Related papers: Hamiltonian dynamics for stochastic reconstruction…
Hamiltonian Monte Carlo (HMC) is an efficient Bayesian sampling method that can make distant proposals in the parameter space by simulating a Hamiltonian dynamical system. Despite its popularity in machine learning and data science, HMC is…
In tomographic reconstruction, the goal is to reconstruct an unknown object from a collection of line integrals. Given a complete sampling of such line integrals for various angles and directions, explicit inverse formulas exist to…
Sample-based Bayesian inference provides a route to uncertainty quantification in the geosciences, and inverse problems in general, though is very computationally demanding in the naive form that requires simulating an accurate computer…
Tomographic imaging is in general an ill-posed inverse problem. Typically, a single regularized image estimate of the sought-after object is obtained from tomographic measurements. However, there may be multiple objects that are all…
In this paper we present a spatially-adaptive method for image reconstruction that is based on the concept of statistical multiresolution estimation as introduced in [Frick K, Marnitz P, and Munk A. "Statistical multiresolution Dantzig…
The stochastic differential and integral equations describing the system of particles weakly interacting among themselves which are absorbed and scattered by particles of a medium are considered. The time-dependent transport equation with…
Image restoration aims to recover high-quality images from degraded observations. When the degradation process is known, the recovery problem can be formulated as an inverse problem, and in a Bayesian context, the goal is to sample a clean…
Adaptive resolution schemes allow the simulation of a molecular fluid treating simultaneously different subregions of the system at different levels of resolution. In this work we present a new scheme formulated in terms of a global…
Hamiltonian Monte Carlo (HMC) has been progressively incorporated within the statistician's toolbox as an alternative sampling method in settings when standard Metropolis-Hastings is inefficient. HMC generates a Markov chain on an augmented…
This paper considers the non-linear inverse problem of reconstructing an electric conductivity distribution from the interior power density in a bounded domain. Applications include the novel tomographic method known as acousto-electric…
Diffusion models have recently attained significant interest within the community owing to their strong performance as generative models. Furthermore, its application to inverse problems have demonstrated state-of-the-art performance.…
We consider the Riemann manifold Hamiltonian Monte Carlo (RMHMC) method for solving statistical inverse problems governed by partial differential equations (PDEs). The power of the RMHMC method is that it exploits the geometric structure…
Indirect imaging problems in biomedical optics generally require repeated evaluation of forward models of radiative transport, for which Monte Carlo is accurate yet computationally costly. We develop a novel approach to reduce this…
Importance sampling (IS) is a powerful Monte Carlo (MC) methodology for approximating integrals, for instance in the context of Bayesian inference. In IS, the samples are simulated from the so-called proposal distribution, and the choice of…
We present an iterative framework to improve the amortized approximations of posterior distributions in the context of Bayesian inverse problems, which is inspired by loop-unrolled gradient descent methods and is theoretically grounded in…
Characterizing noisy quantum devices requires methods for learning the underlying quantum Hamiltonian which governs their dynamics. Often, such methods compare measurements to simulations of candidate Hamiltonians, a task which requires…
Markov Chain Monte Carlo inference of target posterior distributions in machine learning is predominately conducted via Hamiltonian Monte Carlo and its variants. This is due to Hamiltonian Monte Carlo based samplers ability to suppress…
Extracting compact, physically interpretable representations from high-dimensional scientific data is a persistent challenge due to the complex, nonlinear structures inherent in physical systems. We propose a Gaussian Mixture Variational…
The Hamiltonian Monte Carlo method generates samples by introducing a mechanical system that explores the target density. For distributions on manifolds it is not always simple to perform the mechanics as a result of the lack of global…
We introduce in this study an algorithm for the imaging of faults and of slip fields on those faults. The physics of this problem are modeled using the equations of linear elasticity. We define a regularized functional to be minimized for…