# Convergence Acceleration of Ensemble Kalman Inversion in Nonlinear Settings

arXiv: https://arxiv.org/abs/1911.02424 · HTML: https://mlsanity.com/paper/1911.02424/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Nov 2019.

## Built on by (most cited first, 9 of 9)

- [Sampling via Gradient Flows in the Space of Probability Measures](https://mlsanity.com/paper/2310.03597/) (2023)
- [Ensemble Kalman Diffusion Guidance: A Derivative-free Method for Inverse Problems](https://mlsanity.com/paper/2409.20175/) (2024)
- [Gradient Flows for Sampling: Mean-Field Models, Gaussian Approximations and Affine Invariance](https://mlsanity.com/paper/2302.11024/) (2023)
- [Adaptive operator learning for infinite-dimensional Bayesian inverse problems](https://mlsanity.com/paper/2310.17844/) (2023)
- [Efficient Bayesian Physics Informed Neural Networks for Inverse Problems via Ensemble Kalman Inversion](https://mlsanity.com/paper/2303.07392/) (2023)
- [Blade: A Derivative-free Bayesian Inversion Method using Diffusion Priors](https://mlsanity.com/paper/2510.10968/) (2025)
- [The Ensemble Kalman Inversion Race](https://mlsanity.com/paper/2511.15853/) (2025)
- [Nesterov Acceleration for Ensemble Kalman Inversion and Variants](https://mlsanity.com/paper/2501.08779/) (2025)
- [The Ensemble Kalman Update is an Empirical Matheron Update](https://mlsanity.com/paper/2502.03048/) (2025)

## Abstract (arXiv)

Many data-science problems can be formulated as an inverse problem, where the parameters are estimated by minimizing a proper loss function. When complicated black-box models are involved, derivative-free optimization tools are often needed. The ensemble Kalman filter (EnKF) is a particle-based derivative-free Bayesian algorithm originally designed for data assimilation. Recently, it has been applied to inverse problems for computational efficiency. The resulting algorithm, known as ensemble Kalman inversion (EKI), involves running an ensemble of particles with EnKF update rules so they can converge to a minimizer. In this article, we investigate EKI convergence in general nonlinear settings. To improve convergence speed and stability, we consider applying EKI with non-constant step-sizes and covariance inflation. We prove that EKI can hit critical points with finite steps in non-convex settings. We further prove that EKI converges to the global minimizer polynomially fast if the loss function is strongly convex. We verify the analysis presented with numerical experiments on two inverse problems.