A link between gramian based model order reduction and moment matching

(经验)基于Gramian的维度约简用于由分数布朗运动驱动的随机微分方程

(Empirical) Gramian-based dimension reduction for stochastic differential equations driven by fractional Brownian motion

本文研究由分数布朗运动驱动的大规模线性系统，提出经验Gramian方法用于约简，针对H>1/2的情况解决计算难题，并改进Stratonovich方程的ROM方法。

Bilinear systems -- A new link to $\mathcal H_2$-norms, relations to stochastic systems and further properties

In this paper, we prove several new results that give new insights into bilinear systems. We discuss conditions for asymptotic stability using probabilistic arguments. Moreover, we provide a global characterization of reachability in bilinear systems based on a certain Gramian. Reachability energy estimates using the same Gramian have only been local so far. The main result of this paper, however, is a new link between the output error and the $\mathcal H_2$-error of two bilinear systems. This result has several consequences in the field of model order reduction. It explains why $\mathcal H_2$…

Full state approximation by Galerkin projection reduced order models for stochastic and bilinear systems

In this paper, the problem of full state approximation by model reduction is studied for stochastic and bilinear systems. Our proposed approach relies on identifying the dominant subspaces based on the reachability Gramian of a system. Once the desired subspace is computed, the reduced order model is then obtained by a Galerkin projection. We prove that, in the stochastic case, this approach either preserves mean square asymptotic stability or leads to reduced models whose minimal realization is mean square asymptotically stable. This stability preservation guarantees the existence of the redu…

时域模型降阶与线性时不变系统矩匹配之间的一种联系

A Connection Between Time Domain Model Order Reduction and Moment Matching for LTI Systems

本文研究了时域模型降阶方法与线性时不变系统矩匹配之间的联系，通过三个数值例子展示了理论联系，并指出时域方法的精度不高于矩匹配，因为展开点由多项式基的选择决定，而矩匹配可以适应系统。

数据同化问题的限时平衡截断

Time-limited Balanced Truncation for Data Assimilation Problems

本文探讨了将平衡截断应用于线性高斯贝叶斯推断和4D-Var方法，提出限时平衡截断增强方法，支持不稳定系统平衡并改善短观测周期数值结果。