Boosting Monte Carlo simulations of spin glasses using autoregressive neural networks
Boosting Monte Carlo simulations of spin glasses using autoregressive neural networks
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DOI：
10.1103/physreve.101.053312
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发表时间：
2020-05-28
影响因子：
2.4
通讯作者：
Pilati, S.
中科院分区：
文献类型：
--
作者：
McNaughton, B.;Milosevic, M., V;Pilati, S.
自回归神经网络正在成为解决经典力学和量子力学相关问题的强大计算工具。它们的一个吸引人的功能是，在它们从数据集中学习了概率分布之后，它们允许对典型的系统配置进行精确和有效的采样。本文采用神经自回归分布估计器（NADE）来增强自旋玻璃理论经典模型的马尔可夫链蒙特卡罗（MCMC）模拟，即二维爱德华兹-安德森哈密顿量。我们表明，NADE可以通过使用标准MCMC算法生成的系统配置的无监督学习来训练，以准确地模拟Boltzmann分布。然后将训练好的NADE作为Metropolis-Hastings算法的智能建议分布。这允许我们执行有效的MCMC模拟，即使NADE学习的概率分布对应的期望值不精确，也可以提供无偏的结果。值得注意的是，我们实现了一个顺序的回火过程，即在较高温度下训练的NADE在略低温度下运行的MCMC模拟中迭代地用作提议分发。这使得即使在低温状态下也可以有效地模拟自旋玻璃模型，避免了由局部更新算法驱动的MCMC模拟所困扰的分散相关时间。此外，我们证明了nade驱动的模拟快速采样基态配置，为它们未来用于解决二进制优化问题铺平了道路。
The autoregressive neural networks are emerging as a powerful computational tool to solve relevant problems in classical and quantum mechanics. One of their appealing functionalities is that, after they have learned a probability distribution from a dataset, they allow exact and efficient sampling of typical system configurations. Here we employ a neural autoregressive distribution estimator (NADE) to boost Markov chain Monte Carlo (MCMC) simulations of a paradigmatic classical model of spin-glass theory, namely, the two-dimensional Edwards-Anderson Hamiltonian. We show that a NADE can be trained to accurately mimic the Boltzmann distribution using unsupervised learning from system configurations generated using standard MCMC algorithms. The trained NADE is then employed as smart proposal distribution for the Metropolis-Hastings algorithm. This allows us to perform efficient MCMC simulations, which provide unbiased results even if the expectation value corresponding to the probability distribution learned by the NADE is not exact. Notably, we implement a sequential tempering procedure, whereby a NADE trained at a higher temperature is iteratively employed as proposal distribution in a MCMC simulation run at a slightly lower temperature. This allows one to efficiently simulate the spin-glass model even in the low-temperature regime, avoiding the divergent correlation times that plague MCMC simulations driven by local-update algorithms. Furthermore, we show that the NADE-driven simulations quickly sample ground-state configurations, paving the way to their future utilization to tackle binary optimization problems.