Scaling of Stochastic Normalizing Flows in SU(3) lattice gauge theory

2024-11-29

Physical Review D

AI Summary

To address critical slowing-down caused by long autocorrelations in four-dimensional SU(3) lattice gauge theory, this work introduces the Stochastic Normalizing Flow (SNF) framework: a coupling of nonequilibrium Markov chain Monte Carlo (NE-MCMC) with equivariant flow models, enabling thermalization-free, gauge-covariant direct sampling for the first time. Key innovations include SU(3)-covariant neural network layers that rigorously preserve local gauge symmetry, and a differentiable evolution path constructed via the Jarzynski equality. Experimental validation on 4D lattices demonstrates that SNF substantially improves sampling efficiency for long-autocorrelation observables, while computational cost scales nearly linearly with system degrees of freedom—exhibiting exceptional scalability. This approach establishes a new paradigm for large-scale, unbiased Monte Carlo simulations of strongly coupled gauge fields.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Deep Generative Models & Autoencoders
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Social Networks and Social Media: Computational social science
• Security and Privacy: Large-scale security measurements

Abstract

Nonequilibrium 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 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. Published by the American Physical Society 2025

Problem

• Mitigating critical slowing down in lattice gauge theory
• Combining flow-based approaches with NE-MCMC simulations
• Improving sampling efficiency for long autocorrelation observables

Innovation

• Combines NE-MCMC with flow-based approaches
• Uses gauge-equivariant layers in SU(3) theory
• Improves scaling with system degrees freedom