用低维隐空间改进数据同化，让含激波流场的模拟更准确。
Feature-preserving Latent-EnKF for Data Assimilation of Flows with Shocks
- 在学习的隐空间中进行集合更新，保持激波等特征清晰
- 在稀疏噪声观测下恢复激波位置，无虚假振荡
- 无需成员专属训练，适合复杂流动同化任务
集合卡尔曼滤波（EnKF）广泛用于序列数据同化，但在存在不连续解（如可压缩流中的激波）时失效。激波位置不确定性导致集合统计呈现多模态，违背了EnKF的高斯假设，引发分析状态的大范围虚假振荡。本文提出一种保持特征的隐空间EnKF：在学习得到的低维隐空间中执行集合更新，使激波与流动特征呈现光滑流形表示，从而在同化过程中保留尖锐特征。所有成员通过共享解码器将更新后的隐状态映射回物理空间。该方法省去了先前方法所需的成员特定训练和正性截断。在Sod激波管及二维圆柱体上马赫数为2的激波相互作用问题上，使用稀疏且含噪观测的数值实验表明，该算法能准确恢复激波与接触间断，且无虚假振荡。
原文摘要 · Abstract (English)
The ensemble Kalman filter (EnKF) is widely adopted for sequential data assimilation, but fails for solutions with discontinuities, such as shocks in compressible flows. Uncertainty in shock location induces multimodal ensemble statistics that violate the Gaussian assumptions underlying the EnKF, producing large-scale spurious oscillations in the analysis state. We introduce a feature-preserving latent-EnKF that performs the ensemble update in a learned low-dimensional latent space, where shock and flow features admit a smooth manifold representation, thereby preserving sharp features during EnKF analysis. The updated latent state is mapped back to physical state through a shared decoder for all ensemble members. The algorithm eliminates the member-specific ordered training and positivity flooring used in prior approaches. Numerical experiments on a Sod shock tube and Mach 2 shock interaction with a 2D cylinder, using sparse and noisy observations, show accurate feature recovery of shocks and contact discontinuities without spurious oscillations.
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