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Critical slowing down and topological freezing severely hinder Monte Carlo sampling of lattice field theories as the continuum limit is approached. Recently, significant progress has been made in applying a class of generative machine…
We present a formalism of the transition matrix Monte Carlo method. A stochastic matrix in the space of energy can be estimated from Monte Carlo simulation. This matrix is used to compute the density of states, as well as to construct…
We construct importance sampling schemes for stochastic differential equations with small noise and fast oscillating coefficients. Standard Monte Carlo methods perform poorly for these problems in the small noise limit. With multiscale…
Phase diagram and pattern formation in two-dimensional Ising model with coupling between order parameter and lattice vibrations is investigated by Monte-Carlo simulations. It is shown that if the coupling is strong enough (or phonons are…
Hybrid multiscale modelling has emerged as a useful framework for modelling complex biological phenomena. However, when accounting for stochasticity in the internal dynamics of agents, these models frequently become computationally…
This paper describes a new Monte Carlo method based on a novel stochastic potential switching algorithm. This algorithm enables the equilibrium properties of a system with potential $V$ to be computed using a Monte Carlo simulation for a…
We propose a data-driven, coarse-graining formulation in the context of equilibrium statistical mechanics. In contrast to existing techniques which are based on a fine-to-coarse map, we adopt the opposite strategy by prescribing a…
Metropolis Monte Carlo simulation is a powerful tool for studying the equilibrium properties of matter. In complex condensed-phase systems, however, it is difficult to design Monte Carlo moves with high acceptance probabilities that also…
High-quality random samples of quantum states are needed for a variety of tasks in quantum information and quantum computation. Searching the high-dimensional quantum state space for a global maximum of an objective function with many local…
In this paper we introduce and discuss numerical schemes for the approximation of kinetic equations for flocking behavior with phase transitions that incorporate uncertain quantities. This class of schemes here considered make use of a…
In this article we develop a multi-grid multi-level Monte Carlo (MGMLMC) method for the stochastic Stokes-Darcy interface model with random hydraulic conductivity both in the porous media domain and on the interface. Because the randomness…
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 develop a novel advanced Particle Markov chain Monte Carlo algorithm that is capable of sampling from the posterior distribution of non-linear state space models for both the unobserved latent states and the unknown model parameters. We…
The effectiveness of stochastic algorithms based on Monte Carlo dynamics in solving hard optimization problems is mostly unknown. Beyond the basic statement that at a dynamical phase transition the ergodicity breaks and a Monte Carlo…
Recent advances in stochastic gradient techniques have made it possible to estimate posterior distributions from large datasets via Markov Chain Monte Carlo (MCMC). However, when the target posterior is multimodal, mixing performance is…
In the first part of this paper we study approximations of trajectories of Piecewise Deter-ministic Processes (PDP) when the flow is not explicit by the thinning method. We also establish a strong error estimate for PDPs as well as a weak…
We use a Monte Carlo method to assemble finite element matrices for polynomial Chaos approximations of elliptic equations with random coefficients. In this approach, all required expectations are approximated by a Monte Carlo method. The…
A class of Monte Carlo algorithms which incorporate absorbing Markov chains is presented. In a particular limit, the lowest-order of these algorithms reduces to the $n$-fold way algorithm. These algorithms are applied to study the escape…
This paper addresses optimization problems constrained by partial differential equations with uncertain coefficients. In particular, the robust control problem and the average control problem are considered for a tracking type cost…
Science and engineering problems subject to uncertainty are frequently both computationally expensive and feature nonsmooth parameter dependence, making standard Monte Carlo too slow, and excluding efficient use of accelerated uncertainty…