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Learning lattice quantum field theories with equivariant continuous flows

Mathis Gerdes, Pim de Haan, Corrado Rainone, Roberto Bondesan, Miranda C. N. Cheng

SciPost Phys. 15, 238 (2023) · published 13 December 2023


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 $\phi^4$ 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.

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