Practical applications of machine-learned flows on gauge fields

Numerical lattice quantum chromodynamics (QCD) is an integral part of the modern particle and nuclear theory toolkit [1-9]. In this framework, the discretized path integral is computed using Monte Carlo methods. Computationally, this is very expensive, and grows more so as physical limits of interest are approached [10-12]. Consequently, algorithmic developments are an important driver of progress. For example, resolving topological freezing [12-14]--an issue that arises in sampling gauge field configurations with state-of-the-art Markov chain Monte Carlo (MCMC) algorithms like heatbath [15-19] or Hybrid/Hamiltonian Monte Carlo (HMC) [20-22]--would provide access to finer lattice spacings than presently affordable. To such ends, recent work has explored how emerging machine learning (ML) techniques may be applied to lattice QCD [23, 24]. Of particular interest has been the possibility of accelerating gauge-field sampling [25-34] using normalizing flows [35-37], a class of generative statistical models with tractable density functions. In this framework, a flow is a learned, invertible (diffeomorphic) map between gauge fields. Abstractly, flows may be thought of as bridges between different distributions over gauge fields (or, equivalently, different theories or choices of action parameters).