Related papers: Multilevel simulation of hard-sphere mixtures
In this work we propose a hierarchy of Monte Carlo methods for sampling equilibrium properties of stochastic lattice systems with competing short and long range interactions. Each Monte Carlo step is composed by two or more sub - steps…
We extend previously developed two-level coarsening procedures for graph Laplacian problems written in a mixed saddle point form to the fully recursive multilevel case. The resulting hierarchy of discretizations gives rise to a hierarchy of…
The simulation of the expectation of a stochastic quantity E[Y] by Monte Carlo methods is known to be computationally expensive especially if the stochastic quantity or its approximation Y_n is expensive to simulate, e.g., the solution of a…
Accurately and efficiently estimating system performance under uncertainty is paramount in power system planning and operation. Monte Carlo simulation is often used for this purpose, but convergence may be slow, especially when detailed…
Kinetic equations model the position-velocity distribution of particles subject to transport and collision effects. Under a diffusive scaling, these combined effects converge to a diffusion equation for the position density in the limit of…
The Multilevel Monte Carlo method is an efficient variance reduction technique. It uses a sequence of coarse approximations to reduce the computational cost in uncertainty quantification applications. The method is nowadays often considered…
We study multilevel techniques, commonly used in PDE multigrid literature, to solve structured optimization problems. For a given hierarchy of levels, we formulate a coarse model that approximates the problem at each level and provides a…
Multilevel Monte Carlo is a key tool for approximating integrals involving expensive scientific models. The idea is to use approximations of the integrand to construct an estimator with improved accuracy over classical Monte Carlo. We…
A two level sampling method is applied to variational Monte Carlo (VMC) that samples the one and two body parts of the wave function separately. The method is demonstrated on a single Li_2 molecule in free space and 32 H_2 molecules in a…
The microscopic calculation of nuclear level densities in the presence of correlations is a difficult many-body problem. The shell model Monte Carlo method provides a powerful technique to carry out such calculations using the framework of…
Monte Carlo simulations of quantum field theories on a lattice become increasingly expensive as the continuum limit is approached since the cost per independent sample grows with a high power of the inverse lattice spacing. Simulations on…
In this paper, we investigate the use of multilevel Monte Carlo (MLMC) methods for estimating the expectation of discretized random fields. Specifically, we consider a setting in which the input and output vectors of numerical simulators…
We discuss the application of multilevel Monte Carlo methods to elliptic partial differential equations with random coefficients. Such problems arise, for example, in uncertainty quantification in subsurface flow modeling. We give a brief…
We describe and analyze some Monte Carlo methods for manifolds in Euclidean space defined by equality and inequality constraints. First, we give an MCMC sampler for probability distributions defined by un-normalized densities on such…
While generally considered computationally expensive, Uncertainty Quantification using Monte Carlo sampling remains beneficial for applications with uncertainties of high dimension. As an extension of the naive Monte Carlo method, the…
We use a two-level simulation method to analyse the critical point associated with demixing of binary hard sphere mixtures. The method exploits an accurate coarse-grained model with two-body and three-body effective interactions. Using this…
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 Monte Carlo method is presented to evaluate quantum states with many particles moving in the continuum. The scattering state is generated at each time by a Monte Carlo random sampling algorithm. The same calculation are repeated until the…
New hybrid Molecular Dynamics-Monte Carlo methods are proposed to increase the efficiency of constant-pressure simulations. Two variations of the isobaric Molecular Dynamics component of the algorithms are considered. In the first, we use…
We have developed an algorithm coupling mesoscopic simulations on different levels in a hierarchy of Cartesian meshes. Based on the multiscale nature of the chemical reactions, some molecules in the system will live on a fine-grained mesh,…