统计物理中的采样算法：面向统计学与机器学习的指南
Sampling algorithms in statistical physics: a guide for statistics and machine learning
AI总结：
本文以统计学与机器学习语言介绍统计物理中的采样算法，回顾经典与近期方法并探讨其在Ising等模型上的应用，揭示了跨学科交叉研究的未来方向。
摘要：
我们讨论了统计物理中从未归一化概率分布采样的几种算法，但使用的是统计学与机器学习的语言。我们首先对该领域的一些关键思想与概念提供了自成体系的介绍，随后讨论了三个著名问题：Ising model的相变、二维平面上的熔化相变以及全原子液态水模型的模拟。我们回顾了经典的Metropolis、Glauber和分子动力学采样算法，随后讨论了若干更近期的方法，包括cluster algorithms、hybrid Monte Carlo和Langevin dynamics的新变体，以及诸如event chain Monte Carlo的分段确定性过程。我们全程强调了与统计学和机器学习的交叉，并展示了使用统计学文献工具在event chain Monte Carlo和Ising model采样方面的一些结果。我们针对Ising和XY模型提供了模拟研究，可复现代码在线免费提供，随后我们讨论了各学科间尚未探索的若干互动开放领域，并提出了实现这些互动的途径。
英文摘要：
We discuss several algorithms for sampling from unnormalized probability distributions in statistical physics, but using the language of statistics and machine learning. We provide a self-contained introduction to some key ideas and concepts of the field, before discussing three well-known problems: phase transitions in the Ising model, the melting transition on a two-dimensional plane and simulation of an all-atom model for liquid water. We review the classical Metropolis, Glauber and molecular dynamics sampling algorithms before discussing several more recent approaches, including cluster algorithms, novel variations of hybrid Monte Carlo and Langevin dynamics and piece-wise deterministic processes such as event chain Monte Carlo. We highlight cross-over with statistics and machine learning throughout and present some results on event chain Monte Carlo and sampling from the Ising model using tools from the statistics literature. We provide a simulation study on the Ising and XY models, with reproducible code freely available online, and following this we discuss several open areas for interaction between the disciplines that have not yet been explored and suggest avenues for doing so.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
