Learning Lattice Quantum Field Theories with Equivariant Continuous Flows
This work addresses sampling challenges in computational physics for researchers studying quantum field theories, representing an incremental improvement over existing flow-based methods.
The authors tackled the problem of sampling from high-dimensional probability distributions in Lattice Field Theories by proposing a machine learning method based on a neural ODE layer with full symmetry incorporation. They demonstrated that their model systematically outperforms previous flow-based methods in sampling efficiency, especially for larger lattices, and can learn continuous families of theories with transferable results.
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 $φ^4$ 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.