Sampling U(1) gauge theory using a re-trainable conditional flow-based model
arXiv:2306.00581 · doi:10.1103/PhysRevD.108.074518
Abstract
Sampling topological quantities in the Monte Carlo simulation of Lattice Gauge Theory becomes challenging as we approach the continuum limit of the theory. In this work, we introduce a Conditional Normalizing Flow (C-NF) model to sample U(1) gauge theory in two dimensions, aiming to mitigate the impact of topological freezing when dealing with smaller values of the U(1) bare coupling. To train the conditional flow model, we utilize samples generated by Hybrid Monte Carlo (HMC) method, ensuring that the autocorrelation in topological quantities remains low. Subsequently, we employ the trained model to interpolate the coupling parameter to values where training was not performed. We thoroughly examine the quality of the model in this region and generate uncorrelated samples, significantly reducing the occurrence of topological freezing. Furthermore, we propose a re-trainable approach that utilizes the model's own samples to enhance the generalization capability of the conditional model. This method enables sampling for coupling values that are far beyond the initial training region, expanding the applicability of the model.
arXiv comment1. Comments: page 4, added a section on Mode collapse in U(1) Gauge Theory. 2. Comments: page 11, added a section in appendix
References in corpus (24)
- Solving the Quantum Many-Body Problem with Artificial Neural Networks
- Discovering Phase Transitions with Unsupervised Learning
- Critical slowing down and error analysis in lattice QCD simulations
- Machine Learning Topological Invariants with Neural Networks
- Learning Thermodynamics with Boltzmann Machines
- Solving Statistical Mechanics Using Variational Autoregressive Networks
- Flow-based generative models for Markov chain Monte Carlo in lattice field theory
- Equivariant flow-based sampling for lattice gauge theory
- Machine Learning for Quantum Matter
- Asymptotically unbiased estimation of physical observables with neural samplers
- Regressive and generative neural networks for scalar field theory
- Self-Learning Monte Carlo Method in Fermion Systems
- Machine learning action parameters in lattice quantum chromodynamics
- Symmetry Enforced Self-Learning Monte Carlo Method Applied to the Holstein Model
- Gauge-equivariant flow models for sampling in lattice field theories with pseudofermions
- Flow-based sampling in the lattice Schwinger model at criticality
- Multiscale Monte Carlo equilibration: Pure Yang-Mills theory
- Reducing Autocorrelation Times in Lattice Simulations with Generative Adversarial Networks
- Learning Trivializing Gradient Flows for Lattice Gauge Theories
- Generative models for sampling and phase transition indication in spin systems
- Flow-based density of states for complex actions
- Applications of Lattice Gauge Equivariant Neural Networks
- Generative learning for the problem of critical slowing down in lattice Gross Neveu model
- Generative Neural Samplers for the Quantum Heisenberg Chain