潜在自编码器集合卡尔曼滤波器用于非线性数据同化
Latent Autoencoder Ensemble Kalman Filter for Nonlinear Data assimilation
AI总结：
本文提出了一种潜在自编码器集合卡尔曼滤波器，通过在学习的潜在空间中重构同化问题，解决传统卡尔曼滤波在强非线性动态下的性能问题，实现稳定且可解释的同化方法。
摘要：
集合卡尔曼滤波（EnKF）广泛用于高维系统的数据同化，但其性能常因卡尔曼更新与底层系统行为的结构不匹配而下降。本文提出潜在自编码器集合卡尔曼滤波器（LAE-EnKF），通过在学习的潜在空间中重构同化问题，解决这一限制。该方法学习非线性编码器-解码器以及稳定的线性潜在演变算子和一致的潜在观测映射，从而在潜在坐标中构建闭合的线性状态空间模型。这种构造恢复了与卡尔曼滤波框架的兼容性，并允许预报和分析步骤完全在潜在空间中进行。与现有基于自编码器和潜在同化方法相比，本文的方法强调结构一致性、稳定性和可解释性。我们提供了学习低维流形上线性动态的理论分析，并为所提出的潜在模型建立了泛化误差界。在代表性非线性和混沌系统上的数值实验表明，LAE-EnKF比标准EnKF和相关潜在空间方法具有更准确和稳定的同化性能，同时保持了可比的计算成本和数据驱动性。
英文摘要：
The ensemble Kalman filter (EnKF) is widely used for data assimilation in high-dimensional systems, but its performance often deteriorates for strongly nonlinear dynamics due to the structural mismatch between the Kalman update and the underlying system behavior. In this work, we propose a latent autoencoder ensemble Kalman filter (LAE-EnKF) that addresses this limitation by reformulating the assimilation problem in a learned latent space with linear and stable dynamics. The proposed method learns a nonlinear encoder--decoder together with a stable linear latent evolution operator and a consistent latent observation mapping, yielding a closed linear state-space model in the latent coordinates. This construction restores compatibility with the Kalman filtering framework and allows both forecast and analysis steps to be carried out entirely in the latent space. Compared with existing autoencoder-based and latent assimilation approaches that rely on unconstrained nonlinear latent dynamics, the proposed formulation emphasizes structural consistency, stability, and interpretability. We provide a theoretical analysis of learning linear dynamics on low-dimensional manifolds and establish generalization error bounds for the proposed latent model. Numerical experiments on representative nonlinear and chaotic systems demonstrate that the LAE-EnKF yields more accurate and stable assimilation than the standard EnKF and related latent-space methods, while maintaining comparable computational cost and data-driven.
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