Related papers: The Ensemble Kalman Filter for Inverse Problems

The ability of ensemble Kalman filter (EnKF) algorithms to extract information from observations is analyzed with the aid of the concept of the degrees of freedom for signal (DFS). A simple mathematical argument shows that DFS for EnKF is…

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,…

A Data Assimilation (DA) strategy based on an ensemble Kalman filter (EnKF) is used to enhance the predictive capabilities of scale resolving numerical tools for the analysis of flows exhibiting cyclic behaviour. More precisely, an ensemble…

Concurrent observation technologies have made high-precision real-time data available in large quantities. Data assimilation (DA) is concerned with how to combine this data with physical models to produce accurate predictions. For…

The inverse problem of determining parameters in a model by comparing some output of the model with observations is addressed. This is a description for what hat to be done to use the Gauss-Markov-Kalman filter for the Bayesian estimation…

A new ensemble filter that allows for the uncertainty in the prior distribution is proposed and tested. The filter relies on the conditional Gaussian distribution of the state given the model-error and predictability-error covariance…

This paper presents an approach for employing artificial neural networks (NN) to emulate an ensemble Kalman filter (EnKF) as a method of data assimilation. The assimilation methods are tested in the Simplified Parameterizations…

Inferring the state and unknown parameters of a network of coupled oscillators is of utmost importance. This task is made harder when only partial and noisy observations are available, which is a typical scenario in realistic…

Accurate knowledge of time-variation in meridional flow-speed and profile is crucial for estimating a solar cycle's features, which are ultimately responsible for causing space climate variations. However, no consensus has been reached yet…

Filtering - the task of estimating the conditional distribution for states of a dynamical system given partial and noisy observations - is important in many areas of science and engineering, including weather and climate prediction.…

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…

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…

Accurately reconstructing and forecasting high-resolution (HR) states from computationally cheap low-resolution (LR) observations is central to estimation-and-control of spatio-temporal PDE systems. We develop a unified superresolution…

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 Kalman filter (KF) is a widely-used algorithm for tracking the latent state of a dynamical system from noisy observations. For systems that are well-described by linear Gaussian state space models, the KF minimizes the mean-squared…

A physics-infused strategy relying on the Ensemble Kalman Filter (EnKF) is here used to augment the accuracy of a continuous Immersed Boundary Method (IBM). The latter is a classical penalty method accounting for the presence of the…

We present recent results on the existence of a continuous time limit for Ensemble Kalman Filter algorithms. In the setting of continuous signal and observation processes, we apply the original Ensemble Kalman Filter algorithm proposed by…

Due to the state trajectory-independent features of invariant Kalman filtering (InEKF), it has attracted widespread attention in the research community for its significantly improved state estimation accuracy and convergence under…

The extended Kalman filter (EKF) is a cornerstone of nonlinear state estimation, yet its performance is fundamentally limited by noise-model mismatch and linearization errors. We develop a residual-aware distributionally robust EKF that…

We consider the solution of inverse problems in dynamic contrast-enhanced imaging by means of Ensemble Kalman Filters. Our quantity of interest is blood perfusion, i.e. blood flow rates in tissue. While existing approaches to compute blood…