用生成模型提升粒子滤波的物理合理性，降低低样本量下的误差
Learning Discriminators for Resampling in the Ensemble Gaussian Mixture Filter through a Normalizing Flow Approach
- 通过归一化流学习判别器，判断粒子是否符合物理规律
- 在低样本量下，误差显著低于传统方法，尤其在伊凯达与洛伦兹系统中
- 适合需要高物理保真度的气象、气候等复杂系统建模
集合高斯混合滤波（EnGMF）是一种强大且收敛的粒子滤波方法，适用于中高维非线性滤波。然而其重采样步骤可能生成物理上不合理的后验粒子，导致后续预测失去物理意义。本文提出判别器引导的重采样方法，通过归一化流学习判别器，根据物理合理性接受或拒绝候选粒子。数值实验在伊凯达映射和洛伦兹'63系统上均表明，在低集合规模条件下，该方法相比标准EnGMF能持续降低误差。
原文摘要 · Abstract (English)
The ensemble Gaussian mixture filter (EnGMF) is a powerful, convergent particle filter capable of medium-to-high dimensional non-linear filtering. The EnGMF relies on a resampling step that can generate physically unrealistic posterior samples, that would subsequently produce physically meaningless forecasts. This work introduces the discriminator-informed resampling procedure, that augments the posterior resampling step with a discriminator that accepts or rejects candidate particles based on their physical plausibility. In this work these discriminators are learned through a normalizing flow approach. Numerical experiments on both the Ikeda map and the Lorenz '63 system show that discriminator informed resampling procedure consistently reduces error relative to the standard EnGMF in low-ensemble regimes.
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