Related papers: Unscented Kalman Inversion: Efficient Gaussian App…
The unscented Kalman inversion (UKI) presented in [1] is a general derivative-free approach to solving the inverse problem. UKI is particularly suitable for inverse problems where the forward model is given as a black box and may not be…
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…
In the geophysical joint inversion, the gradient and Bayesian Markov Chain Monte Carlo (MCMC) sampling-based methods are widely used owing to their fast convergences or global optimality. However, these methods either require the…
In inverse problems, the goal is to estimate unknown model parameters from noisy observational data. Traditionally, inverse problems are solved under the assumption of a fixed forward operator describing the observation model. In this…
We consider Bayesian inference for large scale inverse problems, where computational challenges arise from the need for repeated evaluations of an expensive forward model. This renders most Markov chain Monte Carlo approaches infeasible,…
The Ensemble Kalman inversion (EKI) method is a method for the estimation of unknown parameters in the context of (Bayesian) inverse problems. The method approximates the underlying measure by an ensemble of particles and iteratively…
The ensemble Kalman inversion (EKI), a recently introduced optimisation method for solving inverse problems, is widely employed for the efficient and derivative-free estimation of unknown parameters. Specifically in cases involving…
In this paper, we study efficient approximate sampling for probability distributions known up to normalization constants. We specifically focus on a problem class arising in Bayesian inference for large-scale inverse problems in science and…
The standard probabilistic perspective on machine learning gives rise to empirical risk-minimization tasks that are frequently solved by stochastic gradient descent (SGD) and variants thereof. We present a formulation of these tasks as…
Ensemble Kalman Inversion (EKI) methods are a family of iterative methods for solving weighted least-squares problems, especially those arising in scientific and engineering inverse problems in which unknown parameters or states are…
Based on the recently developed theory of Unscented Kalman Inversion in computational mathematics, we proposed a Bayesian joint inversion framework, i.e., Multi-task Unscented Kalman Inversion (MTUKI), and apply it to the joint inversion of…
Ensemble Kalman inversion (EKI) is a derivative-free optimizer aimed at solving inverse problems, taking motivation from the celebrated ensemble Kalman filter. The purpose of this article is to consider the introduction of adaptive Tikhonov…
For many scientific inverse problems we are required to evaluate an expensive forward model. Moreover, the model is often given in such a form that it is unrealistic to access its gradients. In such a scenario, standard Markov Chain Monte…
The Ensemble Kalman Inversion (EKI) method is widely used for solving inverse problems, leveraging ensemble-based techniques to iteratively refine parameter estimates. Despite its versatility, the accuracy of EKI is constrained by 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…
The ensemble Kalman inversion (EKI) for the solution of Bayesian inverse problems of type $y = A u +\varepsilon$, with $u$ being an unknown parameter, $y$ a given datum, and $\varepsilon$ measurement noise, is a powerful tool usually…
Many data-science problems can be formulated as an inverse problem, where the parameters are estimated by minimizing a proper loss function. When complicated black-box models are involved, derivative-free optimization tools are often…
The ensemble Kalman inversion (EKI), as a derivative-free methodology, has been widely used in the parameter estimation of inverse problems. Unfortunately, its cost may become moderately large for systems described by high dimensional…
Inverse problems are ubiquitous because they formalize the integration of data with mathematical models. In many scientific applications the forward model is expensive to evaluate, and adjoint computations are difficult to employ; in this…
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…