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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

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

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 derivative-free optimization method that lies between the deterministic and the probabilistic approaches for inverse problems. EKI iterates the Kalman update of ensemble-based Kalman filters, whose…

Numerical Analysis · Mathematics 2021-04-02 Yoonsang Lee

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

The standard probabilistic perspective on machine learning gives rise to empirical risk-minimization tasks that are frequently solved by stochastic gradient descent (SGD) and variants thereof. We present a formulation of these tasks as…

Machine Learning · Computer Science 2019-09-04 Nikola B. Kovachki , Andrew M. Stuart

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

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

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

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) 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

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 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

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

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

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

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) for the solution of Bayesian inverse problems of type $y = A u +\varepsilon$, with $u$ being an unknown parameter, $y$ a given datum, and $\varepsilon$ measurement noise, is a powerful tool usually…

Numerical Analysis · Mathematics 2023-03-16 Leon Bungert , Philipp Wacker

Ensemble Kalman inversion is a parallelizable derivative-free method to solve inverse problems. The method uses an ensemble that follows the Kalman update formula iteratively to solve an optimization problem. The ensemble size is crucial to…

Numerical Analysis · Mathematics 2021-05-25 Yoonsang Lee

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
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