WIAS Preprint No. 2503, (2018)

Energy estimates and model order reduction for stochastic bilinear systems


Authors

  • Redmann, Martin
    ORCID: 0000-0001-5182-9773

2010 Mathematics Subject Classification

  • 93A15 15A24 60J75

Keywords

  • Model order reduction, balanced truncation, Gramians, nonlinear stochastic systems, Lévy process

DOI

10.20347/WIAS.PREPRINT.2503

Abstract

In this paper, we investigate a large-scale stochastic system with bilinear drift and linear diffusion term. Such high dimensional systems appear for example when discretizing a stochastic partial differential equations in space. We study a particular model order reduction technique called balanced truncation (BT) to reduce the order of spatially-discretized systems and hence reduce computational complexity. We introduce suitable Gramians to the system and prove energy estimates that can be used to identify states which contribute only very little to the system dynamics. When BT is applied the reduced system is obtained by removing these states from the original system. The main contribution of this paper is an L2-error bound for BT for stochastic bilinear systems. This result is new even for deterministic bilinear equations. In order to achieve it, we develop a new technique which is not available in the literature so far.

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