Learning Lattice Quantum Field Theories with Equivariant Continuous Flows

TL;DR

This paper introduces a symmetry-aware neural ODE approach for efficient sampling in lattice quantum field theories, demonstrating superior performance and transferability across lattice sizes.

Contribution

The authors develop a novel equivariant continuous flow model using neural ODEs that captures symmetries and improves sampling efficiency in lattice field theories.

Findings

Outperforms previous flow-based methods in sampling efficiency

Shows significant improvements for larger lattices

Can learn and transfer a family of theories across lattice sizes

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 $\phi^4$ 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.