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Bayesian sampling is an important task in statistics and machine learning. Over the past decade, many ensemble-type sampling methods have been proposed. In contrast to the classical Markov chain Monte Carlo methods, these new methods deploy…

The behaviour of the one--dimensional random--forced Burgers equation is investigated in the path integral formalism, using a discrete space--time lattice. We show that by means of Monte Carlo methods one may evaluate observables, such as…

Markov chain Monte Carlo (MCMC) algorithms provide a very general recipe for estimating properties of complicated distributions. While their use has become commonplace and there is a large literature on MCMC theory and practice, MCMC users…

Classical spin systems with nonadditive long-range interactions are studied in the microcanonical ensemble. It is expected that the entropy of such a system is identical to that of the corresponding mean-field model, which is called…

Approximate mean-field equations of motion for the classical chiral field are developed within the linear sigma model by means of a Hartree factorization. Both the approximate and the unapproximated equations of motion are augmented with a…

Field theories are usually quantized by performing a path integral over configurations of classical fields. This is the case both in perturbation theory and in Wilson's nonperturbative lattice field theory. D-theory is an alternative…

Monte Carlo simulations of lattice quantum field theories on Lefschetz thimbles are non trivial. We discuss a new Monte Carlo algorithm based on the idea of computing contributions to the functional integral which come from complete flow…

This paper studies the convergence of mean field games with finite state space to mean field games with a continuous state space. We examine a space discretization of a diffusive dynamics, which is reminiscent of the Markov chain…

Monte Carlo simulations are one of the major tools in statistical physics, complex system science, and other fields, and an increasing number of these simulations is run on distributed systems like clusters or grids. This raises the issue…

Many methods have been proposed to quantify the predictive uncertainty associated with the outputs of deep neural networks. Among them, ensemble methods often lead to state-of-the-art results, though they require modifications to the…

For combinatorial optimization problems that can be formulated as Ising or Potts spin systems, the Mean Field (MF) approximation yields a versatile and simple ANN heuristic, Deterministic Annealing. For assignment problems the situation is…

We consider the Hamiltonians of mean-field spin glasses, which are certain random functions $H_N$ defined on high-dimensional cubes or spheres in $\mathbb R^N$. The asymptotic maximum values of these functions were famously obtained by…

We study continuous symmetry reduction of dynamical systems by the method of slices (method of moving frames) and show that a `slice' defined by minimizing the distance to a single generic `template' intersects the group orbit of every…

Since its formulation in the late 1940s, the Feynman-Kac formula has proven to be an effective tool for both theoretical reformulations and practical simulations of differential equations. The link it establishes between such equations and…

Many machine learning applications require operating on a spatially distributed dataset. Despite technological advances, privacy considerations and communication constraints may prevent gathering the entire dataset in a central unit. In…

We propose a new algorithm which works effectively in global updates in Monte Carlo study. We apply it to the quantum spin chain with next-nearest-neighbor interactions. We observe that Monte Carlo results are in excellent agreement with…

An efficient Monte Carlo algorithm for the simulation of spin models with long-range interactions is discussed. Its central feature is that the number of operations required to flip a spin is independent of the number of interactions…

Microscopic models of classical degrees of freedom coupled to non-interacting fermions occur in many different contexts. Prominent examples from solid state physics are descriptions of colossal magnetoresistance manganites and diluted…

In this paper, we prove the existence of classical solutions for second order stationary mean-field game systems. These arise in ergodic (mean-field) optimal control, convex degenerate problems in calculus of variations, and in the study of…

We investigate a generic, parallel replica-exchange framework for Monte Carlo simulations based on the Wang-Landau method. To demonstrate its advantages and general applicability for massively parallel simulations of complex systems, we…