Introduction to Normalizing Flows for Lattice Field Theory

Abstract

This notebook tutorial demonstrates a method for sampling Boltzmann distributions of lattice field theories using a class of machine learning models known as normalizing flows. The ideas and approaches proposed in arXiv:1904.12072, arXiv:2002.02428, and arXiv:2003.06413 are reviewed and a concrete implementation of the framework is presented. We apply this framework to a lattice scalar field theory and to U(1) gauge theory, explicitly encoding gauge symmetries in the flow-based approach to the latter. This presentation is intended to be interactive and working with the attached Jupyter notebook is recommended.

arXiv comment38 pages, 5 numbered figures, Jupyter notebook included as ancillary file

References in corpus (18)

• NICE: Non-linear Independent Components Estimation
• Density estimation using Real NVP
• Normalizing Flows for Probabilistic Modeling and Inference
• Flow-based generative models for Markov chain Monte Carlo in lattice field theory
• Equivariant flow-based sampling for lattice gauge theory
• How (not) to Train your Generative Model: Scheduled Sampling, Likelihood, Adversary?
• Gauge Equivariant Convolutional Networks and the Icosahedral CNN
• Sampling using $SU(N)$ gauge equivariant flows
• Normalizing Flows on Tori and Spheres
• Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Data
• Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densities
• Lattice gauge equivariant convolutional neural networks
• Normalizing Flows on Riemannian Manifolds
• Equivariant Hamiltonian Flows
• Riemannian Continuous Normalizing Flows
• Stochastic Normalizing Flows
• Neural Ordinary Differential Equations on Manifolds
• Temperature-steerable flows

Cited by in corpus (4)

• Analysis of autocorrelation times in Neural Markov Chain Monte Carlo simulations
• Deep Learning Hamiltonian Monte Carlo
• Scaling Up Machine Learning For Quantum Field Theory with Equivariant Continuous Flows
• Embedded-model flows: Combining the inductive biases of model-free deep learning and explicit probabilistic modeling