叠加增强嵌套采样
Superposition Enhanced Nested Sampling
摘要：
物理学、天文学和应用数学中的许多问题的理论分析需要对表现出破遍历性的多模态参数空间进行有效的数值探索。蒙特卡罗方法被广泛用于处理这类问题，但这样的模拟受到普遍存在的采样问题的困扰：对特定状态进行采样的概率与其熵权成比例。设计一种能够有效地对整个相空间进行采样的算法是一个长期存在的问题。在这里，我们报告了一个新的混合方法探索的多峰参数空间表现出破碎遍历。叠加增强巢式抽样（SENS）结合了巢式抽样的无偏/无热抽样和全局优化的优点，在不增加参数的情况下大大提高了效率。我们报告了广泛的测试，这种新的方法为原子团簇，已知有能源景观，传统的采样方案遭受破坏遍历。我们还介绍了一种新的嵌套采样并行化算法。
英文摘要：
The theoretical analysis of many problems in physics, astronomy and applied mathematics requires an efficient numerical exploration of multimodal parameter spaces that exhibit broken ergodicity. Monte Carlo methods are widely used to deal with these classes of problems, but such simulations suffer from a ubiquitous sampling problem: the probability of sampling a particular state is proportional to its entropic weight. Devising an algorithm capable of sampling efficiently the full phase space is a long-standing problem. Here we report a new hybrid method for the exploration of multimodal parameter spaces exhibiting broken ergodicity. Superposition enhanced nested sampling (SENS) combines the strengths of global optimization with the unbiased/athermal sampling of nested sampling, greatly enhancing its efficiency with no additional parameters. We report extensive tests of this new approach for atomic clusters that are known to have energy landscapes for which conventional sampling schemes suffer from broken ergodicity. We also introduce a novel parallelization algorithm for nested sampling.
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