# Adaptive regularisation for ensemble Kalman inversion

arXiv: https://arxiv.org/abs/2006.14980 · HTML: https://mlsanity.com/paper/2006.14980/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Jun 2020.

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

- [Hyperparameter Optimization for Randomized Algorithms: A Case Study on Random Features](https://mlsanity.com/paper/2407.00584/) (2024)
- [Flow Annealed Kalman Inversion for Gradient-Free Inference in Bayesian Inverse Problems](https://mlsanity.com/paper/2309.11490/) (2023)
- [A unified method of data assimilation and turbulence modeling for separated flows at high Reynolds numbers](https://mlsanity.com/paper/2211.00601/) (2022)
- [Score Operator Newton transport](https://mlsanity.com/paper/2305.09792/) (2023)
- [Nesterov Acceleration for Ensemble Kalman Inversion and Variants](https://mlsanity.com/paper/2501.08779/) (2025)
- [DeepONet-accelerated Bayesian inversion for moving boundary problems](https://mlsanity.com/paper/2512.20268/) (2025)
- [Calibration of a neural network ocean closure for improved mean state and variability](https://mlsanity.com/paper/2604.06398/) (2026)

## Abstract (arXiv)

We propose a new regularisation strategy for the classical ensemble Kalman inversion (EKI) framework. The strategy consists of: (i) an adaptive choice for the regularisation parameter in the update formula in EKI, and (ii) criteria for the early stopping of the scheme. In contrast to existing approaches, our parameter choice does not rely on additional tuning parameters which often have severe effects on the efficiency of EKI. We motivate our approach using the interpretation of EKI as a Gaussian approximation in the Bayesian tempering setting for inverse problems. We show that our parameter choice controls the symmetrised Kulback-Leibler divergence between consecutive tempering measures. We further motivate our choice using a heuristic statistical discrepancy principle. We test our framework using electrical impedance tomography with the complete electrode model. Parameterisations of the unknown conductivity are employed which enable us to characterise both smooth or a discontinuous (piecewise-constant) fields. We show numerically that the proposed regularisation of EKI can produce efficient, robust and accurate estimates, even for the discontinuous case which tends to require larger ensembles and more iterations to converge. We compare the proposed technique with a standard method of choice and demonstrate that the proposed method is a viable choice to address computational efficiency of EKI in practical/operational settings.