The penalty method for random walks with uncertain energies | Zendy

David M. Ceperley | Zendy; Mark Dewing | Zendy

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The penalty method for random walks with uncertain energies

Author(s) -

David M. Ceperley,

Mark Dewing

Publication year - 1999

Publication title -

the journal of chemical physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.071

H-Index - 357

eISSN - 1089-7690

pISSN - 0021-9606

DOI - 10.1063/1.478034

Subject(s) - penalty method , limit (mathematics) , range (aeronautics) , random walk , variance (accounting) , noise (video) , energy (signal processing) , sampling (signal processing) , mathematical optimization , computer science , mathematics , statistical physics , statistics , mathematical analysis , physics , artificial intelligence , materials science , image (mathematics) , accounting , filter (signal processing) , business , composite material , computer vision

We generalize the Metropolis et al. random walk algorithm to the situationwhere the energy is noisy and can only be estimated. Two possible applicationsare for long range potentials and for mixed quantum-classical simulations. Ifthe noise is normally distributed we are able to modify the acceptanceprobability by applying a penalty to the energy difference and thereby achieveexact sampling even with very strong noise. When one has to estimate thevariance we have an approximate formula, good in the limit of large number ofindependent estimates. We argue that the penalty method is nearly optimal. Wealso adapt an existing method by Kennedy and Kuti and compare to the penaltymethod on a one dimensional double well.Comment: 17 pages, 7 figures, accepted to Journal of Chemical Physics; Corrected swap of Figures 2 and 3. Added Figure

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