论文标题
时间限制的平衡截断，用于数据同化问题
Time-limited Balanced Truncation for Data Assimilation Problems
论文作者
论文摘要
平衡截断是一种公认的模型降低方法，已应用于各种问题。最近，已经提出了线性高斯贝叶斯推论问题与平衡截断的系统理论概念之间的联系。尽管这种联系是新的，但是平衡截断在数据同化中的应用并不是一个新颖的想法：它已经用于四维变分数据同化（4D-VAR）。本文讨论了平衡截断对线性高斯贝叶斯推断的应用，尤其是4D-VAR方法，从而进一步加强了系统理论与数据同化之间的联系。两种类型的数据同化问题之间的相似之处使最先进的方法可以将任意先前协方差作为可及性Gramians的概括。此外，我们提出了一种使用时间限制的平衡截断的增强方法，该方法可以平衡贝叶斯对不稳定系统的推断，并改善短期观察期的数值结果。
Balanced truncation is a well-established model order reduction method which has been applied to a variety of problems. Recently, a connection between linear Gaussian Bayesian inference problems and the system-theoretic concept of balanced truncation has been drawn. Although this connection is new, the application of balanced truncation to data assimilation is not a novel idea: it has already been used in four-dimensional variational data assimilation (4D-Var). This paper discusses the application of balanced truncation to linear Gaussian Bayesian inference, and, in particular, the 4D-Var method, thereby strengthening the link between systems theory and data assimilation further. Similarities between both types of data assimilation problems enable a generalisation of the state-of-the-art approach to the use of arbitrary prior covariances as reachability Gramians. Furthermore, we propose an enhanced approach using time-limited balanced truncation that allows to balance Bayesian inference for unstable systems and in addition improves the numerical results for short observation periods.
