发表机构
University of Warwick（华威大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出通用框架，将事件链蒙特卡洛的高效采样策略推广至环面上所有平移对称成对模型，有望超越分子动力学和哈密顿蒙特卡洛，并数值阐明集体动力学及其广泛影响。
AI 中文摘要
事件链蒙特卡洛（ECMC）近年来彻底改变了计算采样领域，为分子动力学（MD）和哈密顿蒙特卡洛（HMC）算法提供了强大的替代方案。每种方法都通过沿确定性轨迹推进粒子而优于无处不在的随机游走Metropolis算法，但ECMC在实现这一目标时不受牛顿动力学的约束。最近的进展利用这种动力学自由度来诱导集体粒子动力学，从而在快速时间尺度上弛豫局部密度变化。在一维环面上$N$个成对相互作用粒子的基础模型中，这导致计算效率比行业领先的MD和HMC提高了$O(N^{3/4})$——但对于一般的吸引/排斥相互作用，在低/高平均粒子密度下，其前置因子小得不切实际。在此，我们提出了一个通用框架，将该高效采样策略推广到环面上所有平移对称的成对模型——从而有可能超越MD和HMC成为最先进的方法。我们还数值上阐明了集体粒子动力学，并讨论了其在物理科学和计算统计学中的广泛影响。
英文摘要
Event-chain Monte Carlo (ECMC) has revolutionised computational sampling over recent years, providing a powerful alternative to the molecular-dynamics (MD) and Hamiltonian Monte Carlo (HMC) algorithms. Each method outperforms the ubiquitous random-walk Metropolis algorithm by advancing particles along deterministic trajectories, but ECMC achieves this without being constrained by Newtonian dynamics. Recent advances exploited this dynamical freedom to induce a collective particle dynamics that relax local density variations on fast timescales. In a foundational model of $N$ pairwise-interacting particles on the 1D torus, this led to an $O(N^{3/4})$ improvement on the industry-leading computational efficiency of MD and HMC - but with an impractically small prefactor at low/high mean particle density for general attractive/repulsive interactions. Here we present a universal framework that generalises this high-efficiency sampling strategy to all translationally symmetric pairwise models on the torus - creating the potential to surpass MD and HMC as the state of the art. We also numerically elucidate the collective particle dynamics and discuss broad impact across the physical sciences and computational statistics.
Comments17 pages, 8 figures
