Learning Discriminators for Resampling in the Ensemble Gaussian Mixture Filter through a Normalizing Flow Approach
For practitioners of non-linear filtering in medium-to-high dimensions, this work improves the physical realism of ensemble filters, though the improvement is incremental.
The authors tackle the problem of physically unrealistic posterior samples in the ensemble Gaussian mixture filter (EnGMF) by introducing a discriminator-informed resampling procedure that accepts or rejects particles based on physical plausibility, learned via normalizing flows. Numerical experiments on the Ikeda map and Lorenz '63 system show consistent error reduction compared to standard EnGMF in low-ensemble regimes.
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.