Related papers: Multilevel Monte Carlo method for simulations of f…
Monte Carlo computer simulations are virtually the only way to analyze the thermodynamic behavior of a system in a precise way. However, the various existing methods exhibit extreme differences in their efficiency, depending on model…
Because of their robustness, efficiency and non-intrusiveness, Monte Carlo methods are probably the most popular approach in uncertainty quantification to computing expected values of quantities of interest (QoIs). Multilevel Monte Carlo…
The multi-level Monte Carlo method proposed by M. Giles (2008) approximates the expectation of some functionals applied to a stochastic process with optimal order of convergence for the mean-square error. In this paper, a modified…
A method is presented to tackle the sign problem in the simulations of systems having indefinite or complex-valued measures. In general, this new approach is shown to yield statistical errors smaller than the crude Monte Carlo using…
We consider systems of stochastic differential equations with multiple scales and small noise and assume that the coefficients of the equations are ergodic and stationary random fields. Our goal is to construct provably-efficient importance…
Monte Carlo simulations are widely employed to measure the physical properties of glass-forming liquids in thermal equilibrium. Combined with local Monte Carlo moves, the Metropolis algorithm can also be used to simulate the relaxation…
Monte Carlo is a simple and flexible tool that is widely used in computational finance. In this context, it is common for the quantity of interest to be the expected value of a random variable defined via a stochastic differential equation.…
Sequential Monte Carlo Samplers are a class of stochastic algorithms for Monte Carlo integral estimation w.r.t. probability distributions, which combine elements of Markov chain Monte Carlo methods and importance sampling/resampling…
We describe a Monte Carlo procedure which allows sampling of the disjoint configuration spaces associated with crystalline and fluid phases, within a single simulation. The method utilises biased sampling techniques to enhance the…
We propose and analyze a method for computing failure probabilities of systems modeled as numerical deterministic models (e.g., PDEs) with uncertain input data. A failure occurs when a functional of the solution to the model is below (or…
Continuous level Monte Carlo is an unbiased, continuous version of the celebrated multilevel Monte Carlo method. The approximation level is assumed to be continuous resulting in a stochastic process describing the quantity of interest.…
Since Giles introduced the multilevel Monte Carlo path simulation method [18], there has been rapid development of the technique for a variety of applications in computational finance. This paper surveys the progress so far, highlights the…
In order to find the equilibrium geometries of molecules and solids and to perform ab initio molecular dynamics, it is necessary to calculate the forces on the nuclei. We present a correlated sampling method to efficiently calculate…
We present a new quantum Monte Carlo algorithm suitable for generically complex problems, such as systems coupled to external magnetic fields or anyons in two spatial dimensions. We find that the choice of gauge plays a nontrivial role, and…
Monte Carlo simulations are widely used in many areas including particle accelerators. In this lecture, after a short introduction and reviewing of some statistical backgrounds, we will discuss methods such as direct inversion, rejection…
This topical review describes the methodology of continuum variational and diffusion quantum Monte Carlo calculations. These stochastic methods are based on many-body wave functions and are capable of achieving very high accuracy. The…
In this article, we study the application of Multi-Level Monte Carlo (MLMC) approaches to numerical random homogenization. Our objective is to compute the expectation of some functionals of the homogenized coefficients, or of the…
Monte Carlo experiments produce samples in order to estimate features of a given distribution. However, simultaneous estimation of means and quantiles has received little attention, despite being common practice. In this setting we…
We generalize the multilevel Monte Carlo (MLMC) method of Giles to the simulation of systems of particles that interact via a mean field. When the number of particles is large, these systems are described by a McKean-Vlasov process - a…
We propose a multilevel Monte Carlo method for a particle-based asymptotic-preserving scheme for kinetic equations. Kinetic equations model transport and collision of particles in a position-velocity phase-space. With a diffusive scaling,…