基于扩散生成模型的非线性滤波器，提升复杂系统数据同化精度。
The Ensemble Schr{ö}dinger Bridge filter for Nonlinear Data Assimilation
- 用扩散生成模型替代传统分析步骤，实现无梯度、免训练的滤波更新。
- 在40维以上混沌系统中表现优异，优于集合卡尔曼滤波与粒子滤波。
- 适合高维非线性系统，尤其适用于气象等实际应用中的复杂动态建模。
本文提出一种新型非线性最优滤波方法——集成薛定谔桥滤波器。该方法将标准预测步骤与基于扩散生成模型的分析步骤结合，完成一次完整的滤波更新。所提方法无结构模型误差，无需导数、无需训练，且高度可并行化。数值实验表明，该算法在高非线性动力学和观测过程（包括维度达40及以上）的混沌系统中均表现出色。结果还显示，该方法在多种非线性程度不同的测试中均优于经典方法，如集合卡尔曼滤波和粒子滤波。未来工作将聚焦于拓展至实际气象应用，并建立严格的收敛性理论。
原文摘要 · Abstract (English)
This work introduces a novel nonlinear optimal filtering method, termed the Ensemble Schr{ö}dinger Bridge nonlinear filter. The proposed filter combines the standard prediction step with a diffusion-generative-modeling-based analysis step, thereby completing one full filtering update. The resulting approach introduces no structural model error, and is derivative-free, training-free, and highly parallelizable. Numerical experiments demonstrate that the proposed algorithm performs effectively for highly nonlinear dynamics and nonlinear observation processes, including chaotic systems with dimension up to 40 and beyond. The results also show that the method outperforms classical approaches such as the ensemble Kalman filter and particle filter across a range of tests with varying degrees of nonlinearity. Future work will focus on extending the proposed method to practical meteorological applications and developing a rigorous convergence theory.
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