基于模拟的滤波的生成模型：公式化与实证比较
Generative models for simulation based filtering: Formulations and Empirical Comparisons
- University of Washington（华盛顿大学）
- Morgan Stanley（摩根士丹利）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出统一生成模型滤波框架，基于输运实现分析步骤，推导三种新滤波器，并与传统方法比较，发现生成滤波器能处理多模态后验，但无单一最优方法，需根据在线预算和集合规模选择。
AI中文摘要：
本文提出了一种统一的公式化框架，并对生成模型方法在非线性滤波问题中的应用进行了受控数值比较。在该框架下，分析步骤通过将预报分布输运到后验分布来实现，不同方法的区别仅在于如何选择和学习这种输运。我们基于随机插值器、其确定性流匹配极限以及通过前向-后向随机微分方程实现的薛定谔桥，推导出三种新的滤波器。我们开发了一个两阶段调参程序，将生成模型的训练与其在线细化分开。所得方法在精度、计算时间以及对集合规模和状态维度的敏感性方面，与最优输运滤波器（OTF）、Knothe-Rosenblatt滤波器（KRF）、序贯重要性重采样（SIR）粒子滤波器和集合卡尔曼滤波器（EnKF）进行了比较。结果表明，每种生成滤波器都能解析EnKF和SIR无法解析的多模态后验分布，没有一种生成框架占主导地位，首选方法取决于可用的在线预算和集合规模，并且这些滤波器在生成的粒子轨迹的规律性上有所不同。
英文摘要：
This letter presents a unified formulation and a controlled numerical comparison of generative-model approaches to the nonlinear filtering problem. Under this formulation the analysis step is realized by a transport of the forecast distribution to the posterior, the approaches differing only in how that transport is selected and learned. We derive three new filters, based on stochastic interpolants, their deterministic flow-matching limit, and Schrödinger bridges realized through forward--backward SDEs. We develop a two-stage tuning procedure that separates the training of the generative model from its online refinement. The resulting methods are compared against the optimal transport filter (OTF), the Knothe--Rosenblatt filter (KRF), the sequential importance resampling (SIR) particle filter and the ensemble Kalman filter (EnKF), in terms of accuracy, computational time, and sensitivity to ensemble size and state dimension. The results indicate that every generative filter resolves multimodal posteriors that the EnKF and SIR do not, that no single generative framework dominates, the preferred method being set by the available online budget and ensemble size, and that the filters differ in the regularity of the particle trajectories they produce.
