水平集集合卡尔曼滤波器：含激波流动的序贯数据同化
The Level Set Ensemble Kalman Filter: Sequential Data Assimilation for Flows With Shocks
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中文总结 AI 辅助
针对标准EnKF在含激波可压缩流中产生伪振荡的问题，本文提出水平集EnKF，通过非线性映射至潜在空间进行分析，以编码间断位置，并在多个一维及二维爆炸波案例中验证其可行性。
中文摘要 AI 辅助
集合卡尔曼滤波器因其在高维状态空间中的稳健性能和可扩展性，常被用于科学与工程中的序贯数据同化。然而，标准EnKF在应用于含激波的可压缩流动时会产生伪振荡；其原因是集合中激波位置的不确定性。本文发展了水平集EnKF，通过采用从原始状态空间到潜在空间的非线性映射来克服这一挑战，分析步骤在该潜在空间中执行。潜在表示包含一个水平集函数，该函数编码间断位置和定义在整个物理域上的光滑状态延拓，分别表示间断两侧的解。我们首先将水平集EnKF表述为在潜在空间中进行数据同化的更一般方法的一个具体实例。随后，我们通过几个一维可压缩流动和一个二维爆炸波演示了水平集EnKF的可行性。
英文摘要
The ensemble Kalman filter is commonly used to perform sequential data assimilation in science and engineering because of its robust performance and scalability when the state space dimension is high. However, the standard EnKF generates spurious oscillations when applied to compressible flows with shocks; the cause is the uncertainty, across the ensemble, in the shock location. This paper develops the \emph{level set EnKF}, which overcomes this challenge by employing a nonlinear mapping from the original state space into a latent space in which the analysis step is undertaken. The latent representation comprises a level set function that encodes the discontinuity location and smooth state extensions, defined over the full physical domain, that represent the solution on either side of the discontinuity. We first formulate the level set EnKF as a specific instance of a more general approach of performing data assimilation in a latent space. We then demonstrate the feasibility of the level set EnKF for several one-dimensional compressible flows and a two-dimensional blast wave.
发表机构
- California Institute of Technology（加州理工学院）
- University of California San Diego（加州大学圣迭戈分校）
- Johns Hopkins University（约翰斯·霍普金斯大学）
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