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We consider the Ensemble Kalman Inversion which has been recently introduced as an efficient, gradient-free optimisation method to estimate unknown parameters in an inverse setting. In the case of large data sets, the Ensemble Kalman…
Many modern algorithms for inverse problems and data assimilation rely on ensemble Kalman updates to blend prior predictions with observed data. Ensemble Kalman methods often perform well with a small ensemble size, which is essential in…
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…
This work proposes ensemble Kalman randomized maximum likelihood estimation, a new derivative-free method for performing randomized maximum likelihood estimation, which is a method that can be used to generate approximate samples from…
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…
We introduce a derivative-free computational framework for approximating solutions to nonlinear PDE-constrained inverse problems. The aim is to merge ideas from iterative regularization with ensemble Kalman methods from Bayesian inference…
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…
The ensemble Kalman inversion is widely used in practice to estimate unknown parameters from noisy measurement data. Its low computational costs, straightforward implementation, and non-intrusive nature makes the method appealing in various…
This paper provides a unified perspective of iterative ensemble Kalman methods, a family of derivative-free algorithms for parameter reconstruction and other related tasks. We identify, compare and develop three subfamilies of ensemble…
Ensemble Kalman methods were initially developed to solve nonlinear data assimilation problems in oceanography, but are now popular in applications far beyond their original use cases. Of particular interest is climate model calibration. As…
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…
We study the use of novel techniques arising in machine learning for inverse problems. Our approach replaces the complex forward model by a neural network, which is trained simultaneously in a one-shot sense when estimating the unknown…
The Ensemble Kalman filter (EnKF) was introduced by Evensen in 1994 [10] as a novel method for data assimilation: state estimation for noisily observed time-dependent problems. Since that time it has had enormous impact in many application…
In data assimilation, an ensemble provides a way to propagate the probability density of a system described by a nonlinear prediction model. Although a large ensemble size is required for statistical accuracy, the ensemble size is typically…
Inverse problems are more challenging when only partial data are available in general. In this paper, we propose a two-step approach combining the extended sampling method and the ensemble Kalman filter to reconstruct an elastic rigid…
Inverse problems are common and important in many applications in computational physics but are inherently ill-posed with many possible model parameters resulting in satisfactory results in the observation space. When solving the inverse…
We are interested in ensemble methods to solve multi-objective optimization problems. An ensemble Kalman method is proposed to solve a formulation of the nonlinear problem using a weighted function approach. An analysis of the mean field…
The ensemble Kalman filter (EnKF) is a widely used methodology for state estimation in partial, noisily observed dynamical systems, and for parameter estimation in inverse problems. Despite its widespread use in the geophysical sciences,…
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…
Many parameter estimation problems arising in applications are best cast in the framework of Bayesian inversion. This allows not only for an estimate of the parameters, but also for the quantification of uncertainties in the estimates.…