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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

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

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

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

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

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

Solving inverse problems without the use of derivatives or adjoints of the forward model is highly desirable in many applications arising in science and engineering. In this paper, we propose a new version of such a methodology, a framework…

Dynamical Systems · Mathematics 2019-10-17 Alfredo Garbuno-Inigo , Franca Hoffmann , Wuchen Li , 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

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 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 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

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

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 filter (EnKF) is a Monte Carlo approximation of the Kalman filter for high dimensional linear Gaussian state space models. EnKF methods have also been developed for parameter inference of static Bayesian models with a…

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

For many scientific inverse problems we are required to evaluate an expensive forward model. Moreover, the model is often given in such a form that it is unrealistic to access its gradients. In such a scenario, standard Markov Chain Monte…

Computation · Statistics 2023-09-21 Richard D. P. Grumitt , Minas Karamanis , Uroš Seljak

This paper addresses the challenging task of guide wire navigation in cardiovascular interventions, focusing on the parameter estimation of a guide wire system using Ensemble Kalman Inversion (EKI) with a subsampling technique. The EKI uses…

Numerical Analysis · Mathematics 2023-12-12 Matei Hanu , Jürgen Hesser , Guido Kanschat , Javier Moviglia , Claudia Schillings , Jan Stallkamp

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), 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
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