Related papers: Quasi-Monte Carlo Radiative Transfer
Many machine learning problems optimize an objective that must be measured with noise. The primary method is a first order stochastic gradient descent using one or more Monte Carlo (MC) samples at each step. There are settings where…
Quasi-Monte Carlo methods are a way of improving the efficiency of Monte Carlo methods. Digital nets and sequences are one of the low discrepancy point sets used in quasi-Monte Carlo methods. This thesis presents the three new results…
The order of convergence of the Monte Carlo method is 1/2 which means that we need quadruple samples to decrease the error in half in the numerical simulation. Multilevel Monte Carlo methods reach the same order of error by spending less…
We combine a Monte Carlo radiative transfer code with an SPH code, so that -- assuming thermal equilibrium -- we can calculate dust-temperature fields, spectral energy distributions, and isophotal maps, for the individual time-frames…
This study presents a comparative analysis of Monte Carlo (MC) and quasi-Monte Carlo (QMC) methods in the context of derivative pricing, emphasizing convergence rates and the curse of dimensionality. After a concise overview of traditional…
We propose an efficient method for Monte Carlo simulation of quantum lattice models. Unlike most other quantum Monte Carlo methods, a single run of the proposed method yields the free energy and the entropy with high precision for the whole…
The Multilevel Monte Carlo method is an efficient variance reduction technique. It uses a sequence of coarse approximations to reduce the computational cost in uncertainty quantification applications. The method is nowadays often considered…
This paper introduces a class of Monte Carlo algorithms which are based upon the simulation of a Markov process whose quasi-stationary distribution coincides with a distribution of interest. This differs fundamentally from, say, current…
This article provides a high-level overview of some recent works on the application of quasi-Monte Carlo (QMC) methods to PDEs with random coefficients. It is based on an in-depth survey of a similar title by the same authors, with an…
In many financial applications Quasi Monte Carlo (QMC) based on Sobol low-discrepancy sequences (LDS) outperforms Monte Carlo showing faster and more stable convergence. However, unlike MC QMC lacks a practical error estimate. Randomized…
We study numerical integration over bounded regions in $\mathbb{R}^s, s\ge1$ with respect to some probability measure. We replace random sampling with quasi-Monte Carlo methods, where the underlying point set is derived from deterministic…
Quasi-Monte Carlo (QMC) methods for estimating integrals are attractive since the resulting estimators typically converge at a faster rate than pseudo-random Monte Carlo. However, they can be difficult to set up on arbitrary posterior…
The Iterative Quasi-Monte Carlo (iQMC) method is a recently developed hybrid method for neutron transport simulations. iQMC replaces standard quadrature techniques used in deterministic linear solvers with Quasi-Monte Carlo simulation for…
Direct sampling of multi-dimensional systems with quantum Monte Carlo methods allows exact account of many-body effects or particle correlations. The most straightforward approach to solve the Schr\"odinger equation, Diffusion Monte Carlo,…
Solving partial differential equations in high dimensions by deep neural network has brought significant attentions in recent years. In many scenarios, the loss function is defined as an integral over a high-dimensional domain. Monte-Carlo…
We propose and analyze a quasi-Monte Carlo (QMC) algorithm for efficient simulation of wave propagation modeled by the Helmholtz equation in a bounded region in which the refractive index is random and spatially heterogenous. Our focus is…
Radiative processes such as synchrotron radiation and Compton scattering play an important role in astrophysics. Radiative processes are fundamentally stochastic in nature, and the best tools currently used for resolving these processes…
We consider the problem of simulating loss probabilities and conditional excesses for linear asset portfolios under the t-copula model. Although in the literature on market risk management there are papers proposing efficient variance…
Quantitative photoacoustic tomography aims at estimating optical parameters from photoacoustic images that are formed utilizing the photoacoustic effect caused by the absorption of an externally introduced light pulse. This optical…
Several models for the Monte Carlo simulation of Compton scattering on electrons are quantitatively evaluated with respect to a large collection of experimental data retrieved from the literature. Some of these models are currently…