Equivariant flow-based sampling for lattice gauge theory

Abstract

We define a class of machine-learned flow-based sampling algorithms for lattice gauge theories that are gauge-invariant by construction. We demonstrate the application of this framework to U(1) gauge theory in two spacetime dimensions, and find that near critical points in parameter space the approach is orders of magnitude more efficient at sampling topological quantities than more traditional sampling procedures such as Hybrid Monte Carlo and Heat Bath.

6 pages, 4 figures

References in corpus (36)

• A Duality Web in 2+1 Dimensions and Condensed Matter Physics
• Trivializing maps, the Wilson flow and the HMC algorithm
• Worm algorithms for classical statistical models
• Reconstructing quantum states with generative models
• Accelerate Monte Carlo Simulations with Restricted Boltzmann Machines
• Lattice QCD without topology barriers
• Solving Statistical Mechanics Using Variational Autoregressive Networks
• Flow-based generative models for Markov chain Monte Carlo in lattice field theory
• Topological order, emergent gauge fields, and Fermi surface reconstruction
• GraphAF: a Flow-based Autoregressive Model for Molecular Graph Generation
• Flow++: Improving Flow-Based Generative Models with Variational Dequantization and Architecture Design
• Neural Network Renormalization Group
• Recent Developments of World-Line Monte Carlo Methods
• Regressive and generative neural networks for scalar field theory
• Meron-Cluster Simulation of the $\theta$-Vacuum in the 2-d $O(3)$-Model
• GraphNVP: An Invertible Flow Model for Generating Molecular Graphs
• Normalizing Flows on Tori and Spheres
• PointFlow: 3D Point Cloud Generation with Continuous Normalizing Flows
• Equivariant Flows: sampling configurations for multi-body systems with symmetric energies
• Fighting topological freezing in the two-dimensional CP${}^{N-1}$ model
• The Kaon B-parameter from Quenched Domain-Wall QCD
• Can Boltzmann Machines Discover Cluster Updates ?
• Topological critical slowing down: variations on a toy model
• Graph Normalizing Flows
• Equivariant Hamiltonian Flows
• Discrete Flows: Invertible Generative Models of Discrete Data
• Monge-Ampère Flow for Generative Modeling
• Dual simulation of the 2-dimensional lattice U(1) gauge-Higgs model with a topological term
• Topological properties of $C{P}^{N-1}$ models in the large-$N$ limit
• Neural Canonical Transformation with Symplectic Flows
• Gauge Theories for the Thermal Hall Effect
• Diffusion of topological charge in lattice QCD simulations
• Testing trivializing maps in the Hybrid Monte Carlo algorithm
• Geometric Algorithm for Abelian-Gauge Models
• Temporal Normalizing Flows
• Testing the event-chain algorithm in asymptotically free models

Cited by in corpus (108)

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• An Efficient Lorentz Equivariant Graph Neural Network for Jet Tagging
• Estimation of Thermodynamic Observables in Lattice Field Theories with Deep Generative Models
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• Neural Importance Sampling for Rapid and Reliable Gravitational-Wave Inference
• Phase Transitions in Particle Physics -- Results and Perspectives from Lattice Quantum Chromo-Dynamics
• Exploring QCD matter in extreme conditions with Machine Learning
• FLAG Review 2024
• A Neural Resampler for Monte Carlo Reweighting with Preserved Uncertainties
• Lattice gauge equivariant convolutional neural networks
• Machine-learning hidden symmetries
• Heavy quark potential in quark-gluon Plasma: Deep neural network meets lattice quantum chromodynamics
• 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
• Phase Transition Study meets Machine Learning
• Quasi Anomalous Knowledge: Searching for new physics with embedded knowledge
• Gauge Invariant and Anyonic Symmetric Transformer and RNN Quantum States for Quantum Lattice Models
• Neural network reconstruction of the dense matter equation of state from neutron star observables
• Learning Mesh-Based Simulation with Graph Networks
• Gauge-equivariant flow models for sampling in lattice field theories with pseudofermions
• Stochastic normalizing flows as non-equilibrium transformations
• Quantum field-theoretic machine learning
• Topological Obstructions to Autoencoding
• Flow-based sampling in the lattice Schwinger model at criticality
• Roadmap on machine learning glassy dynamics
• Learning Lattice Quantum Field Theories with Equivariant Continuous Flows
• Physics-Driven Learning for Inverse Problems in Quantum Chromodynamics
• Reducing Autocorrelation Times in Lattice Simulations with Generative Adversarial Networks
• Machine-learning physics from unphysics: Finding deconfinement temperature in lattice Yang-Mills theories from outside the scaling window
• Gauge equivariant neural networks for quantum lattice gauge theories
• Reconstructing spectral functions via automatic differentiation
• Extending machine learning classification capabilities with histogram reweighting
• Learning Trivializing Gradient Flows for Lattice Gauge Theories
• Normalizing Flows and the Real-Time Sign Problem
• Advances in machine-learning-based sampling motivated by lattice quantum chromodynamics
• Gravitational wave populations and cosmology with neural posterior estimation
• Ab-initio study of interacting fermions at finite temperature with neural canonical transformation
• Topological sampling through windings
• Diffusion Models as Stochastic Quantization in Lattice Field Theory
• A method to challenge symmetries in data with self-supervised learning
• Explainable machine learning of the underlying physics of high-energy particle collisions
• Sampling with flows, diffusion and autoregressive neural networks: A spin-glass perspective
• Inhomogeneities in the $2$-Flavor Chiral Gross-Neveu Model
• Deep Variational Free Energy Approach to Dense Hydrogen
• Lattice Scalar Field Theory At Complex Coupling
• Fourier-Flow model generating Feynman paths
• Machine Learning of Thermodynamic Observables in the Presence of Mode Collapse
• Mitigating the Hubbard Sign Problem with Complex-Valued Neural Networks
• Taming nucleon density distributions with deep neural network method
• Variational Neural-Network Ansatz for Continuum Quantum Field Theory
• Generalization capabilities of translationally equivariant neural networks
• Exploring Parameter Spaces with Artificial Intelligence and Machine Learning Black-Box Optimisation Algorithms
• Flow-based density of states for complex actions
• Non-Hertz-Millis scaling of the antiferromagnetic quantum critical metal via scalable Hybrid Monte Carlo
• Sampling the lattice Nambu-Goto string using Continuous Normalizing Flows
• Algorithmic Differentiation for Automated Modeling of Machine Learned Force Fields
• Introduction to Normalizing Flows for Lattice Field Theory
• Simulating Yang-Mills theories with a complex coupling
• Estimating the Euclidean quantum propagator with deep generative modeling of Feynman paths
• Deep Learning Hamiltonian Monte Carlo
• Differentiable Physics: A Position Piece
• Confinement in non-Abelian lattice gauge theory via persistent homology
• Hierarchical autoregressive neural networks for statistical systems
• Fully probabilistic quasar continua predictions near Lyman-α with conditional neural spline flows
• Applications of Lattice Gauge Equivariant Neural Networks
• Machine learning a fixed point action for SU(3) gauge theory with a gauge equivariant convolutional neural network
• Generative learning for the problem of critical slowing down in lattice Gross Neveu model
• Normalizing flows for microscopic many-body calculations: an application to the nuclear equation of state
• Parallel Tempered Metadynamics: Overcoming potential barriers without surfing or tunneling
• Generative Neural Samplers for the Quantum Heisenberg Chain
• Sampling U(1) gauge theory using a re-trainable conditional flow-based model
• On learning higher-order cumulants in diffusion models
• VAEBM: A Symbiosis between Variational Autoencoders and Energy-based Models
• Gauge covariant neural network for quarks and gluons
• Generative models for sampling of lattice field theories
• Training normalizing flows with computationally intensive target probability distributions
• Scaling of Stochastic Normalizing Flows in $\mathrm{SU}(3)$ lattice gauge theory
• Topology changing update algorithms for SU(3) gauge theory
• Flow-Based Sampling for Entanglement Entropy and the Machine Learning of Defects
• Equivariance and generalization in neural networks
• Trajectory Prediction using Equivariant Continuous Convolution
• Machine-learned RG-improved gauge actions and classically perfect gradient flows
• Scaling Up Machine Learning For Quantum Field Theory with Equivariant Continuous Flows
• Self-learning Monte Carlo with equivariant Transformer
• Report from the A.I. For Nuclear Physics Workshop
• Foundations of automatic feature extraction at LHC--point clouds and graphs
• Vacuum Decay and Euclidean Lattice Monte Carlo
• Metropolis Monte Carlo sampling: convergence, localization transition and optimality
• AdvNF: Reducing Mode Collapse in Conditional Normalising Flows using Adversarial Learning
• Scaling flow-based approaches for topology sampling in $\mathrm{SU}(3)$ gauge theory
• Embedded-model flows: Combining the inductive biases of model-free deep learning and explicit probabilistic modeling
• Multi-Lattice Sampling of Quantum Field Theories via Neural Operator-based Flows
• Preserving gauge invariance in neural networks
• Involutive MCMC: a Unifying Framework
• Deep generative modelling of canonical ensemble with differentiable thermal properties
• Training Invertible Linear Layers through Rank-One Perturbations
• Extended framework for the hybrid Monte Carlo in lattice gauge theory
• Diffusion Models for SU(2) Lattice Gauge Theory in Two Dimensions
• Group-Equivariant Diffusion Models for Lattice Field Theory
• Learning Langevin dynamics with QCD phase transition
• Efficient identification of critical regions via Flow Matching-based Monte Carlo initialization
• Flowing Through Hilbert Space: Quantum-Enhanced Generative Models for Lattice Field Theory
• NeuMC -- a package for neural sampling for lattice field theories
• Continuous normalizing flows on manifolds
• Implicit Riemannian Concave Potential Maps
• A comparative lattice analysis of $SU(2)$ dark gluebal
• Applications of flow models to the generation of correlated lattice QCD ensembles