Learning Enhanced Ensemble Filters Published in JCP

Thu, 11 Dec 2025 00:00:00 +0000

Our paper, “Learning Enhanced Ensemble Filters,” has been published in the Journal of Computational Physics.

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The paper introduces the measure neural mapping enhanced ensemble filter (MNMEF). Starting from a mean-field formulation of filtering, we use a set transformer to learn corrections to ensemble filtering updates while respecting the permutation symmetry of an ensemble. The mean-field perspective allows a model trained at one ensemble size to be deployed at another, with lightweight fine-tuning for ensemble-size-dependent parameters.

Lorenz-96 results across ensemble sizes and two observation-noise levels. The pretrained and fine-tuned MNMEF models remain competitive as the ensemble size changes.

Across Lorenz-63, Lorenz-96, and Kuramoto–Sivashinsky experiments, MNMEF improves on optimized classical ensemble filters over a range of ensemble sizes.

Kuramoto–Sivashinsky filtering with only every eighth dimension observed. With an ensemble of ten members, MNMEF produces a more accurate state estimate than the optimized LETKF benchmark while maintaining a comparable spread.

The method also learns ensemble-size-dependent inflation and localization during the lightweight fine-tuning stage. Although the localization function is not constrained to have a prescribed shape, it learns a distance-decay profile similar to the widely used Gaspari–Cohn function.

Learned localization weights across ensemble sizes. The red curves adapt across assimilation steps, while the blue Gaspari–Cohn reference remains fixed.

I led this work in collaboration with Eviatar Bach, Ricardo Baptista, Edoardo Calvello, and Andrew Stuart.

The final article appears in Journal of Computational Physics, Volume 547, Article 114550: .

Journal of Computational Physics | Bohan Chen's Personal Webpage

Learning Enhanced Ensemble Filters Published in JCP