# Parameterizations for Ensemble Kalman Inversion

arXiv: https://arxiv.org/abs/1709.01781 · HTML: https://mlsanity.com/paper/1709.01781/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Sep 2017.

## Built on by (most cited first, 6 of 6)

- [Out-of-distributional risk bounds for neural operators with applications to the Helmholtz equation](https://mlsanity.com/paper/2301.11509/) (2023)
- [Invertible Fourier Neural Operators for Tackling Both Forward and Inverse Problems](https://mlsanity.com/paper/2402.11722/) (2024)
- [Efficient Bayesian Physics Informed Neural Networks for Inverse Problems via Ensemble Kalman Inversion](https://mlsanity.com/paper/2303.07392/) (2023)
- [Likelihood-Free Inference and Hierarchical Data Assimilation for Geological Carbon Storage](https://mlsanity.com/paper/2410.15302/) (2024)
- [Flow Annealed Kalman Inversion for Gradient-Free Inference in Bayesian Inverse Problems](https://mlsanity.com/paper/2309.11490/) (2023)
- [Meta-Posterior Consistency for the Bayesian Inference of Metastable System](https://mlsanity.com/paper/2408.01868/) (2024)

## Abstract (arXiv)

The use of ensemble methods to solve inverse problems is attractive because it is a derivative-free methodology which is also well-adapted to parallelization. In its basic iterative form the method produces an ensemble of solutions which lie in the linear span of the initial ensemble. Choice of the parameterization of the unknown field is thus a key component of the success of the method. We demonstrate how both geometric ideas and hierarchical ideas can be used to design effective parameterizations for a number of applied inverse problems arising in electrical impedance tomography, groundwater flow and source inversion. In particular we show how geometric ideas, including the level set method, can be used to reconstruct piecewise continuous fields, and we show how hierarchical methods can be used to learn key parameters in continuous fields, such as length-scales, resulting in improved reconstructions. Geometric and hierarchical ideas are combined in the level set method to find piecewise constant reconstructions with interfaces of unknown topology.