Learning Lattice Quantum Field Theories with Equivariant Continuous Flows

Abstract

We propose a novel machine learning method for sampling from the high-dimensional probability distributions of Lattice Field Theories, which is based on a single neural ODE layer and incorporates the full symmetries of the problem. We test our model on the ${\varphi }^4$ theory, showing that it systematically outperforms previously proposed flow-based methods in sampling efficiency, and the improvement is especially pronounced for larger lattices. Furthermore, we demonstrate that our model can learn a continuous family of theories at once, and the results of learning can be transferred to larger lattices. Such generalizations further accentuate the advantages of machine learning methods.

17 pages, 9 figures, 1 table; slightly expanded published version, added 2 figures and 2 sections to appendix

References in corpus (7)

• Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains
• Machine Learning of Explicit Order Parameters: From the Ising Model to SU(2) Lattice Gauge Theory
• Efficient Modelling of Trivializing Maps for Lattice ${\varphi }^4$ Theory Using Normalizing Flows: A First Look at Scalability
• Flow-based sampling for multimodal and extended-mode distributions in lattice field theory
• Learning Trivializing Gradient Flows for Lattice Gauge Theories
• Towards reduction of autocorrelation in HMC by machine learning
• Machine Learning of Thermodynamic Observables in the Presence of Mode Collapse

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