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.

arXiv comment26 pages, 5 figures

References in corpus (53)

• A high-bias, low-variance introduction to Machine Learning for physicists
• The pseudo-marginal approach for efficient Monte Carlo computations
• Trivializing maps, the Wilson flow and the HMC algorithm
• Worm algorithms for classical statistical models
• 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
• The Loop Algorithm
• Self-Learning Monte Carlo Method
• Solving Statistical Mechanics Using Variational Autoregressive Networks
• Flow-based generative models for Markov chain Monte Carlo in lattice field theory
• Event-chain Monte Carlo algorithms for hard-sphere systems
• Equivariant flow-based sampling for lattice gauge theory
• Schwarz-preconditioned HMC algorithm for two-flavour lattice QCD
• HMC algorithm with multiple time scale integration and mass preconditioning
• Neural Network Renormalization Group
• Machine Learning for Quantum Matter
• Recent Developments of World-Line Monte Carlo Methods
• Estimation of Thermodynamic Observables in Lattice Field Theories with Deep Generative Models
• Sampling using $SU(N)$ gauge equivariant flows
• Asymptotically unbiased estimation of physical observables with neural samplers
• Regressive and generative neural networks for scalar field theory
• Accelerating Wilson Fermion Matrix Inversions by Means of the Stabilized Biconjugate Gradient Algorithm
• A New Exact Method for Dynamical Fermion Computations with Non-Local Actions
• Meron-Cluster Simulation of the $\theta$-Vacuum in the 2-d $O(3)$-Model
• Self-Learning Monte Carlo Method in Fermion Systems
• Self-learning Monte Carlo with Deep Neural Networks
• Hadrons and Nuclei
• Self-Learning Monte Carlo Method: Continuous-Time Algorithm
• Lattice QCD and Neutrino-Nucleus Scattering
• The Role of Lattice QCD in Searches for Violations of Fundamental Symmetries and Signals for New Physics
• Symmetry Enforced Self-Learning Monte Carlo Method Applied to the Holstein Model
• Event-chain Monte Carlo for classical continuous spin models
• Machine Learning Holographic Mapping by Neural Network Renormalization Group
• Speeding up the Hybrid-Monte-Carlo algorithm for dynamical fermions
• Fast Fermion Monte Carlo
• Status and Future Perspectives for Lattice Gauge Theory Calculations to the Exascale and Beyond
• Self-learning Hybrid Monte Carlo: A First-principles Approach
• Event-chain algorithm for the Heisenberg model: Evidence for $z\simeq 1$ dynamic scaling
• Reducing Autocorrelation Times in Lattice Simulations with Generative Adversarial Networks
• UV-filtered fermionic Monte Carlo
• Exact Pseudofermion Action for Monte Carlo Simulation of Domain-Wall Fermion
• Dual simulation of the 2-dimensional lattice U(1) gauge-Higgs model with a topological term
• Lattice Gauge Theories and Spin Models
• Opportunities for lattice QCD in quark and lepton flavor physics
• Lattice Gauge Theory for Physics Beyond the Standard Model
• Testing trivializing maps in the Hybrid Monte Carlo algorithm
• Generalization capabilities of translationally equivariant neural networks
• Geometric Algorithm for Abelian-Gauge Models
• Irreversible Markov chains in spin models: Topological excitations
• Testing the event-chain algorithm in asymptotically free models
• Fermions as Global Correction: the QCD Case
• Generative Neural Samplers for the Quantum Heisenberg Chain
• RHMC with Block Solvers and Multiple Pseudofermions

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