Related papers: Space-time multilevel quadrature methods and their…
In this article, we present a review of the recent developments on the topic of Multilevel Monte Carlo (MLMC) algorithm, in the paradigm of applications in financial engineering. We specifically focus on the recent studies conducted in two…
Automatic segmentation of the heart cavity is an essential task for the diagnosis of cardiac diseases. In this paper, we propose a semi-supervised segmentation setup for leveraging unlabeled data to segment Left-ventricle, Right-ventricle,…
Motivation: CMR is the golden standard for cardiac diagnosis, and medical data annotation is time-consuming. Thus, screening techniques from unlabeled data can help streamline the cardiac diagnosis process. Goal: This work aims to enable…
We develop new multilevel Monte Carlo (MLMC) methods to estimate the expectation of the smallest eigenvalue of a stochastic convection-diffusion operator with random coefficients. The MLMC method is based on a sequence of finite element…
We propose a multilevel Markov chain Monte Carlo (MCMC) method for the Bayesian inference of random field parameters in PDEs using high-resolution data. Compared to existing multilevel MCMC methods, we additionally consider level-dependent…
Arrhythmias are potentially fatal disruptions to the normal heart rhythm, but their underlying dynamics is still poorly understood. Theoretical modeling is an important tool to fill this gap. Typical studies often employ detailed…
We consider the application of multilevel Monte Carlo methods to elliptic PDEs with random coefficients. We focus on models of the random coefficient that lack uniform ellipticity and boundedness with respect to the random parameter, and…
We present a novel variant of the multi-level Monte Carlo method that effectively utilizes a reserved computational budget on a high-performance computing system to minimize the mean squared error. Our approach combines concepts of the…
Accurate segmentation of cardiac structures can assist doctors to diagnose diseases, and to improve treatment planning, which is highly demanded in the clinical practice. However, the shortage of annotation and the variance of the data…
We describe and analyze some Monte Carlo methods for manifolds in Euclidean space defined by equality and inequality constraints. First, we give an MCMC sampler for probability distributions defined by un-normalized densities on such…
We study signal processing tasks in which the signal is mapped via some generalized time-frequency transform to a higher dimensional time-frequency space, processed there, and synthesized to an output signal. We show how to approximate such…
We consider the application of multilevel Monte Carlo methods to steady state Darcy flow in a random porous medium, described mathematically by elliptic partial differential equations with random coefficients. The levels in the multilevel…
We study the coherence in time and space of electromagnetic fields propagated through complex media. Whether for localization, imaging or telecommunication, the development of dedicated numerical techniques is generally based on the…
Quasi-Monte Carlo (QMC) methods are applied to multi-level Finite Element (FE) discretizations of elliptic partial differential equations (PDEs) with a random coefficient, to estimate expected values of linear functionals of the solution.…
While multilevel Monte Carlo (MLMC) methods for the numerical approximation of partial differential equations with random coefficients enjoy great popularity, combinations with spatial adaptivity seem to be rare. We present an adaptive MLMC…
This work addresses the inverse problem of electrocardiography from a new perspective, by combining electrical and mechanical measurements. Our strategy relies on the defini-tion of a model of the electromechanical contraction which is…
In this article, we study the application of Multi-Level Monte Carlo (MLMC) approaches to numerical random homogenization. Our objective is to compute the expectation of some functionals of the homogenized coefficients, or of the…
We present a massively parallel quantum Monte Carlo based implementation of real-space dynamical mean-field theory for general inhomogeneous correlated fermionic lattice systems. As a first application, we study magnetic order in a binary…
A high-fidelity kinetic Monte Carlo (KMC) simulation method (T. Treeratanaphitak, M. Pritzker, N. M. Abukhdeir, Electrochim. Acta 121 (2014) 407--414) using the semi-empirical multi-body embedded-atom method (EAM) potential has been…
We propose a new Markov Chain Monte Carlo (MCMC) method for constrained target distributions. Our method first maps the $D$-dimensional constrained domain of parameters to the unit ball ${\bf B}_0^D(1)$. Then, it augments the resulting…