We propose a novel machine learning method for sampling from the high-dimensional probability distributions of Lattice Quantum Field Theories. Instead of the deep architectures used so far for this task, our proposal 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. Compared to the previous baseline model, we improve a key metric, the effective sample size, from 1% to 91% on a lattice of size $32\times 32$. We also demonstrate that our model can successfully learn a continuous family of theories at once, and the results of learning can be transferred to larger lattices. Such generalization capacities further accentuate the potential advantages of machine learning methods compared to traditional MCMC-based methods.
翻译:我们提出一种新的机器学习方法,从Lattice Quantum Field理论的高维概率分布中进行取样。 我们的提议没有使用迄今为止用于这项任务的深层结构,而是以单一的神经极极分层为基础,并包含了问题的全部对称性。 我们用$\phie4$的理论测试我们的模型,表明它在取样效率方面系统地优于先前提议的以流动为基础的方法,而改进对于较大的顶层来说尤为明显。 与以前的基线模型相比,我们改进了一种关键指标,即有效抽样规模,从32小时320美元,从1%提高到91%。 我们还表明,我们的模型可以一次成功地学习一系列连续的理论,学习结果可以转移到更大的层层。 与传统的MCM方法相比,这种一般化能力进一步突出了机器学习方法的潜在优势。