Related papers: A regularizing iterative ensemble Kalman method fo…
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…
The focus of this work is on an alternative implementation of the iterative ensemble smoother (iES). We show that iteration formulae similar to those used in \cite{chen2013-levenberg,emerick2012ensemble} can be derived by adopting a…
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…
The Ensemble Kalman methodology in an inverse problems setting can be viewed as an iterative scheme, which is a weakly tamed discretization scheme for a certain stochastic differential equation (SDE). Assuming a suitable approximation…
The iterative ensemble Kalman filter (IEnKF) is widely used in inverse problems to estimate system parameters from limited observations. However, the IEnKF, when applied to nonlinear systems, can be plagued by poor convergence. Here we…
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 the process of reproducing the state dynamics of parameter dependent distributed systems, data from physical measurements can be incorporated into the mathematical model to reduce the parameter uncertainty and, consequently, improve the…
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…
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 present a novel algorithm based on the ensemble Kalman filter to solve inverse problems involving multiscale elliptic partial differential equations. Our method is based on numerical homogenization and finite element discretization and…
The increasing availability of data presents an opportunity to calibrate unknown parameters which appear in complex models of phenomena in the biomedical, physical and social sciences. However, model complexity often leads to…
Ensemble methods, such as the ensemble Kalman filter (EnKF), the local ensemble transform Kalman filter (LETKF), and the ensemble Kalman smoother (EnKS) are widely used in sequential data assimilation, where state vectors are of huge…
This paper develops an efficient implementation of the ensemble Kalman filter based on a modified Cholesky decomposition for inverse covariance matrix estimation. This implementation is named EnKF-MC. Background errors corresponding to…
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…
We analyze the Ensemble and Polynomial Chaos Kalman filters applied to nonlinear stationary Bayesian inverse problems. In a sequential data assimilation setting such stationary problems arise in each step of either filter. We give a new…
The Ensemble Kalman Filter method can be used as an iterative numerical scheme for parameter identification or nonlinear filtering problems. We study the limit of infinitely large ensemble size and derive the corresponding mean-field limit…
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…
Despite the widespread usage of discrete generation Ensemble Kalman particle filtering methodology to solve nonlinear and high dimensional filtering and inverse problems, little is known about their mathematical foundations. As genetic-type…
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…
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…