论文标题
使用分层自回归网络模拟一阶相变
Simulating first-order phase transition with hierarchical autoregressive networks
论文作者
论文摘要
我们将分层自动回归神经（HAN）网络采样算法应用于二维$ Q $ - 状态POTTS模型，并在$ q = 12 $的情况下进行仿真。我们量化了一阶相变附近方法的性能，并将其与Wolff群集算法的性能进行了比较。我们发现，就统计不确定性而言，在类似的数值努力方面涉及统计不确定性。为了有效地训练大型神经网络，我们介绍了预训练的技术。它允许使用较小的系统尺寸训练一些神经网络，然后将它们作为较大系统尺寸的启动配置。由于我们的分层方法的递归结构，这是可能的。我们的结果表明了表现双峰分布的系统的层次方法的性能。此外，我们还提供了相过渡的附近的自由能和熵的估计，其统计不确定性为$ 10^{ - 7} $的前者和$ 10^{ - 3} $，而后者根据$ 10^6 $的统计信息。
We apply the Hierarchical Autoregressive Neural (HAN) network sampling algorithm to the two-dimensional $Q$-state Potts model and perform simulations around the phase transition at $Q=12$. We quantify the performance of the approach in the vicinity of the first-order phase transition and compare it with that of the Wolff cluster algorithm. We find a significant improvement as far as the statistical uncertainty is concerned at a similar numerical effort. In order to efficiently train large neural networks we introduce the technique of pre-training. It allows to train some neural networks using smaller system sizes and then employing them as starting configurations for larger system sizes. This is possible due to the recursive construction of our hierarchical approach. Our results serve as a demonstration of the performance of the hierarchical approach for systems exhibiting bimodal distributions. Additionally, we provide estimates of the free energy and entropy in the vicinity of the phase transition with statistical uncertainties of the order of $10^{-7}$ for the former and $10^{-3}$ for the latter based on a statistics of $10^6$ configurations.
