Work

Complexity reduction of large-scale stochastic systems using linear quadratic Gaussian balancing

Year: 2023

Type: preprint

Abstract: In this paper, we consider a model reduction technique for stabilizable and detectable stochastic systems. It is based on a pair of Gramians that we analyze in terms of well-posedness. Subsequently, dominant subspaces of the stochastic systems are identified exploiting these Gramians. An associated balancing related scheme is proposed that removes unimportant information from the stochastic dynamics in order to obtain a reduced system. We show that this reduced model preserves important features like stabilizability and detectability. Additionally, a comprehensive error analysis based on eigenvalues of the Gramian pair product is conducted. This provides an a-priori criterion for the reduction quality which we illustrate in numerical experiments.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2303.13460

Authors: Damm, Tobias, Redmann, Martin

Institutions: University of Kaiserslautern, Rheinland-Pfälzische Technische Universität Kaiserslautern-Landau, Martin Luther University Halle-Wittenberg

Language: English

Topic: Model Reduction and Neural Networks

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funder: Deutsche Forschungsgemeinschaft

Award: Niedrigdimensionale Approximationen von Problemen großer Ordnung im Zusammenhang mit hochdimensionalen PDEs und räumlich diskretisierten SPDEs

OpenAlex ID: W4360891780

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