A Multifidelity Ensemble Kalman Filter with Reduced Order Control Variates
A Multifidelity Ensemble Kalman Filter with Reduced Order Control Variates
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DOI：
10.1137/20m1349965
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发表时间：
2020-07
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影响因子：
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通讯作者：
A. Popov;Changhong Mou;T. Iliescu;Adrian Sandu
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文献类型：
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作者：
A. Popov;Changhong Mou;T. Iliescu;Adrian Sandu
这项工作开发了一种基于线性控制变量框架的新的多保真集成卡尔曼滤波器（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粗保真度的不确定性代表较精细保真度不确定性的控制变量。高保真度模型运行的小型集成得到更便宜、保真度较低的大型集成的补充，只需少量的额外计算成本即可获得改进的分析。我们研究了使用降阶模型作为 MFEnKF 中的粗保真度控制变量，并提供分析来量化相对于传统集成卡尔曼滤波器的改进。我们应用这些想法，使用直接数值模拟和相应的 POD-Galerkin 降阶模型，对准地转测试问题进行数据同化。数值结果表明，与现有 EnKF 算法相比，双保真 MFEnKF 提供了更好的分析，且计算成本相当或更低。
This work develops a new multifidelity ensemble Kalman filter (MFEnKF) algorithm based on 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 represent 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 POD-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.