Optimization based model order reduction for stochastic systems

TL;DR

This paper develops error bounds linking stochastic system output errors to deterministic $\

Contribution

It extends $\

Findings

Error bounds for stochastic differential equations

Modified IRKA algorithms effectively reduce stochastic system dimensions

Numerical experiments demonstrate efficiency of proposed methods

Abstract

In this paper, we bring together the worlds of model order reduction for stochastic linear systems and $\mathcal H_2$-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 $\mathcal H_2$-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.