Related papers: Absolute Monte Carlo estimation of integrals and p…
Monte Carlo is a versatile and frequently used tool in statistical physics and beyond. Correspondingly, the number of algorithms and variants reported in the literature is vast, and an overview is not easy to achieve. In this pedagogical…
When a Monte Carlo algorithm is used to evaluate a physical observable A, it is possible to slightly modify the algorithm so that it evaluates simultaneously A and the derivatives $\partial$ $\varsigma$ A of A with respect to each…
In this note, we study a concatenation of quasi-Monte Carlo and plain Monte Carlo rules for high-dimensional numerical integration in weighted function spaces. In particular, we consider approximating the integral of periodic functions…
Multilevel Monte Carlo is a key tool for approximating integrals involving expensive scientific models. The idea is to use approximations of the integrand to construct an estimator with improved accuracy over classical Monte Carlo. We…
The computational complexity of naive, sampling-based uncertainty quantification for 3D partial differential equations is extremely high. Multilevel approaches, such as multilevel Monte Carlo (MLMC), can reduce the complexity significantly,…
Any search or sampling algorithm for solution of inverse problems needs guidance to be efficient. Many algorithms collect and apply information about the problem on the fly, and much improvement has been made in this way. However, as a…
Monte Carlo method is a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. They are often used in physical and mathematical problems and are most useful when it is difficult or…
Differentiable programming has emerged as a key programming paradigm empowering rapid developments of deep learning while its applications to important computational methods such as Monte Carlo remain largely unexplored. Here we present the…
Monte-Carlo simulations are routinely used for estimating the scaling exponents of complex systems. However, due to finite-size effects, determining the exponent values is often difficult and not reliable. Here we present a novel technique…
Acceptance-rejection (AR), Independent Metropolis Hastings (IMH) or importance sampling (IS) Monte Carlo (MC) simulation algorithms all involve computing ratios of probability density functions (pdfs). On the other hand, classifiers…
We introduce a powerful Monte Carlo (MC) algorithm for the atomistic simulation of bulk models of oligo- and poly-thiophenes by redesigning MC moves originally developed for considerably simpler polymer structures and architectures, such as…
Development of exponentially scaling methods has seen great progress in tackling larger systems than previously thought possible. One such technique, full configuration interaction quantum Monte Carlo, is a useful algorithm that allows…
We construct numerical integrators for Hamiltonian problems that may advantageously replace the standard Verlet time-stepper within Hybrid Monte Carlo and related simulations. Past attempts have often aimed at boosting the order of accuracy…
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 a new path integral Monte Carlo method for investigating nonadiabatic systems in thermal equilibrium and demonstrate an approach to reducing stochastic error. We derive a general path integral expression for the partition…
The computational cost of a Monte Carlo algorithm can only be meaningfully discussed when taking into account the magnitude of the resulting statistical error. Aiming for a fixed error per particle, we study the scaling behavior of the…
Recent advances in machine learning have led to the development of new methods for enhancing Monte Carlo methods such as Markov chain Monte Carlo (MCMC) and importance sampling (IS). One such method is normalizing flows, which use a neural…
The purely numerical evaluation of multi-loop integrals and amplitudes can be a viable alternative to analytic approaches, in particular in the presence of several mass scales, provided sufficient accuracy can be achieved in an acceptable…
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…
Performing exact Bayesian inference for complex models is computationally intractable. Markov chain Monte Carlo (MCMC) algorithms can provide reliable approximations of the posterior distribution but are expensive for large datasets and…