Related papers: Jittering Samples using a kd-Tree Stratification
It has been known for a long time that stratification is one possible strategy to obtain higher convergence rates for the Monte Carlo estimation of integrals over the hyper-cube $[0, 1]^s$ of dimension $s$. However, stratified estimators…
We propose to use deep neural networks for generating samples in Monte Carlo integration. Our work is based on non-linear independent components estimation (NICE), which we extend in numerous ways to improve performance and enable its…
Many problems in materials science and biology involve particles interacting with strong, short-ranged bonds, that can break and form on experimental timescales. Treating such bonds as constraints can significantly speed up sampling their…
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…
In the context of Monte Carlo sampling for lattice models, the complexity of the energy landscape often leads to Markov chains being trapped in local optima, thereby increasing the correlation between samples and reducing sampling…
The efficient evaluation of high-dimensional integrals is of importance in both theoretical and practical fields of science, such as data science, statistical physics, and machine learning. However, exact computation methods suffer from the…
While generally considered computationally expensive, Uncertainty Quantification using Monte Carlo sampling remains beneficial for applications with uncertainties of high dimension. As an extension of the naive Monte Carlo method, the…
A novel hybrid Monte Carlo transport scheme is demonstrated in a scene with solar illumination, scattering and absorbing 2D atmosphere, a textured reflecting mountain, and a small detector located in the sky (mounted on a satellite or a…
Quantum Monte Carlo methods are powerful tools for studying quantum many-body systems but face difficulties in accessing excited states and in treating sign problems. We present a continuous-time path-integral Monte Carlo method for…
Monte Carlo methods represent the "de facto" standard for approximating complicated integrals involving multidimensional target distributions. In order to generate random realizations from the target distribution, Monte Carlo techniques use…
Science and engineering problems subject to uncertainty are frequently both computationally expensive and feature nonsmooth parameter dependence, making standard Monte Carlo too slow, and excluding efficient use of accelerated uncertainty…
Adjoint methods form a class of importance sampling methods that are used to accelerate Monte Carlo (MC) simulations of transport equations. Ideally, adjoint methods allow for zero-variance MC estimators provided that the solution to an…
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 present a hybrid method for time-dependent particle transport that combines Monte Carlo (MC) estimation with a deterministic discrete ordinates (\(S_N\)) solve, augmented by quasi-Monte Carlo (QMC) sampling. For spatial discretizations,…
Monte Carlo (MC) simulations are extensively used for various purposes in modern high-energy physics (HEP) experiments. Precision measurements of established Standard Model processes or searches for new physics often require the collection…
In image processing, solving inverse problems is the task of finding plausible reconstructions of an image that was corrupted by some (usually known) degradation operator. Commonly, this process is done using a generative image model that…
This paper concerns the approximation of smooth, high-dimensional functions from limited samples using polynomials. This task lies at the heart of many applications in computational science and engineering - notably, some of those arising…
This paper investigates the use of stratified sampling as a variance reduction technique for approximating integrals over large dimensional spaces. The accuracy of this method critically depends on the choice of the space partition, the…
In this paper, we aim to compute numerical approximation integral by using an adaptive Monte Carlo algorithm. We propose a stratified sampling algorithm based on an iterative method which splits the strata following some quantities called…
Jittered Sampling is a refinement of the classical Monte Carlo sampling method. Instead of picking $n$ points randomly from $[0,1]^2$, one partitions the unit square into $n$ regions of equal measure and then chooses a point randomly from…