Related papers: A multilevel algorithm for flow observables in gau…
We analyse a multilevel Monte Carlo method for the approximation of distribution functions of univariate random variables. Since, by assumption, the target distribution is not known explicitly, approximations have to be used. We provide an…
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…
A Markov chain update scheme using a machine-learned flow-based generative model is proposed for Monte Carlo sampling in lattice field theories. The generative model may be optimized (trained) to produce samples from a distribution…
We define a class of machine-learned flow-based sampling algorithms for lattice gauge theories that are gauge-invariant by construction. We demonstrate the application of this framework to U(1) gauge theory in two spacetime dimensions, and…
In lattice quantum field theory studies, parameters defining the lattice theory must be tuned toward criticality to access continuum physics. Commonly used Markov chain Monte Carlo (MCMC) methods suffer from critical slowing down in this…
We investigate a family of approximate multi-step proximal point methods, framed as implicit linear discretizations of gradient flow. The resulting methods are multi-step proximal point methods, with similar computational cost in each…
Machine-learned normalizing flows can be used in the context of lattice quantum field theory to generate statistically correlated ensembles of lattice gauge fields at different action parameters. This work demonstrates how these…
(Neal and Hinton, 1998) recast maximum likelihood estimation of any given latent variable model as the minimization of a free energy functional $F$, and the EM algorithm as coordinate descent applied to $F$. Here, we explore alternative…
We analyze topological objects in pure gluonic $SU(2)$ lattice gauge theory and compute correlation functions between instantons and monopoles. Concerning the instantons we use geometric and field theoretic definitions of the topological…
We report on the progress of our study on the color-electric correlation functions under gradient flow on the lattice. This calculation is the first step of our long-term project to estimate a series of important transport coefficients, of…
Monte Carlo methods play important part in modern statistical physics. The application of these methods suffer from two main difficulties.The first is caused by the relatively small number of particles that can participate in any numerical…
In this paper we address the problem of the prohibitively large computational cost of existing Markov chain Monte Carlo methods for large--scale applications with high dimensional parameter spaces, e.g. in uncertainty quantification in…
This article overviews how gradient flows, and discretizations thereof, are useful to design and analyze optimization and sampling algorithms. The interplay between optimization, sampling, and gradient flows is an active research area; our…
Multiscale correlation functions in high Reynolds number experimental turbulence, numerical simulations and synthetic signals are investigated. Fusion Rules predictions as they arise from multiplicative, almost uncorrelated, random…
Perturbative calculations of gradient flow observables are technically challenging. Current results are limited to a few quantities and, in general, to low perturbative orders. Numerical stochastic perturbation theory is a potentially…
Lattice calculations of hadronic observables are aggravated by short-distance fluctuations. The gradient flow, which can be viewed as a particular realisation of the coarse-graining step of momentum space RG transformations, proves a…
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 propose a multilevel Monte-Carlo scheme, applicable to local actions, which is expected to reduce statistical errors on correlation functions. We give general arguments to show how the efficiency and parameters of the algorithm are…
A recent mode coupling theory of higher-order correlation functions is tested on a simple hard-sphere fluid system at intermediate densities. Multi-point and multi-time correlation functions of the densities of conserved variables are…
We present a new method for analyzing directed and elliptic flow in heavy ion collisions. Unlike standard methods, it separates the contribution of flow to azimuthal correlations from contributions due to other effects. The separation…