Related papers: An efficient implementation algorithm for quasi-Mo…
We discuss hybrid Monte Carlo algorithms for odd-flavor lattice QCD simulations. The algorithms include a polynomial approximation which enables us to simulate odd-flavor QCD in the framework of the hybrid Monte Carlo algorithm. In order to…
We review the basic outline of the highly successful diffusion Monte Carlo technique commonly used in contexts ranging from electronic structure calculations to rare event simulation and data assimilation, and propose a new class of…
Reinforcement learning constantly deals with hard integrals, for example when computing expectations in policy evaluation and policy iteration. These integrals are rarely analytically solvable and typically estimated with the Monte Carlo…
The behavior of a Lattice Monte Carlo algorithm (if it is designed correctly) must approach that of the continuum system that it is designed to simulate as the time step and the mesh step tend to zero. However, we show for an algorithm for…
Ab initio quantum Monte Carlo (QMC) is a stochastic approach for solving the many-body Schr\"odinger equation without resorting to one-body approximations. QMC algorithms are readily parallelizable via ensembles of $N_w$ walkers, making…
Owing to their favorable scaling with dimensionality, Monte Carlo (MC) methods have become the tool of choice for numerical integration across the quantitative sciences. Almost invariably, efficient MC integration schemes are strictly…
Monte Carlo (MC) simulations are essential computational approaches with widespread use throughout all areas of science. We present a method for accelerating lattice MC simulations using fully connected and convolutional artificial neural…
The goal of this work is to lay the groundwork to construct and characterize a quantum device; which we refer to as a superfluid ring lattice; that could serve as a multi-qubit system in the future. Accordingly, a mathematical framework,…
Quasi-Monte Carlo (QMC) integration over unbounded domains $\mathbb{R}^s$ remains challenging due to the high dimensionality of sampling space and the boundary growth of the integrand. In applications such as uncertainty quantification…
A novel linear integration rule called $\textit{control neighbors}$ is proposed in which nearest neighbor estimates act as control variates to speed up the convergence rate of the Monte Carlo procedure on metric spaces. The main result is…
Low-discrepancy (LD) sequences have been extensively used as efficient experimental designs across many scientific disciplines. QMCPy (https://qmcsoftware.github.io/QMCSoftware/) is an accessible Python library which provides a unified…
Monte Carlo simulations of lattice quantum field theories on Lefschetz thimbles are non trivial. We discuss a new Monte Carlo algorithm based on the idea of computing contributions to the functional integral which come from complete flow…
Based on the scheme of variational Monte Carlo sampling, we develop an accurate and efficient two-dimensional tensor-network algorithm to simulate quantum lattice models. We find that Monte Carlo sampling shows huge advantages in dealing…
Inspired by the latest developments in multilevel Monte Carlo (MLMC) methods and randomised sketching for linear algebra problems we propose a MLMC estimator for real-time processing of matrix structured random data. Our algorithm is…
Many machine learning problems involve Monte Carlo gradient estimators. As a prominent example, we focus on Monte Carlo variational inference (MCVI) in this paper. The performance of MCVI crucially depends on the variance of its stochastic…
We combine a generic method for finding fast orthogonal transforms for a given quasi-Monte Carlo integration problem with the multilevel Monte Carlo method. It is shown by example that this combined method can vastly improve the efficiency…
Monte Carlo and Quasi-Monte Carlo methods present a convenient approach for approximating the expected value of a random variable. Algorithms exist to adaptively sample the random variable until a user defined absolute error tolerance is…
We discuss recent algorithmic improvements in simulating finite temperature QCD on a lattice. In particular, the Rational Hybrid Monte Carlo(RHMC) algorithm is employed to generate lattice configurations for 2+1 flavor QCD. Unlike the…
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…
Langevin Monte Carlo (LMC) and its stochastic gradient versions are powerful algorithms for sampling from complex high-dimensional distributions. To sample from a distribution with density $\pi(\theta)\propto \exp(-U(\theta)) $, LMC…