论文标题
基于优化的随机系统模型降低
Optimization based model order reduction for stochastic systems
论文作者
论文摘要
在本文中，我们将随机线性系统的模型订单减少和$ \ Mathcal H_2 $ - 最佳模型订单减少汇总。特别是，我们为降低随机微分方程的模型顺序降低误差界的理论并完成了误差理论。使用这些误差界，我们在随机系统的输出误差（带有添加性和乘法噪声）与$ \ Mathcal H_2 $ -Norm的修改版本之间建立了一个链接，用于线性和双线性确定性系统。当推导各自的最佳条件以最大程度地减少误差界限时，我们看到与迭代有理Krylov算法（IRKA）相关的模型订购降低技术是降低具有添加性和/或倍增噪声的大规模随机系统尺寸的非常自然而有效的方法。我们将（线性和双线性）IRKA的修改版本应用于随机线性系统，并在数值实验中显示其效率。
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.
