Emergence of AdS geometry in the simulated tempering algorithm
Emergence of AdS geometry in the simulated tempering algorithm
复制标题
AdS 几何形状在模拟回火算法中的出现
DOI：
10.1007/jhep11(2018)060
复制
发表时间：
2018
影响因子：
5.4
通讯作者：
N. Umeda
中科院分区：
文献类型：
--
作者：
M. Fukuma;N. Matsumoto;N. Umeda
在文献[1]中，我们在任意马尔可夫链蒙特卡罗算法中引入了组态间的距离。这测量了从一种构型过渡到另一种构型的难度，并使我们能够从几何的角度研究概率分布的弛豫。本文研究了一个平衡分布为多峰且含有大量退化真空的随机系统的全局几何。我们表明，当模拟回火算法实现这样一个系统，扩展的配置空间具有渐近欧几里德反德西特（AdS）几何。我们进一步表明，这种知识的几何形状使我们能够优化回火参数在一个简单的，几何的方式。
In our previous work [1], we introduced to an arbitrary Markov chain Monte Carlo algorithm a distance between configurations. This measures the difficulty of transition from one configuration to the other, and enables us to investigate the relaxation of probability distribution from a geometrical point of view. In this paper, we investigate the global geometry of a stochastic system whose equilibrium distribution is highly multimodal with a large number of degenerate vacua. We show that, when the simulated tempering algorithm is implemented to such a system, the extended configuration space has an asymptotically Euclidean anti-de Sitter (AdS) geometry. We further show that this knowledge of geometry enables us to optimize the tempering parameter in a simple, geometrical way.