论文标题
对模型降低的有效误差估计不均匀初始条件
Effective error estimation for model reduction with inhomogeneous initial conditions
论文作者
论文摘要
对于不同的平衡相关模型还原方法，已经得出了先验误差界限。最经典的结果是用于平衡截断和奇异扰动近似结合，该近似适用于具有均匀初始条件的渐近线性时间传播系统。最近，已经有一些尝试将与平衡相关的还原方法推广到案例的情况下，但具有不均匀的初始条件，但是这些概括的现有误差界限非常有限。特别是，需要将初始条件限制在低维子空间中，该子空间必须在构建还原模型之前选择。在本文中，我们提出了一个估算器，该估计量完全规避了这一硬性约束。我们的估计器适用于大量的还原方法，而前者仅针对某些特定方法得出。此外，我们的方法会产生更大的有效误差估计，也将在数值上证明。
A priori error bounds have been derived for different balancing-related model reduction methods. The most classical result is a bound for balanced truncation and singular perturbation approximation that is applicable for asymptotically stable linear time-invariant systems with homogeneous initial conditions. Recently, there have been a few attempts to generalize the balancing-related reduction methods to the case with inhomogeneous initial conditions, but the existing error bounds for these generalizations are quite restrictive. Particularly, it is required to restrict the initial conditions to a low-dimensional subspace, which has to be chosen before the reduced model is constructed. In this paper, we propose an estimator that circumvents this hard constraint completely. Our estimator is applicable to a large class of reduction methods, whereas the former results were only derived for certain specific methods. Moreover, our approach yields to significantly more effective error estimation, as also will be demonstrated numerically.
