Related papers: Optimized Monte Carlo Methods
We apply extensive Monte Carlo simulations to study the probability distribution $P(m)$ of the order parameter $m$ for the simple cubic Ising model with periodic boundary condition at the transition point. Sampling is performed with the…
The results of numerical simulation using a modified Monte Carlo method with a thermostat algorithm for a pseudospin model of orthonickelates are presented. Temperature phase diagrams are constructed for various degrees of filling and for…
The EM algorithm is a powerful tool for maximum likelihood estimation with missing data. In practice, the calculations required for the EM algorithm are often intractable. We review numerous methods to circumvent this intractability, all of…
Recent Monte Carlo simulations of the critical point of the restricted primitive model for ionic solutions are reported. Only the continuum version of the model is considered. A finite size scaling analysis based in the Bruce-Wilding…
This article reviews the application of advanced Monte Carlo techniques in the context of Multilevel Monte Carlo (MLMC). MLMC is a strategy employed to compute expectations which can be biased in some sense, for instance, by using the…
This review covers applications of quantum Monte Carlo methods to quantum mechanical problems in the study of electronic and atomic structure, as well as applications to statistical mechanical problems both of static and dynamic nature. The…
We discuss the application of multilevel Monte Carlo methods to elliptic partial differential equations with random coefficients. Such problems arise, for example, in uncertainty quantification in subsurface flow modeling. We give a brief…
The critical behavior of the disordered ferromagnetic Ising model is studied numerically by the Monte Carlo method in a wide range of variation of concentration of nonmagnetic impurity atoms. The temperature dependences of correlation…
As the vocabulary size of modern word-based language models becomes ever larger, many sampling-based training criteria are proposed and investigated. The essence of these sampling methods is that the softmax-related traversal over the…
Monte Carlo sampling of any system may be analyzed in terms of an associated glass model -- a variant of the Random Energy Model -- with, whenever there is a sign problem, complex fields. This model has three types of phases (liquid, frozen…
Diffusion models enable the synthesis of highly accurate samples from complex distributions and have become foundational in generative modeling. Recently, they have demonstrated significant potential for solving Bayesian inverse problems by…
Multicanonical MCMC (Multicanonical Markov Chain Monte Carlo; Multicanonical Monte Carlo) is discussed as a method of rare event sampling. Starting from a review of the generic framework of importance sampling, multicanonical MCMC is…
This paper surveys the machine learning literature and presents in an optimization framework several commonly used machine learning approaches. Particularly, mathematical optimization models are presented for regression, classification,…
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…
Data augmentation is an effective technique to improve the generalization of deep neural networks. However, previous data augmentation methods usually treat the augmented samples equally without considering their individual impacts on the…
Efficient and accurate algorithm for partition function, free energy and thermal entropy calculations is of great significance in statistical physics and quantum many-body physics. Here we present an unbiased but low-technical-barrier…
We introduce a Monte Carlo method, as a modification of existing cluster algorithms, which allows simulations directly on systems of infinite size, and for quantum models also at beta=infinity. All two-point functions can be obtained,…
Monte Carlo simulation is an important tool for modeling highly nonlinear systems (like particle colliders and cellular membranes), and random, floating-point numbers are their fuel. These random samples are frequently generated via the…
We study an induced dynamics in the space of energy of single-spin-flip Monte Carlo algorithm. The method gives an efficient reweighting technique. This dynamics is shown to have relaxation times proportional to the specific heat. Thus, it…
Monte Carlo methods are widely used for approximating complicated, multidimensional integrals for Bayesian inference. Population Monte Carlo (PMC) is an important class of Monte Carlo methods, which utilizes a population of proposals to…