Related papers: Implementing Quasi-Monte Carlo Simulations with Li…
Elastic systems that are spatially heterogeneous in their mechanical response pose special challenges for molecular simulations. Standard methods for sampling thermal fluctuations of a system's size and shape proceed through a series of…
Sensitivity analysis (SA) is a procedure for studying how sensitive are the output results of large-scale mathematical models to some uncertainties of the input data. The models are described as a system of partial differential equations.…
We introduce methodologies for highly scalable quantum Monte Carlo simulations of electron-phonon models, and report benchmark results for the Holstein model on the square lattice. The determinant quantum Monte Carlo (DQMC) method is a…
Nonlinear systems of polynomial equations arise naturally in many applied settings, for example loglinear models on contingency tables and Gaussian graphical models. The solution sets to these systems over the reals are often positive…
Many machine learning problems optimize an objective that must be measured with noise. The primary method is a first order stochastic gradient descent using one or more Monte Carlo (MC) samples at each step. There are settings where…
The multilevel Monte Carlo (MLMC) method for continuous-time Markov chains, first introduced by Anderson and Higham (SIAM Multiscal Model. Simul. 10(1), 2012), is a highly efficient simulation technique that can be used to estimate various…
Monte Carlo sampling is a powerful toolbox of algorithmic techniques widely used for a number of applications wherein some noisy quantity, or summary statistic thereof, is sought to be estimated. In this paper, we survey the literature for…
We introduce a significant improvement for a relatively new machine learning method called Transformation-Based Learning. By applying a Monte Carlo strategy to randomly sample from the space of rules, rather than exhaustively analyzing all…
We apply multilevel Monte Carlo for option pricing problems using exponential L\'{e}vy models with a uniform timestep discretisation to monitor the running maximum required for lookback and barrier options. The numerical results demonstrate…
We propose a quantum Monte Carlo (QMC) algorithm for non-equilibrium dynamics in a system with a parameter varying as a function of time. The method is based on successive applications of an evolving Hamiltonian to an initial state and…
Quasi-Monte Carlo (qMC) methods are a powerful alternative to classical Monte-Carlo (MC) integration. Under certain conditions, they can approximate the desired integral at a faster rate than the usual Central Limit Theorem, resulting in…
Classical algorithms in numerical analysis for numerical integration (quadrature/cubature) follow the principle of approximate and integrate: the integrand is approximated by a simple function (e.g. a polynomial), which is then integrated…
When approximating the expectations of a functional of a solution to a stochastic differential equation, the numerical performance of deterministic quadrature methods, such as sparse grid quadrature and quasi-Monte Carlo (QMC) methods, may…
We study quasi-Monte Carlo (QMC) integration over the multi-dimensional unit cube in several weighted function spaces with different smoothness classes. We consider approximating the integral of a function by the median of several integral…
We investigate in this paper an alternative method to simulation based recursive importance sampling procedure to estimate the optimal change of measure for Monte Carlo simulations. We propose an algorithm which combines (vector and…
We have developed an efficient Monte Carlo algorithm, which accelerates slow Monte Carlo dynamics in quasi-one-dimensional Ising spin systems. The loop algorithm of the quantum Monte Carlo method is applied to the classical spin models with…
We introduce a novel Multi-Order Monte Carlo approach for uncertainty quantification in the context of multiscale time-dependent partial differential equations. The new framework leverages Implicit-Explicit Runge-Kutta time integrators to…
The principle and the efficiency of the Monte Carlo transfer-matrix algorithm are discussed. Enhancements of this algorithm are illustrated by applications to several phase transitions in lattice spin models. We demonstrate how the…
Sequential Monte Carlo samplers represent a compelling approach to posterior inference in Bayesian models, due to being parallelisable and providing an unbiased estimate of the posterior normalising constant. In this work, we significantly…
The classical approaches to numerically integrating a function $f$ are Monte Carlo (MC) and quasi-Monte Carlo (QMC) methods. MC methods use random samples to evaluate $f$ and have error $O(\sigma(f)/\sqrt{n})$, where $\sigma(f)$ is the…