论文标题
统计物理学中的采样算法：统计和机器学习指南
Sampling algorithms in statistical physics: a guide for statistics and machine learning
论文作者
论文摘要
我们讨论了从统计物理学中的未归一化概率分布进行采样的几种算法，但使用统计和机器学习的语言。在讨论三个众所周知的问题之前，我们为该领域的一些关键思想和概念提供了一个独立的介绍：Ising模型中的相变，二维平面上的熔化过渡以及对液态水的全原子模型的模拟。在讨论最近的几种方法，包括群集算法，混合蒙特卡洛和兰格文动力学的新型变化以及诸如赛事链莫特·卡洛（Monte Carlo）等确定性过程的过程中，我们在讨论了几种最新方法之前，回顾了经典的大都市，格劳伯和分子动力学采样算法。我们强调了整个统计和机器学习的交叉，并使用统计文献中的工具对事件链蒙特卡洛进行了一些结果，并从Ising模型中进行了抽样。我们提供了有关ISING和XY模型的模拟研究，并在线免费提供可再现的代码，然后我们讨论了尚未探索的学科之间互动的几个开放区域，这些领域尚未探索并建议这样做的途径。
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.
