相关论文: Determining White Noise Forcing From Eulerian Obse…

Sparse linear inverse problems appear in a variety of settings, but often the noise contaminating observations cannot accurately be described as bounded by or arising from a Gaussian distribution. Poisson observations in particular are a…

A common task in experimental sciences is to fit mathematical models to real-world measurements to improve understanding of natural phenomenon (reverse-engineering or inverse modeling). When complex dynamical systems are considered, such as…

Uncertainty quantification is essential when dealing with ill-conditioned inverse problems due to the inherent nonuniqueness of the solution. Bayesian approaches allow us to determine how likely an estimation of the unknown parameters is…

We generalise the problem of inverse reinforcement learning to multiple tasks, from multiple demonstrations. Each one may represent one expert trying to solve a different task, or as different experts trying to solve the same task. Our main…

We derive an efficient stochastic algorithm for inverse problems that present an unknown linear forcing term and a set of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of the problem is…

An inverse scattering problem for the 3D acoustic equation in time domain is considered. The unknown spatially distributed speed of sound is the subject of the solution of this problem. A single location of the point source is used. Using a…

This article shows that a large class of posterior measures that are absolutely continuous with respect to a Gaussian prior have strong maximum a posteriori estimators in the sense of Dashti et al. (2013). This result holds in any separable…

In this work, we investigate the use of Besov priors in the context of Bayesian inverse problems. The solution to Bayesian inverse problems is the posterior distribution which naturally enables us to interpret the uncertainties. Besov…

By now Bayesian methods are routinely used in practice for solving inverse problems. In inverse problems the parameter or signal of interest is observed only indirectly, as an image of a given map, and the observations are typically further…

In this work, we study the problem of learning the volatility under market microstructure noise. Specifically, we consider noisy discrete time observations from a stochastic differential equation and develop a novel computational method to…

We propose and study a temporal, and spatio-temporal discretisation of the 2D stochastic Navier--Stokes equations in bounded domains supplemented with no-slip boundary conditions. Considering additive noise, we base its construction on the…

The Bayesian approach to inverse problems with functional unknowns, has received significant attention in recent years. An important component of the developing theory is the study of the asymptotic performance of the posterior distribution…

In a Bayesian setting, inverse problems and uncertainty quantification (UQ) - the propagation of uncertainty through a computational (forward) model - are strongly connected. In the form of conditional expectation the Bayesian update…

The predictability of turbulent flows remains a challenging problem for mathematicians, physicists, and meteorologists. In this context, we consider the 3D incompressible Navier-Stokes equations with small-scale random forcing on…

In this work, we present some new Carleman inequalities for Stokes and Oseen equations with non-homogeneous boundary conditions. These estimates lead to log type stability inequalities for the problem of recovering the solution of the…

The paper addresses an error analysis of an Eulerian finite element method used for solving a linearized Navier--Stokes problem in a time-dependent domain. In this study, the domain's evolution is assumed to be known and independent of the…

The paper studies the issue of stability of solutions to the Navier-Stokes and damped Euler systems in periodic boxes. We show that under action of fast oscillating-in- time external forces all two dimensional regular solutions converge to…

We prove ergodicity of the finite dimensional approximations of the three dimensional Navier-Stokes equations, driven by a random force. The forcing noise acts only on a few modes and some algebraic conditions on the forced modes are found…

Uncertainty quantification for large-scale inverse problems remains a challenging task. For linear inverse problems with additive Gaussian noise and Gaussian priors, the posterior is Gaussian but sampling can be challenging, especially for…

This study presents a conditional flow matching framework for solving physics-constrained Bayesian inverse problems. In this setting, samples from the joint distribution of inferred variables and measurements are assumed available, while…