用分层神经网络加速三维自旋系统蒙特卡洛模拟，提升采样效率。
Hierarchical autoregressive neural networks in three-dimensional statistical system
- 设计分层自回归网络，逐层建模三维自旋系统的条件概率分布。
- 在伊辛模型上实现熵与自由能的高精度估算，覆盖相变区域。
- 相比传统算法，显著降低计算耗时，适合研究临界现象。
自回归神经网络（ANN）最近被提出用于提升多种自旋系统的蒙特卡洛算法效率。其核心思想是将配置的总概率分解为每个自旋的条件概率，再由神经网络近似。训练完成后，可用来从近似概率分布中采样，并显式计算给定配置的概率。此外，这些条件概率还可用于计算信息论可观测量，如互信息或纠缠熵。本文描述了三维空间中的分层自回归网络（HAN）算法，并以伊辛模型为例评估其性能。将HAN与三种其他自回归架构及经典Wolff聚类算法进行比较。最终，给出了三维伊辛模型在相变温度附近多个温度下的热力学可观测量估计，包括熵和自由能。
原文摘要 · Abstract (English)
Autoregressive Neural Networks (ANN) have been recently proposed as a mechanism to improve the efficiency of Monte Carlo algorithms for several spin systems. The idea relies on the fact that the total probability of a configuration can be factorized into conditional probabilities of each spin, which in turn can be approximated by a neural network. Once trained, the ANNs can be used to sample configurations from the approximated probability distribution and to explicitly evaluate this probability for a given configuration. It has also been observed that such conditional probabilities give access to information-theoretic observables such as mutual information or entanglement entropy. In this paper, we describe the hierarchical autoregressive network (HAN) algorithm in three spatial dimensions and study its performance using the example of the Ising model. We compare HAN with three other autoregressive architectures and the classical Wolff cluster algorithm. Finally, we provide estimates of thermodynamic observables for the three-dimensional Ising model, such as entropy and free energy, in a range of temperatures across the phase transition.
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