Related papers: Adaptive regularisation for ensemble Kalman invers…

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…

We propose the application of iterative regularization for the development of ensemble methods for solving Bayesian inverse problems. In concrete, we construct (i) a variational iterative regularizing ensemble Levenberg-Marquardt method…

Ensemble Kalman Inversion (EnKI) and Ensemble Square Root Filter (EnSRF) are popular sampling methods for obtaining a target posterior distribution. They can be seem as one step (the analysis step) in the data assimilation method Ensemble…

The Bayesian approach to inverse problems is widely used in practice to infer unknown parameters from noisy observations. In this framework, the ensemble Kalman inversion has been successfully applied for the quantification of uncertainties…

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…

Standard maximum likelihood or Bayesian approaches to parameter estimation for stochastic differential equations are not robust to perturbations in the continuous-in-time data. In this paper, we give a rather elementary explanation of this…

Bayesian experimental design (BED) for complex physical systems is often limited by the nested inference required to estimate the expected information gain (EIG) or its gradients. Each outer sample induces a different posterior, creating a…

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…

We propose a generalised framework for the updating of a prior ensemble to a posterior ensemble, an essential yet challenging part in ensemble-based filtering methods. The proposed framework is based on a generalised and fully Bayesian view…

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…

The ensemble Kalman filter (EnKF) is widely used for nonlinear and high-dimensional state estimation because it replaces complex covariance propagation with simple ensemble statistics. However, conventional EnKF implementations can become…

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…

High-fidelity simulations are essential for predicting material behavior under high-velocity impact (HVI), but their accuracy depends on material models and parameters that are often calibrated by manual fitting to multiple costly…

Attitude estimation is crucial in aerospace engineering, robotics, and virtual reality applications, but faces difficulties due to nonlinear system dynamics and sensor limitations. This paper addresses the challenge of attitude estimation…

Accurate estimation of noise parameters is critical for optimal filter performance, especially in systems where true noise parameter values are unknown or time-varying. This article presents a quaternion left-invariant extended Kalman…

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 choice of the parameter value for regularized inverse problems is critical to the results and remains a topic of interest. This article explores a criterion for selecting a good parameter value by maximizing the probability of the data,…

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…

This paper proposes new methodology for sequential state and parameter estimation within the ensemble Kalman filter. The method is fully Bayesian and propagates the joint posterior density of states and parameters over time. In order to…

The Ensemble Kalman filter and Ensemble square root filters are data assimilation methods used to combine high dimensional nonlinear models with observed data. These methods have proved to be indispensable tools in science and engineering…