Flow-based sampling in the lattice Schwinger model at criticality

Abstract

Recent results suggest that flow-based algorithms may provide efficient sampling of field distributions for lattice field theory applications, such as studies of quantum chromodynamics and the Schwinger model. In this work, we provide a numerical demonstration of robust flow-based sampling in the Schwinger model at the critical value of the fermion mass. In contrast, at the same parameters, conventional methods fail to sample all parts of configuration space, leading to severely underestimated uncertainties.

5 pages main text, 3 pages supplementary material. 4 figures

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• Diffusion Models as Stochastic Quantization in Lattice Field Theory
• Quantum-probabilistic Hamiltonian learning for generative modelling & anomaly detection
• Flow-based density of states for complex actions
• Parallel Tempered Metadynamics: Overcoming potential barriers without surfing or tunneling
• Sampling U(1) gauge theory using a re-trainable conditional flow-based model
• Training normalizing flows with computationally intensive target probability distributions
• Scaling of Stochastic Normalizing Flows in $\mathrm{SU}(3)$ lattice gauge theory
• Simulating first-order phase transition with hierarchical autoregressive networks
• Topology changing update algorithms for SU(3) gauge theory
• Self-learning Monte Carlo with equivariant Transformer
• Scaling flow-based approaches for topology sampling in $\mathrm{SU}(3)$ gauge theory
• AdvNF: Reducing Mode Collapse in Conditional Normalising Flows using Adversarial Learning
• Efficient identification of critical regions via Flow Matching-based Monte Carlo initialization
• Group-Equivariant Diffusion Models for Lattice Field Theory