Related papers: Multilevel Monte Carlo for quantum mechanics on a …
A grand canonical Monte Carlo (MC) algorithm is presented for studying the lattice gas model (LGM) of multiple protein sequence alignment, which coherently combines long-range interactions and variable-length insertions. MC simulations are…
The Hamiltonian Monte Carlo (HMC) sampling algorithm exploits Hamiltonian dynamics to construct efficient Markov Chain Monte Carlo (MCMC), which has become increasingly popular in machine learning and statistics. Since HMC uses the gradient…
In many real-world engineering systems, the performance or reliability of the system is characterised by a scalar parameter. The distribution of this performance parameter is important in many uncertainty quantification problems, ranging…
Sampling from complicated probability distributions is a hard computational problem arising in many fields, including statistical physics, optimization, and machine learning. Quantum computers have recently been used to sample from…
We explain in detail how to estimate mean values and assess statistical errors for arbitrary functions of elementary observables in Monte Carlo simulations. The method is to estimate and sum the relevant autocorrelation functions, which is…
We introduce and discuss Monte Carlo methods in quantum field theories. Methods of independent Monte Carlo, such as random sampling and importance sampling, and methods of dependent Monte Carlo, such as Metropolis sampling and Hamiltonian…
In this paper we address the problem of the prohibitively large computational cost of existing Markov chain Monte Carlo methods for large--scale applications with high dimensional parameter spaces, e.g. in uncertainty quantification in…
Applications that require substantial computational resources today cannot avoid the use of heavily parallel machines. Embracing the opportunities of parallel computing and especially the possibilities provided by a new generation of…
Optimizing or sampling complex cost functions of combinatorial optimization problems is a longstanding challenge across disciplines and applications. When employing family of conventional algorithms based on Markov Chain Monte Carlo (MCMC)…
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 study the critical slowing down towards the continuum limit of lattice QCD simulations with Hybrid Monte Carlo type algorithms. In particular for the squared topological charge we find it to be very severe with an effective dynamical…
We develop a novel Monte Carlo algorithm for the vector consisting of the supremum, the time at which the supremum is attained and the position at a given (constant) time of an exponentially tempered L\'evy process. The algorithm, based on…
Inspired by the latest developments in multilevel Monte Carlo (MLMC) methods and randomised sketching for linear algebra problems we propose a MLMC estimator for real-time processing of matrix structured random data. Our algorithm is…
A recent reformulation [1] of the problem of Coulomb gases in the presence of a dynamical dielectric medium showed that finite temperature simulations of such systems can be accomplished on the basis of completely local Hamiltonians on a…
Markov chain Monte Carlo (MCMC) algorithms are ubiquitous in Bayesian computations. However, they need to access the full data set in order to evaluate the posterior density at every step of the algorithm. This results in a great…
In this paper we propose a new class of coupling methods for the sensitivity analysis of high dimensional stochastic systems and in particular for lattice Kinetic Monte Carlo. Sensitivity analysis for stochastic systems is typically based…
When solving stochastic partial differential equations (SPDEs) driven by additive spatial white noise, the efficient sampling of white noise realizations can be challenging. Here, we present a new sampling technique that can be used to…
Uncertainty quantification (UQ) is an active area of research, and an essential technique used in all fields of science and engineering. The most common methods for UQ are Monte Carlo and surrogate-modelling. The former method is…
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…
Restricted Boltzmann Machines are simple and powerful generative models that can encode any complex dataset. Despite all their advantages, in practice the trainings are often unstable and it is difficult to assess their quality because the…