Non-Perturbative Trivializing Flows for Lattice Gauge Theories

Abstract

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 present a general continuous normalizing flow architecture for matrix Lie groups that is equivariant under group transformations. We apply this to lattice gauge theories in two dimensions as a proof of principle and demonstrate competitive performance, showing its potential as a tool for future lattice computations.

7+7 pages, 5 figures, 4 tables; expanded published version, added 2 appendices with computational cost analysis and numerical evaluations (added 1 table and 2 figures)

References in corpus (11)

• Trivializing maps, the Wilson flow and the HMC algorithm
• Two Dimensional QCD is a String Theory
• Flow-based generative models for Markov chain Monte Carlo in lattice field theory
• Estimation of Thermodynamic Observables in Lattice Field Theories with Deep Generative Models
• Sampling using $SU(N)$ gauge equivariant flows
• Efficient Modelling of Trivializing Maps for Lattice ${\varphi }^4$ Theory Using Normalizing Flows: A First Look at Scalability
• Learning Lattice Quantum Field Theories with Equivariant Continuous Flows
• Learning Trivializing Gradient Flows for Lattice Gauge Theories
• Sampling the lattice Nambu-Goto string using Continuous Normalizing Flows
• Gauge covariant neural network for quarks and gluons
• Scaling of Stochastic Normalizing Flows in $\mathrm{SU}(3)$ lattice gauge theory

Cited by in corpus (2)

• Machine-learned RG-improved gauge actions and classically perfect gradient flows
• Scaling flow-based approaches for topology sampling in $\mathrm{SU}(3)$ gauge theory