Flow-based sampling for fermionic lattice field theories

Abstract

Algorithms based on normalizing flows are emerging as promising machine learning approaches to sampling complicated probability distributions in a way that can be made asymptotically exact. In the context of lattice field theory, proof-of-principle studies have demonstrated the effectiveness of this approach for scalar theories, gauge theories, and statistical systems. This work develops approaches that enable flow-based sampling of theories with dynamical fermions, which is necessary for the technique to be applied to lattice field theory studies of the Standard Model of particle physics and many condensed matter systems. As a practical demonstration, these methods are applied to the sampling of field configurations for a two-dimensional theory of massless staggered fermions coupled to a scalar field via a Yukawa interaction.

26 pages, 5 figures

References in corpus (6)

• The pseudo-marginal approach for efficient Monte Carlo computations
• Critical slowing down and error analysis in lattice QCD simulations
• Accelerating Dynamical Fermion Computations using the Rational Hybrid Monte Carlo (RHMC) Algorithm with Multiple Pseudofermion Fields
• Self-Learning Monte Carlo Method
• Generalization capabilities of translationally equivariant neural networks
• Generative Neural Samplers for the Quantum Heisenberg Chain

Cited by in corpus (16)

• Machine Learning in Nuclear Physics
• Matrix Model simulations using Quantum Computing, Deep Learning, and Lattice Monte Carlo
• Efficient Modelling of Trivializing Maps for Lattice ${\varphi }^4$ Theory Using Normalizing Flows: A First Look at Scalability
• Gauge-equivariant flow models for sampling in lattice field theories with pseudofermions
• Stochastic normalizing flows as non-equilibrium transformations
• Flow-based sampling in the lattice Schwinger model at criticality
• Learning Trivializing Gradient Flows for Lattice Gauge Theories
• Lattice Scalar Field Theory At Complex Coupling
• Variational Neural-Network Ansatz for Continuum Quantum Field Theory
• Flow-based density of states for complex actions
• Estimating the Euclidean quantum propagator with deep generative modeling of Feynman paths
• Generative learning for the problem of critical slowing down in lattice Gross Neveu model
• Gauge covariant neural network for quarks and gluons
• Simulating first-order phase transition with hierarchical autoregressive networks
• Scaling Up Machine Learning For Quantum Field Theory with Equivariant Continuous Flows
• Variational Monte Carlo Approach to Partial Differential Equations with Neural Networks