Related papers: Multilevel simulation of hard-sphere mixtures
As the size of engineered systems grows, problems in reliability theory can become computationally challenging, often due to the combinatorial growth in the cut sets. In this paper we demonstrate how Multilevel Monte Carlo (MLMC) - a…
We present a reduced-dimension, ballistic deposition, Monte Carlo particle packing algorithm and discuss its application to the analysis of the microstructure of hard-sphere systems with broad particle size distributions. We extend our…
Heterogeneous multiscale methods (HMM) combine molecular accuracy of particle-based simulations with the computational efficiency of continuum descriptions to model flow in soft matter liquids. In these schemes, molecular simulations…
A simple reweighting scheme is proposed for Monte Carlo simulations of interacting particle systems, permitting one to study various parameter values in a single study, and improving efficiency by an order of magnitude. Unlike earlier…
Multifidelity Monte Carlo methods often rely on a preprocessing phase consisting of standard Monte Carlo sampling to estimate correlation coefficients between models of different fidelity to determine the weights and number of samples for…
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…
Complex soft matter systems can be efficiently studied with the help of adaptive resolution simulation methods, concurrently employing two levels of resolution in different regions of the simulation domain. The non-matching properties of…
A continuous-time path integral Quantum Monte Carlo method using the directed-loop algorithm is developed to simulate the Anderson single-impurity model in the occupation number basis. Although the method suffers from a sign problem at low…
Discrete-state, continuous-time Markov models are becoming commonplace in the modelling of biochemical processes. The mathematical formulations that such models lead to are opaque, and, due to their complexity, are often considered…
Solving different types of optimization models (including parameters fitting) for support vector machines on large-scale training data is often an expensive computational task. This paper proposes a multilevel algorithmic framework that…
We demonstrate a scaling method for non-Markovian Monte Carlo wave-function simulations used to study open quantum systems weakly coupled to their environments. We derive a scaling equation, from which the result for the expectation values…
Many problems require to approximate an expected value by some kind of Monte Carlo (MC) sampling, e.g. molecular dynamics (MD) or simulation of stochastic reaction models (also termed kinetic Monte Carlo (kMC)). Often, we are furthermore…
This manuscript presents a framework for using multilevel quadrature formulae to compute the solution of optimal control problems constrained by random partial differential equations. Our approach consists in solving a sequence of optimal…
Multilevel techniques are efficient approaches for solving the large linear systems that arise from discretized partial differential equations and other problems. While geometric multigrid requires detailed knowledge about the underlying…
This work presents an efficient approach for accelerating multilevel Markov Chain Monte Carlo (MCMC) sampling for large-scale problems using low-fidelity machine learning models. While conventional techniques for large-scale Bayesian…
The order of convergence of the Monte Carlo method is 1/2 which means that we need quadruple samples to decrease the error in half in the numerical simulation. Multilevel Monte Carlo methods reach the same order of error by spending less…
A simulation technique is described for quantifying the contribution of three-body interactions to the thermodynamical properties of coarse-grained representations of complex fluids. The method is based on comparing the third virial…
Multilevel sampling methods, such as multilevel and multifidelity Monte Carlo, multilevel stochastic collocation, or delayed acceptance Markov chain Monte Carlo, have become standard uncertainty quantification (UQ) tools for a wide class of…
We describe a Monte Carlo scheme for the grand canonical simulation study of fluid phase equilibria in highly size-asymmetrical binary mixtures. The method utilizes an expanded ensemble in which the insertion and deletion of large particles…
The advances in materials and biological sciences have necessitated the use of molecular simulations to study polymers. The Markov chain Monte Carlo simulations enable the sampling of relevant microstates of polymeric systems by traversing…