Learning Discriminators for Resampling in the Ensemble Gaussian Mixture Filter through a Normalizing Flow Approach

2026-05-01

AI Summary

This study addresses a key limitation of the standard ensemble Gaussian mixture filter (EnGMF), which can generate physically implausible posterior samples during resampling, leading to distorted forecasts. To mitigate this issue, the authors propose a novel discriminative resampling mechanism that, for the first time, integrates a physics-aware discriminator based on normalizing flow learning into the EnGMF framework to selectively retain candidate particles satisfying physical constraints. This approach significantly enhances both the physical consistency and estimation accuracy of the filter while maintaining a small ensemble size. Experimental results on the Ikeda map and Lorenz '63 system demonstrate that the proposed method consistently reduces analysis error under limited sample conditions and markedly outperforms the conventional EnGMF.

Abstract

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.

Problem

• resampling
• physical plausibility
• ensemble Gaussian mixture filter
• posterior samples
• nonlinear filtering

Innovation

• discriminator-informed resampling
• normalizing flow
• ensemble Gaussian mixture filter
• physical plausibility
• nonlinear filtering