Related papers: Adaptive regularisation for ensemble Kalman invers…

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…

The dynamic ensemble selection of classifiers is an effective approach for processing label-imbalanced data classifications. However, such a technique is prone to overfitting, owing to the lack of regularization methods and the dependence…

We address the problem of observation noise misspecification in Bayesian filtering of dynamical systems via recent advances in generalised Bayesian inference. Mis-match in tail decay between the true data generating process and an assumed…

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…

Many imaging problems require solving an inverse problem that is ill-conditioned or ill-posed. Imaging methods typically address this difficulty by regularising the estimation problem to make it well-posed. This often requires setting the…

We propose a new algorithm for an adaptive optics system control law, based on the Linear Quadratic Gaussian approach and a Kalman Filter adaptation with localizations. It allows to handle non-stationary behaviors, to obtain performance…

The capability of a novel Kullback-Leibler divergence method is examined herein within the Kalman filter framework to select the input-parameter-state estimation execution with the most plausible results. This identification suffers from…

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…

The iterative ensemble Kalman filter (IEnKF) in a deterministic framework was introduced in Sakov et al. (2012) to extend the ensemble Kalman filter (EnKF) and improve its performance in mildly up to strongly nonlinear cases. However, the…

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…

The unscented Kalman inversion (UKI) method presented in [1] is a general derivative-free approach for the inverse problem. UKI is particularly suitable for inverse problems where the forward model is given as a black box and may not be…

Kullback-Leibler divergence (KL) regularization is widely used in reinforcement learning, but it becomes infinite under support mismatch and can degenerate in low-noise limits. Utilizing a unified information-geometric framework, we…

Over the years data assimilation methods have been developed to obtain estimations of uncertain model parameters by taking into account a few observations of a model state. The most reliable methods of MCMC are computationally expensive.…

System identification remains an intriguing challenge for lithium-ion batteries, as many models are nonlinear, exhibit multi-physics coupling, and involve a large number of parameters. In this paper, we address this challenge using the…

In this paper, we develop a new elegant framework relying on the Kullback-Leibler Information Criterion to address the design of one-stage adaptive detection architectures for multiple hypothesis testing problems. Specifically, at the…

State estimation that combines observational data with mathematical models is central to many applications and is commonly addressed through filtering methods, such as ensemble Kalman filters. In this article, we examine the signal-tracking…

We study non-linear Bayesian inverse problems arising from semilinear partial differential equations (PDEs) that can be transformed into linear Bayesian inverse problems. We are then able to extend the early stopping for Ensemble…

Many modern algorithms for inverse problems and data assimilation rely on ensemble Kalman updates to blend prior predictions with observed data. Ensemble Kalman methods often perform well with a small ensemble size, which is essential in…

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 use of ensemble methods to solve inverse problems is attractive because it is a derivative-free methodology which is also well-adapted to parallelization. In its basic iterative form the method produces an ensemble of solutions which…