Related papers: Diffusion Monte Carlo using domains in configurati…
Here, a dichotomy of particles and waves is employed in a quantum Monte Carlo calculation of interacting electrons. Through the creation and propagation of concurrent stochastic ensembles of walkers in physical space and in Hilbert space…
One of the most demanding calculations is to generate random samples from a specified probability distribution (usually with an unknown normalizing prefactor) in a high-dimensional configuration space. One often has to resort to using a…
The computational cost of a Monte Carlo algorithm can only be meaningfully discussed when taking into account the magnitude of the resulting statistical error. Aiming for a fixed error per particle, we study the scaling behavior of the…
We study one-dimensional (1D) and two-dimensional (2D) Helium atoms using a new time-dependent quantum Monte Carlo (TDQMC) method. The TDQMC method employs random walkers, with a separate guiding wave attached to each walker. The ground…
The size of the population of random walkers required to obtain converged estimates in DMC increases dramatically with system size. We illustrate this by comparing ground state energies of small clusters of parahydrogen (up to 48 molecules)…
Quantum Monte Carlo (QMC) methods represent a powerful family of computational techniques for tackling complex quantum many-body problems and performing calculations of stationary state properties. QMC is among the most accurate and…
Using quantum Monte Carlo (QMC) simulations we study the ground-state properties of the one-dimensional fermionic Hubbard model in traps with an underlying lattice. Since due to the confining potential the density is space dependent,…
The Hamiltonian Monte Carlo (HMC) algorithm is a powerful Markov Chain Monte Carlo (MCMC) method that uses Hamiltonian dynamics to generate samples from a target distribution. To fully exploit its potential, we must understand how…
This paper studies a non-random-walk Markov Chain Monte Carlo method, namely the Hamiltonian Monte Carlo (HMC) method in the context of Subset Simulation used for structural reliability analysis. The HMC method relies on a deterministic…
We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…
Hamiltonian Monte Carlo has emerged as a standard tool for posterior computation. In this article, we present an extension that can efficiently explore target distributions with discontinuous densities. Our extension in particular enables…
Representations based on random walks can exploit discrete data distributions for clustering and classification. We extend such representations from discrete to continuous distributions. Transition probabilities are now calculated using a…
The one-dimensional random trap model with a power-law distribution of mean sojourn times exhibits a phenomenon of dynamical localization in the case where diffusion is anomalous: The probability to find two independent walkers at the same…
The iterated conditional sequential Monte Carlo (i-CSMC) algorithm from Andrieu, Doucet and Holenstein (2010) is an MCMC approach for efficiently sampling from the joint posterior distribution of the $T$ latent states in challenging…
Diagrammatic Monte Carlo (DiagMC) is a numeric technique that allows one to calculate quantities specified in terms of diagrammatic expansions, the latter being a standard tool of many-body quantum statistics. The sign problem that is…
Hamiltonian Monte Carlo (HMC) is a Markov chain algorithm for sampling from a high-dimensional distribution with density $e^{-f(x)}$, given access to the gradient of $f$. A particular case of interest is that of a $d$-dimensional Gaussian…
A Monte Carlo method based on a density-of-states sampling is proposed for study of arbitrary statistical mechanical ensembles in a continuum. A random walk in the two-dimensional space of particle number and energy is used to estimate the…
Markov chain Monte Carlo samplers based on discretizations of (overdamped) Langevin dynamics are commonly used in the Bayesian inference and computational statistical physics literature to estimate high-dimensional integrals. One can…
Colloids have a striking relevance in a wide spectrum of industrial formulations, spanning from personal care products to protective paints. Their behaviour can be easily influenced by extremely weak forces, which disturb their…
We propose a modification, based on the RESTART (repetitive simulation trials after reaching thresholds) and DPR (dynamics probability redistribution) rare event simulation algorithms, of the standard diffusion Monte Carlo (DMC) algorithm.…