Learning Enhanced Ensemble Filters Published in JCP

Dec 11, 2025·
Bohan Chen
Bohan Chen
· 2 min read

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

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.

Relative RMSE and improvement of ensemble filters on Lorenz-96 across ensemble sizes
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 ground truth, observations, MNMEF estimate, errors, and ensemble spread
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 adaptive localization functions compared with Gaspari-Cohn localization
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: https://doi.org/10.1016/j.jcp.2025.114550.

News Journal of Computational Physics Data Assimilation Ensemble Kalman Filter Measure Neural Mapping Neural Operator Set Transformer
Bohan Chen
Authors
Bohan Chen
Postdoctoral Researcher