Related papers: Jittering Samples using a kd-Tree Stratification
We propose in this work a Monte Carlo method for three dimensional scalar radiative transfer equations with non-integrable, space-dependent scattering kernels. Such kernels typically account for long-range statistical features, and arise…
We describe an efficient Monte Carlo algorithm for a restricted class of scattering problems in radiation transfer. This class includes many astrophysically interesting problems, including the scattering of ultraviolet and visible light by…
We design and implement a novel algorithm for computing a multilevel Monte Carlo (MLMC) estimator of the cumulative distribution function of a quantity of interest in problems with random input parameters or initial conditions. Our approach…
We present in this paper a hybrid, Multi-Level Monte Carlo (MLMC) method for solving the neutral particle transport equation. MLMC methods, originally developed to solve parametric integration problems, work by using a cheap, low fidelity…
Quasi-Monte Carlo (QMC) is a powerful method for evaluating high-dimensional integrals. However, its use is typically limited to distributions where direct sampling is straightforward, such as the uniform distribution on the unit hypercube…
We present a Monte Carlo rendering framework for the physically-accurate simulation of speckle patterns arising from volumetric scattering of coherent waves. These noise-like patterns are characterized by strong statistical properties, such…
This project investigates the applicability of quasi-Monte Carlo methods to Euclidean lattice systems in order to improve the asymptotic error scaling of observables for such theories. The error of an observable calculated by averaging over…
Slice sampling is a well-established Markov chain Monte Carlo method for (approximate) sampling of target distributions which are only known up to a normalizing constant. The method is based on choosing a new state on a slice, i.e., a…
This paper considers the problem of sampling from non-logconcave distribution, based on queries of its unnormalized density. It first describes a framework, Denoising Diffusion Monte Carlo (DDMC), based on the simulation of a denoising…
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…
High-dimensional distributions, especially those with heavy tails, are notoriously difficult for off-the-shelf MCMC samplers: the combination of unbounded state spaces, diminishing gradient information, and local moves results in…
Flat-histogram Monte Carlo simulations are well-established, robust methods to perform random walks in a physical observable or parameter space, making them suitable for finding ground states or studying phase transitions in complex systems…
Markov chain Monte Carlo is a class of algorithms for drawing Markovian samples from high-dimensional target densities to approximate the numerical integration associated with computing statistical expectation, especially in Bayesian…
We propose a Monte Carlo sampler from the reverse diffusion process. Unlike the practice of diffusion models, where the intermediary updates -- the score functions -- are learned with a neural network, we transform the score matching…
Dynamic Programming (DP) suffers from the well-known ``curse of dimensionality'', further exacerbated by the need to compute expectations over process noise in stochastic models. This paper presents a Monte Carlo-based sampling approach for…
The self-learning Metropolis-Hastings algorithm is a powerful Monte Carlo method that, with the help of machine learning, adaptively generates an easy-to-sample probability distribution for approximating a given hard-to-sample distribution.…
Monte Carlo sampling of any system may be analyzed in terms of an associated glass model -- a variant of the Random Energy Model -- with, whenever there is a sign problem, complex fields. This model has three types of phases (liquid, frozen…
Efficient sampling of many-dimensional and multimodal density functions is a task of great interest in many research fields. We describe an algorithm that allows parallelizing inherently serial Markov chain Monte Carlo (MCMC) sampling by…
An efficient method for the simulation of strained heteroepitaxial growth with intermixing using kinetic Monte Carlo is presented. The model used is based on a solid-on-solid bond counting formulation in which elastic effects are…
Precision theoretical predictions for high multiplicity scattering rely on the evaluation of increasingly complicated scattering amplitudes which come with an extremely high CPU cost. For state-of-the-art processes this can cause technical…