论文标题
具有降低订单控制变体的多重级集合卡尔曼滤波器
A Multifidelity Ensemble Kalman Filter with Reduced Order Control Variates
论文作者
论文摘要
这项工作开发了一种基于线性控制变化框架的新的多重集合Kalman滤波器（MFENKF）算法。该方法允许ENKF进行严格的多余性扩展，其中模型层次结构中较粗糙的保真度的不确定性代表了较不确定性的不确定性的控制变化。较大的更便宜，较低的保真度运行的较大合奏，以仅需以较小的额外计算成本而获得大量改进的分析，从而补充了高忠诚模型运行的小型合奏。我们研究了减少订单模型作为MFENKF中粗富度控制变体的使用，并提供了分析以量化对传统的集合卡尔曼过滤器的改进。我们将这些想法应用于使用直接数值模拟和相应的Pod-Galerkin降低订单模型，以准确的藻类测试问题进行数据同化。数值结果表明，与现有的ENKF算法相比，以可比或降低的计算成本相比，两因素MFENKF提供了更好的分析。
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.
