English
Related papers

Related papers: Ensemble Kalman inversion with non-smooth regulari…

200 papers

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), 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 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

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

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

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

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) 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

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

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

Enforcing sparse structure within learning has led to significant advances in the field of data-driven discovery of dynamical systems. However, such methods require access not only to time-series of the state of the dynamical system, but…

Optimization and Control · Mathematics 2020-10-21 Tapio Schneider , Andrew M. Stuart , Jin-Long Wu

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 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

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

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 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

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

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
‹ Prev 1 2 3 10 Next ›