Related papers: Interacting Langevin Diffusions: Gradient Structur…
Despite the widespread usage of discrete generation Ensemble Kalman particle filtering methodology to solve nonlinear and high dimensional filtering and inverse problems, little is known about their mathematical foundations. As genetic-type…
The method of choice for integrating the time-dependent Fokker-Planck equation in high-dimension is to generate samples from the solution via integration of the associated stochastic differential equation. Here, we study an alternative…
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…
Efficient and accurate integration of stochastic (partial) differential equations with multiplicative noise can be obtained through a split-step scheme, which separates the integration of the deterministic part from that of the stochastic…
In this paper, we exploit the gradient flow structure of continuous-time formulations of Bayesian inference in terms of their numerical time-stepping. We focus on two particular examples, namely, the continuous-time ensemble Kalman-Bucy…
In this paper, we develop a class of interacting particle Langevin algorithms to solve inverse problems for partial differential equations (PDEs). In particular, we leverage the statistical finite elements (statFEM) formulation to obtain a…
The ensemble Kalman filter (EnKF) is a widely used methodology for state estimation in partial, noisily observed dynamical systems, and for parameter estimation in inverse problems. Despite its widespread use in the geophysical sciences,…
The recent statistical finite element method (statFEM) provides a coherent statistical framework to synthesise finite element models with observed data. Through embedding uncertainty inside of the governing equations, finite element…
The Ensemble Kalman methodology in an inverse problems setting can be viewed as an iterative scheme, which is a weakly tamed discretization scheme for a certain stochastic differential equation (SDE). Assuming a suitable approximation…
Many physical systems characterized by nonlinear multiscale interactions can be effectively modeled by treating unresolved degrees of freedom as random fluctuations. However, even when the microscopic governing equations and qualitative…
We present a novel algorithm based on the ensemble Kalman filter to solve inverse problems involving multiscale elliptic partial differential equations. Our method is based on numerical homogenization and finite element discretization and…
This paper proposes a probabilistic approach to the problem of intrinsic filtering of a system on a matrix Lie group with invariance properties. The problem of an invariant continuous-time model with discrete-time measurements is cast into…
We study Bayesian inverse problems with mixed noise, modeled as a combination of additive and multiplicative Gaussian components. While traditional inference methods often assume fixed or known noise characteristics, real-world…
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…
The aim of this note is to revisit propagation of chaos for a Langevin-type interacting particle system used for sampling probability measures. The interacting particle system we consider coincides, in the setting of a log-quadratic target…
We use Langevin dynamics simulations to study the mass diffusion problem across two adjacent porous layers of different transport property. At the interface between the layers, we impose the Kedem-Katchalsky (KK) interfacial boundary…
The covariant form of the multivariable diffusion-drift process is described by the covariant Fokker--Planck equation using the standard toolbox of Riemann geometry. The covariant form of the equivalent Langevin stochastic differential…
This paper develops efficient ensemble Kalman filter (EnKF) implementations based on shrinkage covariance estimation. The forecast ensemble members at each step are used to estimate the background error covariance matrix via the…
We consider systems of interacting particles which are described by a second order Langevin equation. The class of equations considered includes the situation where the particle evolution is governed by Hamiltonian dynamics with additional…
In the context of non-convex optimization, we let the temperature of a Langevin diffusion to depend on the diffusion's own density function. The rationale is that the induced density captures to some extent the landscape imposed by the…