将随机归一化流用于4维SU(3)规范理论，缓解临界慢化问题。
Scaling of Stochastic Normalizing Flows in $\mathrm{SU}(3)$ lattice gauge theory
- 在非平衡蒙特卡洛更新中引入规范等变层，构建随机归一化流架构。
- 系统自由度增加时，采样效率保持良好，体现优良缩放性。
- 适合研究长自相关时间下的物理可观测量，尤其适用于精细格点计算。
非平衡马尔可夫链蒙特卡洛（NE-MCMC）模拟基于Jarzynski等式，提供了一种无需热化的采样框架。通过将基分布驱离平衡态，可观测量可直接计算。若基分布具有弱自相关性，该方法能有效缓解临界慢化。非平衡演化与基于流的方法共享同一框架，可自然结合形成随机归一化流（SNFs）。本文首次实现4维SU(3)格点规范理论中的SNFs，通过在非平衡蒙特卡洛更新间引入规范等变层定义。核心分析聚焦于该架构随系统自由度增长的优异缩放特性，直接继承自NE-MCMC。最后讨论了系统性改进路径，有望在精细格点间距下，为长自相关时间的可观测量提供通用且高效的采样策略。
原文摘要 · Abstract (English)
Non-equilibrium Markov Chain Monte Carlo (NE-MCMC) simulations provide a well-understood framework based on Jarzynski's equality to sample from a target probability distribution. By driving a base probability distribution out of equilibrium, observables are computed without the need to thermalize. If the base distribution is characterized by mild autocorrelations, this approach provides a way to mitigate critical slowing down. Out-of-equilibrium evolutions share the same framework of flow-based approaches and they can be naturally combined into a novel architecture called Stochastic Normalizing Flows (SNFs). In this work we present the first implementation of SNFs for $\mathrm{SU}(3)$ lattice gauge theory in 4 dimensions, defined by introducing gauge-equivariant layers between out-of-equilibrium Monte Carlo updates. The core of our analysis is focused on the promising scaling properties of this architecture with the degrees of freedom of the system, which are directly inherited from NE-MCMC. Finally, we discuss how systematic improvements of this approach can realistically lead to a general and yet efficient sampling strategy at fine lattice spacings for observables affected by long autocorrelation times.
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