Related papers: The Factorization Method for Monte Carlo Simulatio…
Computing systems interacting with real-world processes must safely and reliably process uncertain data. The Monte Carlo method is a popular approach for computing with such uncertain values. This article introduces a framework for…
Contemporary scientific studies often rely on the understanding of complex quantum systems via computer simulation. This paper initiates the statistical study of quantum simulation and proposes a Monte Carlo method for estimating…
We introduce the Quantization Monte Carlo method to solve thermal radiative transport equations with possibly several collision regimes, ranging from few collisions to massive number of collisions per time unit. For each particle in a given…
The recently-introduced self-learning Monte Carlo method is a general-purpose numerical method that speeds up Monte Carlo simulations by training an effective model to propose uncorrelated configurations in the Markov chain. We implement…
We consider the problem of estimating the probability of a large loss from a financial portfolio, where the future loss is expressed as a conditional expectation. Since the conditional expectation is intractable in most cases, one may…
We present novel Monte Carlo methods for treating the interacting shell model that allow exact calculations much larger than those heretofore possible. The two-body interaction is linearized by an auxiliary field; Monte Carlo evaluation of…
The basic idea of fast Monte Carlo (MC) simulations is to perform particle-based MC simulations with the excluded-volume interactions modeled by "soft" repulsive potentials that allow particle overlapping. This gives much faster system…
Various kinetic Monte Carlo algorithms become inefficient when some of the population sizes in a system are large, which gives rise to a large number of reaction events per unit time. Here, we present a new acceleration algorithm based on…
Biological tissues are complex structures composed of many elements which make light-based tissue diagnostics challenging. Over the past decades, Monte Carlo technique has been used as a fundamental and versatile approach toward modeling…
I show how to construct Monte Carlo algorithms (programs), prove that they are correct and document them. Complicated algorithms are build using a handful of elementary methods. This construction process is transparently illustrated using…
Monte Carlo methods play an important role in scientific computation, especially when problems have a vast phase space. In this lecture an introduction to the Monte Carlo method is given. Concepts such as Markov chains, detailed balance,…
In this paper, we demonstrate the simulation of fundamental solution for the parabolic equation by the relationship with Ito diffusion. The factorization and Monte Carlo methods of the fundamental solution are considered. With the fact that…
In this review we discuss, from a unified point of view, a variety of Monte Carlo methods used to solve eigenvalue problems in statistical mechanics and quantum mechanics. Although the applications of these methods differ widely, the…
In this paper, we propose a general analysis framework for inexact power iteration, which can be used to efficiently solve high dimensional eigenvalue problems arising from quantum many-body problems. Under the proposed framework, we…
We present an algorithmic framework for a variant of the quantum Monte Carlo operator-loop algorithm, where non-local cluster updates are constructed in a way that makes each individual loop smaller. The algorithm is designed to increase…
We propose a new method for simulating QCD at finite density, where interesting phases such as the color superconductivity phase is conjectured to appear. The method is based on a general factorization property of distribution functions of…
Using a common technique for approximating distributions [generalized functions], we are able to use standard Monte Carlo methods to compute QFT quantities in Minkowski spacetime, under phase transitions, or when dealing with coalescing…
Population annealing Monte Carlo is an efficient sequential algorithm for simulating k-local Boolean Hamiltonians. Because of its structure, the algorithm is inherently parallel and therefore well suited for large-scale simulations of…
To minimise systematic errors in Monte Carlo simulations of charged particles, long range electrostatic interactions have to be calculated accurately and efficiently. Standard approaches, such as Ewald summation or the naive application of…
Real-world distributed systems and networks are often unreliable and subject to random failures of its components. Such a stochastic behavior affects adversely the complexity of optimization tasks performed routinely upon such systems, in…