Related papers: Unscented Kalman Inversion: Efficient Gaussian App…

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…

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…

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…

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'',…

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…

This paper studies the problem of distributed state estimation (DSE) over sensor networks on matrix Lie groups, which is crucial for applications where system states evolve on Lie groups rather than vector spaces. We propose 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…

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…

Recent diffusion models provide a promising zero-shot solution to noisy linear inverse problems without retraining for specific inverse problems. In this paper, we reveal that recent methods can be uniformly interpreted as employing a…

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…

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…

Rapid advances in designing cognitive and counter-adversarial systems have motivated the development of inverse Bayesian filters. In this setting, a cognitive 'adversary' tracks its target of interest via a stochastic framework such as a…

When solving inverse problems, one increasingly popular approach is to use pre-trained diffusion models as plug-and-play priors. This framework can accommodate different forward models without re-training while preserving the generative…

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…

For linear inverse problems with a large number of unknown parameters, uncertainty quantification remains a challenging task. In this work, we use Krylov subspace methods to approximate the posterior covariance matrix and describe efficient…

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…

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…

In counter-adversarial systems, to infer the strategy of an intelligent adversarial agent, the defender agent needs to cognitively sense the information that the adversary has gathered about the latter. Prior works on the problem employ…

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…

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…