# Deterministic Mean-field Ensemble Kalman Filtering

arXiv: https://arxiv.org/abs/1409.0628 · HTML: https://mlsanity.com/paper/1409.0628/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Sep 2014.

## Built on by (most cited first, 7 of 7)

- [Auto-differentiable Ensemble Kalman Filters](https://mlsanity.com/paper/2107.07687/) (2021)
- [Ensemble Kalman Diffusion Guidance: A Derivative-free Method for Inverse Problems](https://mlsanity.com/paper/2409.20175/) (2024)
- [Non-Asymptotic Analysis of Ensemble Kalman Updates: Effective Dimension and Localization](https://mlsanity.com/paper/2208.03246/) (2022)
- [Expanding the Chaos: Neural Operator for Stochastic (Partial) Differential Equations](https://mlsanity.com/paper/2601.01021/) (2026)
- [Machine learning-based conditional mean filter: a generalization of the ensemble Kalman filter for nonlinear data assimilation](https://mlsanity.com/paper/2106.07908/) (2021)
- [Affine-Mapping based Variational Ensemble Kalman Filter](https://mlsanity.com/paper/2103.06315/) (2021)
- [Filtered Markovian Projection: Dimensionality Reduction in Filtering for Stochastic Reaction Networks](https://mlsanity.com/paper/2502.07918/) (2025)

## Abstract (arXiv)

The proof of convergence of the standard ensemble Kalman filter (EnKF) from Legland etal. (2011) is extended to non-Gaussian state space models. A density-based deterministic approximation of the mean-field limit EnKF (DMFEnKF) is proposed, consisting of a PDE solver and a quadrature rule. Given a certain minimal order of convergence kappa between the two, this extends to the deterministic filter approximation, which is therefore asymptotically superior to standard EnKF when the dimension d<2kappa. The fidelity of approximation of the true distribution is also established using an extension of total variation metric to random measures. This is limited by a Gaussian bias term arising from non-linearity/non-Gaussianity of the model, which exists for both DMFEnKF and standard EnKF. Numerical results support and extend the theory.