Superposition enhanced nested sampling

Stefano Martiniani, Jacob D. Stevenson, David J. Wales, Daan Frenkel

Research output: Contribution to journalArticlepeer-review

37 Scopus citations


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 combines the strengths of global optimization with the unbiased or 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.

Original languageEnglish (US)
Article number31034
JournalPhysical Review X
Issue number3
StatePublished - 2014
Externally publishedYes


  • Chemical physics
  • Computational physics
  • Statistical physics


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