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.

翻译：我们提出了一种新颖的机器学习方法，用于从晶格场论的高维概率分布中进行采样。该方法基于单层神经ODE，并融入问题的全部对称性。我们在$\phi^4$理论上测试了模型，结果表明其在采样效率上系统性地优于先前提出的基于流的方法，且对于较大晶格，改进尤为显著。此外，我们证明了该模型能够同时学习一个连续的理论族，并且学习结果可迁移至更大的晶格。此类泛化进一步凸显了机器学习方法的优势。