Data: Learning Lattice Quantum Field Theories with Equivariant Continuous Flows

Network parameters of continuous normalizing flows trained for the \(\varphi^4\) theory. Corresponding article: Learning Lattice Quantum Field Theories with Equivariant Continuous Flows [2207.00283] 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.

用于φ⁴理论训练的连续归一化流（continuous normalizing flows）的网络参数。对应研究论文：《利用等变连续流（equivariant continuous flows）学习格点量子场论（Lattice Quantum Field Theories）》[2207.00283]。摘要：我们提出了一种面向格点场论（Lattice Field Theories）高维概率分布采样的新型机器学习方法，该方法基于单神经常微分方程层（neural ODE layer），并完整融入了问题的全部对称性。我们在φ⁴理论上对所提模型开展测试，结果表明该模型在采样效率上系统性优于此前提出的基于流的方法（flow-based methods），且该提升在更大尺寸的格点上尤为显著。此外，我们证明所提模型可同时学习一整族连续演化的理论，且训练得到的结果可迁移至更大尺寸的格点。这类泛化能力进一步凸显了机器学习方法的优势。