反射哈密顿蒙特卡罗的共振。

IF 2.4 3区 物理与天体物理 Q1 Mathematics
Namu Kroupa, Gábor Csányi, Will Handley
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引用次数: 0

摘要

在高维中,当粒子系综从狄拉克δ分布初始化并以均匀分布为目标时,具有不精确反射的反射哈密顿蒙特卡罗表现出缓慢的混合。通过量化带有Sinkhorn散度的分布的瞬时非均匀性,我们阐明了混合问题的主要机制。在球体和立方体中,我们证明了集体运动在流体和离散化主导行为之间的转变,临界步长缩放为维度中的幂律。在这两种情况下,粒子可以自发分解,导致粒子密度共振和上述问题。此外,构建了再现高维问题主要特征的低维玩具模型。最后,与精确的哈密顿粒子流进行了动力学对比,并讨论了调谐方法。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Resonances in reflective Hamiltonian Monte Carlo.

In high dimensions, reflective Hamiltonian Monte Carlo with inexact reflections exhibits slow mixing when the particle ensemble is initialized from a Dirac δ distribution and the uniform distribution is targeted. By quantifying the instantaneous nonuniformity of the distribution with the Sinkhorn divergence, we elucidate the principal mechanisms underlying the mixing problems. In spheres and cubes, we show that the collective motion transitions between fluidlike and discretization-dominated behavior, with the critical step size scaling as a power law in the dimension. In both regimes, the particles can spontaneously unmix, leading to resonances in the particle density and the aforementioned problems. Additionally, low-dimensional toy models of the dynamics are constructed which reproduce the dominant features of the high-dimensional problem. Finally, the dynamics is contrasted with the exact Hamiltonian particle flow and tuning practices are discussed.

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来源期刊
Physical review. E
Physical review. E 物理-物理:流体与等离子体
CiteScore
4.60
自引率
16.70%
发文量
0
审稿时长
3.3 months
期刊介绍: Physical Review E (PRE), broad and interdisciplinary in scope, focuses on collective phenomena of many-body systems, with statistical physics and nonlinear dynamics as the central themes of the journal. Physical Review E publishes recent developments in biological and soft matter physics including granular materials, colloids, complex fluids, liquid crystals, and polymers. The journal covers fluid dynamics and plasma physics and includes sections on computational and interdisciplinary physics, for example, complex networks.
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