发表机构
Massachusetts Institute of Technology; École Polytechnique Fédérale de Lausanne（麻省理工学院; 洛桑联邦理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对高维数据同化中平滑过程计算成本过高的问题，研究提出动态低秩近似平滑方法，扩展联合均值与协方差优化滤波设置，构建降阶平滑算法以降低计算时间与存储需求。
AI 中文摘要
计算成本常使平滑过程难以适用于高维数据同化问题。为解决这一挑战，我们针对基于随机微分方程的框架提出动态低秩近似（DLRA）平滑方法。我们扩展先前开发的联合均值与协方差优化（JMCO）滤波设置，通过Rauch-Tung-Striebel递推导出降阶平滑器，并为仿射漂移动力学建立对应的Kalman-Bucy平滑。所得算法保留DLRA的自适应特性，同时大幅降低整个平滑过程的计算时间与存储需求。
英文摘要
Computational costs often make smoothing procedures prohibitive for high-dimensional data assimilation problems. To address this challenge, we propose a dynamical low-rank approximation (DLRA) methodology for smoothing concerning frameworks based on stochastic differential equations. We extend the previously developed joint mean-and-covariance optimization (JMCO) filtering setting to derive a reduced-order smoother via the Rauch--Tung--Striebel recursion and establish the corresponding Kalman--Bucy smoothing for affine drift dynamics. The resulting algorithms retain the adaptive nature of DLRA while significantly reducing the computational time and storage of the whole smoothing procedure.
Comments12 pages, 4 figures
