Related papers: Localization in Ensemble Kalman inversion

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…

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 presents new results and understanding of the Ensemble Kalman filter (EnKF) for inverse problems. In particular, using a Lagrangian dual perspective we show that EnKF can be derived from the sample average approximation (SAA) of…

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…

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…

State-of-the-art ensemble Kalman filtering (EnKF) algorithms require incorporating localization techniques to cope with the rank deficiency and the inherited spurious correlations in their error covariance matrices. Localization techniques…

Ensemble Kalman filter (EnKF) is an important data assimilation method for high dimensional geophysical systems. Efficient implementation of EnKF in practice often involves the localization technique, which updates each component using only…

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…

Although the governing equations of many systems, when derived from first principles, may be viewed as known, it is often too expensive to numerically simulate all the interactions they describe. Therefore researchers often seek simpler…

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…

We introduce a practical method for incorporating equality and inequality constraints in global optimization methods based on stochastic interacting particle systems, specifically consensus-based optimization (CBO) and ensemble Kalman…

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…

Ensemble methods such as the Ensemble Kalman Filter (EnKF) are widely used for data assimilation in large-scale geophysical applications, as for example in numerical weather prediction (NWP). There is a growing interest for physical models…

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…

This work proposes a novel Alternating Direction Method of Multipliers (ADMM)-based Ensemble Kalman Inversion (EKI) algorithm for solving constrained nonlinear model predictive control (NMPC) problems. First, stage-wise nonlinear inequality…

This manuscript derives locally weighted ensemble Kalman methods from the point of view of ensemble-based function approximation. This is done by using pointwise evaluations to build up a local linear or quadratic approximation of a…

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…

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.…

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…

In recent years, operator learning, particularly the DeepONet, has received much attention for efficiently learning complex mappings between input and output functions across diverse fields. However, in practical scenarios with limited and…