Related papers: Comparative Monte Carlo Efficiency by Monte Carlo …
Nested Monte Carlo is widely used for risk estimation, but its efficiency is limited by the discontinuity of the indicator function and high computational cost. This paper proposes a nested Multilevel Monte Carlo (MLMC) method combined with…
The tempered Lefschetz thimble method (TLTM) is a parallel-tempering algorithm towards solving the numerical sign problem, where the system is tempered by the antiholomorphic gradient flow to tame both the sign and ergodicity problems…
To minimise systematic errors in Monte Carlo simulations of charged particles, long range electrostatic interactions have to be calculated accurately and efficiently. Standard approaches, such as Ewald summation or the naive application of…
In any valid Monte Carlo sampling that realizes microcanonical property we can collect statistics for a transition matrix in energy. This matrix is used to determine the density of states, from which most of the thermodynamical averages can…
We propose a new sampling algorithm combining two quite powerful ideas in the Markov chain Monte Carlo literature -- adaptive Metropolis sampler and two-stage Metropolis-Hastings sampler. The proposed sampling method will be particularly…
Continuous-time random disturbances from the renewable generation pose a significant impact on power system dynamic behavior. In evaluating this impact, the disturbances must be considered as continuous-time random processes instead of…
Recent years have seen a growing interest in the thermodynamic cost of dissipative structures formed by active particles. Given the strong finite-size effects of such systems, it is essential to develop efficient numerical approaches that…
Hamiltonian Monte Carlo (HMC) has been widely adopted in the statistics community because of its ability to sample high-dimensional distributions much more efficiently than other Metropolis-based methods. Despite this, HMC often performs…
We construct Monte Carlo methods for the $L^2$-approximation in Hilbert spaces of multivariate functions sampling no more than $n$ function values of the target function. Their errors catch up with the rate of convergence and the…
Current trends in parallel processors call for the design of efficient massively parallel algorithms for scientific computing. Parallel algorithms for Monte Carlo simulations of thermodynamic ensembles of particles have received little…
We present Tethered Monte Carlo, a simple, general purpose method of computing the effective potential of the order parameter (Helmholtz free energy). This formalism is based on a new statistical ensemble, closely related to the…
In 2002 Biskup et al. [Europhys. Lett. 60, 21 (2002)] sketched a rigorous proof for the behavior of the 2D Ising lattice gas, at a finite volume and a fixed excess \delta M of particles (spins) above the ambient gas density (spontaneous…
Metropolis algorithm has been extensively employed for simulating a canonical ensemble and estimating macroscopic properties of a closed system at any desired temperature. A mechanical property, like energy can be calculated by averaging…
The jump-walking Monte-Carlo algorithm is revisited and updated to study the equilibrium properties of systems exhibiting quasi-ergodicity. It is designed for a single processing thread as opposed to currently predominant algorithms for…
We present a study of the parallel tempering (replica exchange) Monte Carlo method, with special focus on the feedback-optimized parallel tempering algorithm, used for generating an optimal set of simulation temperatures. This method is…
Hamiltonian Monte Carlo (HMC) is a popular Markov Chain Monte Carlo (MCMC) algorithm to sample from an unnormalized probability distribution. A leapfrog integrator is commonly used to implement HMC in practice, but its performance can be…
We study the integration of functions with respect to an unknown density. We compare the simple Monte Carlo method (which is almost optimal for a certain large class of inputs) and compare it with the Metropolis algorithm (based on a…
Many physical systems can be described in terms of matrix models that we often cannot solve analytically. Fortunately, they can be studied numerically in a straightforward way. Many commonly used algorithms follow the Monte Carlo method,…
The Worldvolume Hybrid Monte Carlo (WV-HMC) method [arXiv:2012.08468] is an efficient algorithm for addressing the numerical sign problem at moderate computational cost. It mitigates the sign problem while avoiding the ergodicity issues…
Building on our previously introduced Multi-cell Monte Carlo (MC)^2 method for modeling phase coexistence, this paper provides important improvements for efficient determination of phase equilibria in solids. The (MC)^2 method uses multiple…