied mathematics and computation 2021-06, Vol.398, p.125783, Article 125783
• Main Authors: Redmann, Martin, Freitag, Melina A.
• Format: Article
• Language: English
• Subjects: Lévy process; Model order reduction; Optimality conditions; Stochastic systems; Sylvester equations
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2020.125783

•New error bound analysis for model order reduction methods applied to stochastic systems with additive and multiplicative noise.•Derivation of optimality conditions for these error bounds guaranteeing local minimality of these bounds.•Provision of algorithms that lead to reduced order models satisfying the optimality conditions.•Numerical experiments that show the effectiveness of the reduced systems. 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.