Pan Feng, Zhou Pengfei, Zhou Hai-Jun, Zhang Pan
CAS Key Laboratory for Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China.
School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China.
Phys Rev E. 2021 Jan;103(1-1):012103. doi: 10.1103/PhysRevE.103.012103.
We propose a method for solving statistical mechanics problems defined on sparse graphs. It extracts a small feedback vertex set (FVS) from the sparse graph, converting the sparse system to a much smaller system with many-body and dense interactions with an effective energy on every configuration of the FVS, then learns a variational distribution parametrized using neural networks to approximate the original Boltzmann distribution. The method is able to estimate free energy, compute observables, and generate unbiased samples via direct sampling without autocorrelation. Extensive experiments show that our approach is more accurate than existing approaches for sparse spin glasses. On random graphs and real-world networks, our approach significantly outperforms the standard methods for sparse systems, such as the belief-propagation algorithm; on structured sparse systems, such as two-dimensional lattices our approach is significantly faster and more accurate than recently proposed variational autoregressive networks using convolution neural networks.
我们提出了一种用于解决定义在稀疏图上的统计力学问题的方法。它从稀疏图中提取一个小的反馈顶点集（FVS），将稀疏系统转换为一个小得多的系统，该系统具有多体和密集相互作用，且在FVS的每个配置上都有一个有效能量，然后学习一个使用神经网络参数化的变分分布，以近似原始的玻尔兹曼分布。该方法能够估计自由能、计算可观测量，并通过无自相关的直接采样生成无偏样本。大量实验表明，我们的方法比现有的稀疏自旋玻璃方法更准确。在随机图和真实世界网络上，我们的方法显著优于稀疏系统的标准方法，如置信传播算法；在结构化稀疏系统上，如二维晶格，我们的方法比最近提出的使用卷积神经网络的变分自回归网络显著更快且更准确。
