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.

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