Related papers: Sampling Nambu-Goto theory using Normalizing Flows

The sampling of probability distributions specified up to a normalization constant is an important problem in both machine learning and statistical mechanics. While classical stochastic sampling methods such as Markov Chain Monte Carlo…

In this work, we demonstrate how to reliably estimate epistemic uncertainty while maintaining the flexibility needed to capture complicated aleatoric distributions. To this end, we propose an ensemble of Normalizing Flows (NF), which are…

The low-energy effective action on long string-like objects in quantum field theory, such as confining strings, includes the Nambu-Goto action and then higher-derivative corrections. This action is diffeomorphism-invariant, and can be…

Modeling real-world distributions can often be challenging due to sample data that are subjected to perturbations, e.g., instrumentation errors, or added random noise. Since flow models are typically nonlinear algorithms, they amplify these…

In this review, after a general introduction to the effective string theory (EST) description of confinement in pure gauge theories, we discuss the behaviour of EST as the temperature is increased. We show that, as the deconfinement point…

Non-equilibrium Markov Chain Monte Carlo (NE-MCMC) simulations provide a well-understood framework based on Jarzynski's equality to sample from a target probability distribution. By driving a base probability distribution out of…

Non-equilibrium Monte Carlo simulations based on Jarzynski's equality are a well-understood method to compute differences in free energy and also to sample from a target probability distribution without the need to thermalize the system…

Normalizing Flows (NFs) are likelihood-based models for continuous inputs. They have demonstrated promising results on both density estimation and generative modeling tasks, but have received relatively little attention in recent years. In…

In the vicinity of the deconfinement transition the behaviour of the interquark potential can be precisely predicted using the Effective String Theory (EST). If the transition is continuous we can combine EST results with a conformal…

Motivated by the recent progress in the effective string description of the interquark potential in lattice gauge theory, we study interfaces with periodic boundary conditions in the three-dimensional Ising model. Our Monte Carlo results…

Yang-Mills theories supplemented by an additional coordinate constraint, which is solved and substituted in the original Lagrangian, provide examples of the so called Nambu models, in the case where such constraints arise from spontaneous…

We measure the energy levels of the excitations of the flux tube between static quark and antiquark in three-dimensional SU(2) gauge theory. Combining exponential error reduction techniques and a variational method we are able to reduce the…

We show that the Nambu-Goto string, and its higher dimensional generalizations, can be quantized, in the sense of an effective theory, in any dimension of the target space. The crucial point is to consider expansions around classical string…

Normalizing Flows (NFs) describe a class of models that express a complex target distribution as the composition of a series of bijective transformations over a simpler base distribution. By limiting the space of candidate transformations…

Continuous normalizing flows are known to be highly expressive and flexible, which allows for easier incorporation of large symmetries and makes them a powerful computational tool for lattice field theories. Building on previous work, we…

This notebook tutorial demonstrates a method for sampling Boltzmann distributions of lattice field theories using a class of machine learning models known as normalizing flows. The ideas and approaches proposed in arXiv:1904.12072,…

We introduce ImitationFlow, a novel Deep generative model that allows learning complex globally stable, stochastic, nonlinear dynamics. Our approach extends the Normalizing Flows framework to learn stable Stochastic Differential Equations.…

The effective action on long strings, such as confining strings in pure Yang-Mills theories, is well-approximated by the Nambu-Goto action, but this action cannot be exact. The leading possible corrections to this action (in a long string…

We study the ``effective string picture'' of confinement, deriving theoretical predictions for the interquark potential at finite temperature. At low temperatures, the leading string correction to the linear confining potential between a…

Normalizing Flows are generative models that directly maximize the likelihood. Previously, the design of normalizing flows was largely constrained by the need for analytical invertibility. We overcome this constraint by a training procedure…