Stochastic normalizing flows as non-equilibrium transformations

Abstract

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 theoretical framework of stochastic normalizing flows, in which neural-network layers are combined with Monte Carlo updates, is the same that underlies out-of-equilibrium simulations based on Jarzynski's equality, which have been recently deployed to compute free-energy differences in lattice gauge theories. We lay out a strategy to optimize the efficiency of this extended class of generative models and present examples of applications.

1+28 pages, 8 figures; v2: 1+29 pages, 8 figures, added references, discussion in section 4 improved; v3: 1+31 pages, 9 figures, added references, discussion in section 4 expanded, matches published version

References in corpus (18)

• The order of the quantum chromodynamics transition predicted by the standard model of particle physics
• Fluctuation-Dissipation: Response Theory in Statistical Physics
• Comparison of far-from-equilibrium work relations
• Jarzynski-like equality for the out-of-time-ordered correlator
• Machine Learning of Explicit Order Parameters: From the Ising Model to SU(2) Lattice Gauge Theory
• Parton Shower Uncertainties in Jet Substructure Analyses with Deep Neural Networks
• Sampling using $SU(N)$ gauge equivariant flows
• The density of states in gauge theories
• Equation of State for SU(3) Gauge Theory via the Energy-Momentum Tensor under Gradient Flow
• A neural network clustering algorithm for the ATLAS silicon pixel detector
• Lattice gauge equivariant convolutional neural networks
• The density of states approach to dense quantum systems
• Efficient Modelling of Trivializing Maps for Lattice ${\varphi }^4$ Theory Using Normalizing Flows: A First Look at Scalability
• Flow-based sampling for fermionic lattice field theories
• Quantum field-theoretic machine learning
• Machine-learning physics from unphysics: Finding deconfinement temperature in lattice Yang-Mills theories from outside the scaling window
• Probability distributions of the work in the 2D-Ising model
• Estimating the Euclidean quantum propagator with deep generative modeling of Feynman paths

Cited by in corpus (7)

• Phase Transitions in Particle Physics -- Results and Perspectives from Lattice Quantum Chromo-Dynamics
• Gauge-equivariant flow models for sampling in lattice field theories with pseudofermions
• Learning Trivializing Gradient Flows for Lattice Gauge Theories
• Fourier-Flow model generating Feynman paths
• Flow-based density of states for complex actions
• Estimating the Euclidean quantum propagator with deep generative modeling of Feynman paths
• Free Energy Evaluation Using Marginalized Annealed Importance Sampling