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We use the diffusion quantum Monte Carlo (DMC) method to calculate the ground state phase diagram of solid molecular hydrogen and examine the stability of the most important insulating phases relative to metallic crystalline molecular…
We analyze the accuracy and sample complexity of variational Monte Carlo approaches to simulate the dynamics of many-body quantum systems classically. By systematically studying the relevant stochastic estimators, we are able to: (i) prove…
Fermionic cold atoms in optical traps provide viable quantum simulators of correlation effects in electronic systems. For dressed Rydberg atoms in two-dimensional traps with out-of-plane dipole moments, a realistic model of the pairwise…
We present a study of spin-unpolarized and spin-polarized two-dimensional uniform electron liquids using variational and diffusion quantum Monte Carlo (VMC and DMC) methods with Slater-Jastrow-backflow trial wave functions. Ground-state VMC…
This article considers the sequential Monte Carlo (SMC) approximation of ratios of normalizing constants associated to posterior distributions which in principle rely on continuum models. Therefore, the Monte Carlo estimation error and the…
The Direct Simulation Monte Carlo (DSMC) method, developed originally to calculate rarefied gas dynamical problems, is applied to continuous flow including shocks assuming that the Knudsen number is sufficiently small. In particular, we…
Monte Carlo simulations of diffusion processes often introduce bias in the final result, due to time discretization. Using an auxiliary Poisson process, it is possible to run simulations which are unbiased. In this article, we propose such…
The Direct Simulation Monte Carlo (DSMC) method is the gold standard for non-equilibrium rarefied gas dynamics, yet its computational cost can be prohibitive, especially for near-continuum regimes and high-fidelity \emph{ab initio}…
Convection-diffusion equations arise in a variety of applications such as particle transport, electromagnetics, and magnetohydrodynamics. Simulation of the convection-dominated regime for these problems, even with high-fidelity techniques,…
Determinant Quantum Monte Carlo (DQMC) provides numerically exact solutions for strongly correlated fermionic systems but faces significant computational challenges with increasing system size. While submatrix updates were originally…
This paper develops an efficient Monte Carlo interior penalty discontinuous Galerkin method for electromagnetic wave propagation in random media. This method is based on a multi-modes expansion of the solution to the time-harmonic random…
Due to their diverse nature, the faithful description of excited states within electronic structure theory methods remains one of the grand challenges of modern theoretical chemistry. Quantum Monte Carlo (QMC) methods have been applied very…
The recently developed auxiliary field diffusion Monte Carlo method is applied to compute the equation of state and the compressibility of neutron matter. By combining diffusion Monte Carlo for the spatial degrees of freedom and auxiliary…
Neutrino Direct Simulation Monte Carlo ($\nu$DSMC) is a Monte Carlo method for solving the neutrino Boltzmann equation in the early Universe, designed to track the evolution of cosmic neutrinos across a wide range of cosmological scenarios.…
Variational Monte Carlo (VMC) is a powerful and fast-growing method for optimizing and evolving parameterized many-body wave functions, especially with modern neural-network quantum states. In practice, however, the stochastic estimators…
The ab initio thermodynamic simulation of correlated Fermi systems is of central importance for many applications, such as warm dense matter, electrons in quantum dots, and ultracold atoms. Unfortunately, path integral Monte Carlo (PIMC)…
This work aims at understanding of bold diagrammatic Monte Carlo (BDMC) methods for stochastic summation of Feynman diagrams from the angle of stochastic iterative methods. The convergence enhancement trick of the BDMC is investigated from…
The present study addresses the challenge of enhancing computational efficiency without compromising accuracy in numerical simulations of vacuum gas dynamics using the direct simulation Monte Carlo (DSMC) method. A technique termed "fixed…
We investigate the inclusion of variable spins in electronic structure quantum Monte Carlo, with a focus on diffusion Monte Carlo with Hamiltonians that include spin-orbit interactions. Following our previous introduction of fixed-phase…
We propose that a combination of the semiclassical approximation with Monte Carlo simulations can be an efficient and reliable impurity solver for dynamical mean field theory equations and their cluster extensions with large cluster sizes.…