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SubmittedOpen Access (License Unspecified), Open
Journal article
SAMPLING FROM ROUGH ENERGY LANDSCAPES
Communications in mathematical sciences, v 18(8), pp 2271-2303
01 Jan 2020
Featured in Collection : UN Sustainable Development Goals @ Drexel
Abstract
We examine challenges to sampling from Boltzmann distributions associated with multiscale energy landscapes. The multiscale features, or "roughness", corresponds to highly oscillatory, but bounded, perturbations of a smooth landscape. Through a combination of numerical experiments and analysis we demonstrate that the performance of Metropolis adjusted Langevin algorithm can be severely attenuated as the roughness increases. In contrast, we prove that random walk Metropolis is insensitive to such roughness. We also formulate two alternative sampling strategies that incorporate large scale features of the energy landscape, while resisting the impact of fine scale roughness; these also outperform random walk Metropolis. Numerical experiments on these landscapes are presented that confirm our predictions. Open questions and numerical challenges are also highlighted.
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Details
- Title
- SAMPLING FROM ROUGH ENERGY LANDSCAPES
- Creators
- Petr Plechac - University of DelawareGideon Simpson - Drexel University
- Publication Details
- Communications in mathematical sciences, v 18(8), pp 2271-2303
- Publisher
- Int Press Boston, Inc
- Number of pages
- 33
- Grant note
- DMS-1818716 / US National Science Foundation; National Science Foundation (NSF) W911NF-15-2-0122 / DARPA project
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000601322100009
- Scopus ID
- 2-s2.0-85099130349
- Other Identifier
- 991019173852004721
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- Collaboration types
- Domestic collaboration
- Web of Science research areas
- Mathematics, Applied