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Superposition enhanced nested sampling

Accepted version
Peer-reviewed

Type

Article

Change log

Authors

Martiniani, Stefano  ORCID logo  https://orcid.org/0000-0003-2028-2175
Stevenson, JD 
Wales, DJ 

Abstract

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.

Description

Keywords

cond-mat.stat-mech, cond-mat.stat-mech, astro-ph.IM, physics.data-an

Journal Title

Physical Review X

Conference Name

Journal ISSN

2160-3308
2160-3308

Volume Title

4

Publisher

American Physical Society (APS)
Sponsorship
Engineering and Physical Sciences Research Council (EP/I001352/1)
Engineering and Physical Sciences Research Council (EP/I000844/1)
The Royal Society (wm072834)
European Research Council (227758)
European Commission (275544)