Learning Enhanced Ensemble Filters

Sun, 15 Feb 2026 00:00:00 +0000

This work introduces the measure neural mapping enhanced ensemble filter (MNMEF), a learning-based data-assimilation method derived from a mean-field formulation of the filtering problem. Measure neural mappings extend neural operators to maps acting on probability measures; their finite-ensemble implementation uses a permutation-invariant set transformer.

The mean-field construction allows most learned parameters to be shared across ensemble sizes. A model can therefore be trained efficiently using a small ensemble and deployed at other ensemble sizes, while lightweight fine-tuning adapts a limited number of parameters such as inflation and localization.

Experiments on Lorenz-63, Lorenz-96, and Kuramoto–Sivashinsky systems show improved filtering accuracy relative to optimized classical ensemble methods across both small and larger ensembles.

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: .

Measure Neural Mapping | Bohan Chen's Personal Webpage

Learning Enhanced Ensemble Filters

Learning Enhanced Ensemble Filters Published in JCP