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

TL;DR

This paper introduces a discriminator-informed resampling method for the ensemble Gaussian mixture filter, using normalizing flows to improve physical plausibility of particles in nonlinear filtering tasks.

Contribution

It proposes a novel resampling technique that incorporates learned discriminators via normalizing flows to enhance EnGMF performance.

Findings

Reduces error in low-ensemble regimes on Ikeda map and Lorenz '63 system.

Improves physical plausibility of posterior samples.

Demonstrates effectiveness of learned discriminators in filtering.

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.