Related papers: The Ensemble Kalman Filter for Dynamic Inverse Pro…
In this study, we consider an ensemble Kalman inversion (EKI) for the numerical solution of time-fractional diffusion inverse problems (TFDIPs). Computational challenges in the EKI arise from the need for repeated evaluations of the forward…
Numerical models of geothermal reservoirs typically depend on hundreds or thousands of unknown parameters, which must be estimated using sparse, noisy data. However, these models capture complex physical processes, which frequently results…
Among the class of nonlinear particle filtering methods, the Ensemble Kalman Filter (EnKF) has gained recent attention for its use in solving inverse problems. We review the original method and discuss recent developments in particular in…
In recent years, uncertainty-aware full waveform inversion (FWI) has received increasing attention, with a growing emphasis on producing informative uncertainty estimates alongside inversion results. Bayesian inference methods--particularly…
The ensemble Kalman filter (EnKF) is a data assimilation technique that uses an ensemble of models, updated with data, to track the time evolution of a usually non-linear system. It does so by using an empirical approximation to the…
The performance of ensemble-based data assimilation techniques that estimate the state of a dynamical system from partial observations depends crucially on the prescribed uncertainty of the model dynamics and of the observations. These are…
The ensemble Kalman filter (EnKF) is a method for combining a dynamical model with data in a sequential fashion. Despite its widespread use, there has been little analysis of its theoretical properties. Many of the algorithmic innovations…
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…
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…
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…
Ensemble methods have become ubiquitous for the solution of Bayesian inference problems. State-of-the-art Langevin samplers such as the Ensemble Kalman Sampler (EKS), Affine Invariant Langevin Dynamics (ALDI) or its extension using weighted…
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…
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…
Large-scale dynamic inverse problems are often ill-posed due to model complexity and the high dimensionality of the unknown parameters. Regularization is commonly employed to mitigate ill-posedness by incorporating prior information and…
Ensemble Kalman Inversion (EKI) has been proposed as an efficient method for the approximate solution of Bayesian inverse problems with expensive forward models. However, when applied to the Bayesian inverse problem EKI is only exact in the…
The literature dealing with data-driven analysis and control problems has significantly grown in the recent years. Most of the recent literature deals with linear time-invariant systems in which the uncertainty (if any) is assumed to be…
Data assimilation provides algorithms for widespread applications in various fields. It is of practical use to deal with a large amount of information in the complex system that is hard to estimate. Weather forecasting is one of the…
The filtering distribution captures the statistics of the state of a dynamical system from partial and noisy observations. Classical particle filters provably approximate this distribution in quite general settings; however they behave…
Filtering is concerned with online estimation of the state of a dynamical system from partial and noisy observations. In applications where the state of the system is high dimensional, ensemble Kalman filters are often the method of choice.…
Mathematical modeling and simulation of complex physical systems based on partial differential equations (PDEs) have been widely used in engineering and industrial applications. To enable reliable predictions, it is crucial yet challenging…