SIAM Journal on Scientific Computing, Volume 43, Issue 2, Page A1134-A1162, January 2021.
This work develops a new multifidelity ensemble Kalman filter (MFEnKF) algorithm based on a linear control variate framework. The approach allows for rigorous multifidelity extensions of the EnKF, where the uncertainty in coarser fidelities in the hierarchy of models represents control variates for the uncertainty in finer fidelities. Small ensembles of high-fidelity model runs are complemented by larger ensembles of cheaper, lower-fidelity runs to obtain much improved analyses at only small additional computational costs. We investigate the use of reduced order models as coarse fidelity control variates in the MFEnKF and provide analyses to quantify the improvements over the traditional ensemble Kalman filters. We apply these ideas to perform data assimilation with a quasi-geostrophic test problem, using direct numerical simulation and a corresponding proper orthogonal decomposition--Galerkin reduced order model. Numerical results show that the two-fidelity MFEnKF provides better analyses than existing EnKF algorithms at comparable or reduced computational costs.

中文翻译：

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降阶控制变量的多保真集成卡尔曼滤波器

SIAM科学计算杂志，第43卷，第2期，第A1134-A1162页，2021年1月。
这项工作开发了一种新的基于线性控制变量框架的多保真合奏卡尔曼滤波器（MFEnKF）算法。该方法允许对EnKF进行严格的多保真度扩展，其中模型层次结构中较高保真度的不确定性表示较高保真度的不确定性的控制变量。高保真模型运行的小集合由便宜，低保真度运行的大集合补充，以仅需很少的额外计算成本即可获得大大改进的分析。我们研究了使用降阶模型作为MFEnKF中的粗略保真度控制变量，并提供了分析以量化对传统集成Kalman滤波器的改进。我们运用这些想法对准地转测试问题进行数据同化，使用直接数值模拟和相应的适当正交分解-Galerkin降阶模型。数值结果表明，与现有EnKF算法相比，双保真MFEnKF可以以可比或更低的计算成本提供更好的分析。