Scaling of Stochastic Normalizing Flows in $\mathrm{SU}(3)$ lattice gauge theory
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 equilibrium, observables are computed without the need to thermalize. If the base distribution is characterized by mild autocorrelations, this approach provides a way to mitigate critical slowing down. Out-of-equilibrium evolutions share the same framework of flow-based approaches and they can be naturally combined into a novel architecture called Stochastic Normalizing Flows (SNFs). In this work we present the first implementation of SNFs for $\mathrm{SU}(3)$ lattice gauge theory in 4 dimensions, defined by introducing gauge-equivariant layers between out-of-equilibrium Monte Carlo updates. The core of our analysis is focused on the promising scaling properties of this architecture with the degrees of freedom of the system, which are directly inherited from NE-MCMC. Finally, we discuss how systematic improvements of this approach can realistically lead to a general and yet efficient sampling strategy at fine lattice spacings for observables affected by long autocorrelation times.
Code (0)
등록된 구현이 없습니다.
Methods 이 논문이 사용한 방법론
Similar Papers 제목 키워드 기반
Toward Scalable Normalizing Flows for the Hubbard Model
Normalizing flows have recently demonstrated the ability to learn the Boltzmann distribution of the Hubbard model, opening new avenues for generative modeling in condensed matter physics. In this work, we investigate the…
Scaling flow-based approaches for topology sampling in $\mathrm{SU}(3)$ gauge theory
We develop a methodology based on out-of-equilibrium simulations to mitigate topological freezing when approaching the continuum limit of lattice gauge theories. We reduce the autocorrelation of the topological charge em…
Stochastic normalizing flows as non-equilibrium transformations
Normalizing flows are a class of deep generative models that provide a promising route to sample lattice field theories more efficiently than conventional Monte Carlo simulations. In this work we show that the theoretica…
Generative models for scalar field theories: how to deal with poor scaling?
Generative models, such as the method of normalizing flows, have been suggested as alternatives to the standard algorithms for generating lattice gauge field configurations. Studies with the method of normalizing flows d…
Stochastic normalizing flows for Effective String Theory
Effective String Theory (EST) is a powerful tool used to study confinement in pure gauge theories by modeling the confining flux tube connecting a static quark-anti-quark pair as a thin vibrating string. Recently, flow-b…