Related papers: Well-Posed Bayesian Geometric Inverse Problems Ari…
We perform a Bayesian parameter inference in the context of resonantly damped transverse coronal loop oscillations. The forward problem is solved in terms of parametric results for kink waves in one-dimensional flux tubes in the thin tube…
Characterizing the properties of groundwater aquifers is essential for predicting aquifer response and managing groundwater resources. In this work, we develop a high-dimensional scalable Bayesian inversion framework governed by a…
Solving Bayesian inverse problems typically involves deriving a posterior distribution using Bayes' rule, followed by sampling from this posterior for analysis. Sampling methods, such as general-purpose Markov chain Monte Carlo (MCMC), are…
The paper presents a workflow for fast pore-scale simulation of single-phase flow in tight reservoirs typically characterized by low, multiscale porosity. Multiscale porosity implies that the computational domain contains porous voxels…
We consider the management of sloping, long and thin, coastal aquifers. We first develop a simple mathematical model, based on Darcy flow for porous media, which gives the water table height, and the flow velocity as a function of the…
We introduce a Bayesian solution to the problem of inferring the density profile of strong gravitational lenses when the lens galaxy may contain multiple dark or faint substructures. The source and lens models are based on a superposition…
The Bayesian approach to Inverse Problems relies predominantly on Markov Chain Monte Carlo methods for posterior inference. The typical nonlinear concentration of posterior measure observed in many such Inverse Problems presents severe…
Recent studies demonstrate that diffusion models can serve as a strong prior for solving inverse problems. A prominent example is Diffusion Posterior Sampling (DPS), which approximates the posterior distribution of data given the measure…
We investigate how ideas from covariance localization in numerical weather prediction can be used in Markov chain Monte Carlo (MCMC) sampling of high-dimensional posterior distributions arising in Bayesian inverse problems. To localize an…
We describe a Bayesian framework for an inverse problem arising from monitoring block caving operations via muon tomography. We work with a low dimensional surface-based representation of the geometry of the block cave, which dramatically…
In statistical applications, it is common to encounter parameters supported on a varying or unknown dimensional space. Examples include the fused lasso regression, the matrix recovery under an unknown low rank, etc. Despite the ease of…
This work investigates the scattering coefficients for inverse medium scattering problems. It shows some fundamental properties of the coefficients such as symmetry and tensorial properties. The relationship between the scattering…
This paper is concerned with analysis of electromagnetic wave scattering by an obstacle which is embedded in a two-layered lossy medium separated by an unbounded rough surface. Given a dipole point source, the direct problem is to determine…
Commercial Microwave Links (CMLs) offer dense spatial coverage for rainfall sensing but produce path-integrated measurements that make accurate ground-level reconstruction challenging. Existing methods typically oversimplify CMLs as point…
We propose a novel framework for joint magnetic resonance image reconstruction and uncertainty quantification using under-sampled k-space measurements. The problem is formulated as a Bayesian linear inverse problem, where prior…
Inverse problems governed by partial differential equations (PDEs) play a crucial role in various fields, including computational science, image processing, and engineering. Particularly, Darcy flow equation is a fundamental equation in…
Inverse problems lend themselves naturally to a Bayesian formulation, in which the quantity of interest is a posterior distribution of state and/or parameters given some uncertain observations. For the common case in which the forward…
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…
Geophysical methods offer several key advantages over conventional subsurface measurement approaches, yet their use for hydrologic interpretation is often problematic. Here, we introduce theory and concepts of a novel Bayesian approach for…
Bayesian inference in the physical sciences faces a fundamental challenge: the imperative for high-fidelity physical modeling often clashes with the intrinsic limitations of stochastic sampling algorithms. Complex, high-dimensional…