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Ensemble Kalman inversion (EKI) is a derivative-free optimizer aimed at solving inverse problems, taking motivation from the celebrated ensemble Kalman filter. The purpose of this article is to consider the introduction of adaptive Tikhonov…

Numerical Analysis · Mathematics 2022-03-23 Simon Weissmann , Neil K. Chada , Claudia Schillings , Xin T. Tong

Ensemble Kalman inversion (EKI) is an ensemble-based method to solve inverse problems. Its gradient-free formulation makes it an attractive tool for problems with involved formulation. However, EKI suffers from the ''subspace property'',…

Numerical Analysis · Mathematics 2025-04-11 Shuigen Liu , Sebastian Reich , Xin T. Tong

The ensemble Kalman inversion (EKI), a recently introduced optimisation method for solving inverse problems, is widely employed for the efficient and derivative-free estimation of unknown parameters. Specifically in cases involving…

Numerical Analysis · Mathematics 2023-12-22 Matei Hanu , Simon Weissmann

Ensemble Kalman inversion is a parallelizable methodology for solving inverse or parameter estimation problems. Although it is based on ideas from Kalman filtering, it may be viewed as a derivative-free optimization method. In its most…

Numerical Analysis · Mathematics 2024-12-20 Neil K. Chada , Andrew M. Stuart , Xin T. Tong

This paper investigates ensemble Kalman inversion (EKI) for variational inverse problems with convex, potentially non-smooth regularization. While deterministic EKI and its Tikhonov-regularized variants have primarily been analyzed for…

Numerical Analysis · Mathematics 2026-03-24 Simon Weissmann

Ensemble Kalman inversion (EKI) is a technique for the numerical solution of inverse problems. A great advantage of the EKI's ensemble approach is that derivatives are not required in its implementation. But theoretically speaking, EKI's…

Numerical Analysis · Mathematics 2023-05-03 Xin T. Tong , Matthias Morzfeld

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…

Numerical Analysis · Mathematics 2020-09-24 Marco Iglesias , Yuchen Yang

The Ensemble Kalman Inversion (EKI) method is widely used for solving inverse problems, leveraging ensemble-based techniques to iteratively refine parameter estimates. Despite its versatility, the accuracy of EKI is constrained by the…

Numerical Analysis · Mathematics 2025-03-17 Ruben Harris , Claudia Schillings

Ensemble Kalman inversion (EKI) is a sequential Monte Carlo method used to solve inverse problems within a Bayesian framework. Unlike backpropagation, EKI is a gradient-free optimization method that only necessitates the evaluation of…

Machine Learning · Computer Science 2023-07-18 Lucas Böttcher

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…

Numerical Analysis · Mathematics 2021-10-19 Neil K. Chada , Xin T. Tong

The Ensemble Kalman inversion (EKI) method is a method for the estimation of unknown parameters in the context of (Bayesian) inverse problems. The method approximates the underlying measure by an ensemble of particles and iteratively…

Numerical Analysis · Mathematics 2021-08-02 Dirk Blömker , Claudia Schillings , Philipp Wacker , Simon Weissmann

Ensemble Kalman inversion (EKI) is a derivative-free, particle-based optimization method for solving inverse problems. It can be shown that EKI approximates a gradient flow, which allows the application of methods for accelerating gradient…

Optimization and Control · Mathematics 2025-07-04 Sydney Vernon , Eviatar Bach , Oliver R. A. Dunbar

This paper is focused on the optimization approach to the solution of inverse problems. We introduce a stochastic dynamical system in which the parameter-to-data map is embedded, with the goal of employing techniques from nonlinear Kalman…

Numerical Analysis · Mathematics 2022-04-29 Daniel Zhengyu Huang , Tapio Schneider , Andrew M. Stuart

Ensemble Kalman Inversion (EKI) methods are a family of iterative methods for solving weighted least-squares problems, especially those arising in scientific and engineering inverse problems in which unknown parameters or states are…

Numerical Analysis · Mathematics 2025-05-26 Elizabeth Qian , Christopher Beattie

In inverse problems, the goal is to estimate unknown model parameters from noisy observational data. Traditionally, inverse problems are solved under the assumption of a fixed forward operator describing the observation model. In this…

Numerical Analysis · Mathematics 2024-09-26 Simon Weissmann , Neil K. Chada , Xin T. Tong

The ensemble Kalman inversion (EKI), as a derivative-free methodology, has been widely used in the parameter estimation of inverse problems. Unfortunately, its cost may become moderately large for systems described by high dimensional…

Numerical Analysis · Mathematics 2018-09-25 Liang Yan , Tao Zhou

In this paper we discuss a deterministic form of ensemble Kalman inversion as a regularization method for linear inverse problems. By interpreting ensemble Kalman inversion as a low-rank approximation of Tikhonov regularization, we are able…

Numerical Analysis · Mathematics 2023-10-31 Fabian Parzer , Otmar Scherzer

The ensemble Kalman filter is a well-known and celebrated data assimilation algorithm. It is of particular relevance as it used for high-dimensional problems, by updating an ensemble of particles through a sample mean and covariance…

Numerical Analysis · Mathematics 2022-07-27 Neil K. Chada

The ensemble Kalman inversion (EKI) is a particle based method which has been introduced as the application of the ensemble Kalman filter to inverse problems. In practice it has been widely used as derivative-free optimization method in…

Numerical Analysis · Mathematics 2022-09-21 Simon Weissmann

The Ensemble Kalman Filter (EnKF) belongs to the class of iterative particle filtering methods and can be used for solving control--to--observable inverse problems. In this context, the EnKF is known as Ensemble Kalman Inversion (EKI). In…

Numerical Analysis · Mathematics 2022-02-17 Dieter Armbruster , Michael Herty , Giuseppe Visconti
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