dorsal/arxiv
View SchemaThe Penalty Method for Random Walks with Uncertain Energies
| Authors | D. M. Ceperley, M. Dewing |
|---|---|
| Categories | |
| ArXiv ID | physics/9812035 |
| URL | https://arxiv.org/abs/physics/9812035 |
| DOI | 10.1063/1.478034 |
| Journal | J. Chem. Phys. 110, 9812 (1999) |
Abstract
We generalize the Metropolis et al. random walk algorithm to the situation where the energy is noisy and can only be estimated. Two possible applications are for long range potentials and for mixed quantum-classical simulations. If the noise is normally distributed we are able to modify the acceptance probability by applying a penalty to the energy difference and thereby achieve exact sampling even with very strong noise. When one has to estimate the variance we have an approximate formula, good in the limit of large number of independent estimates. We argue that the penalty method is nearly optimal. We also adapt an existing method by Kennedy and Kuti and compare to the penalty method on a one dimensional double well.
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"abstract": "We generalize the Metropolis et al. random walk algorithm to the situation\nwhere the energy is noisy and can only be estimated. Two possible applications\nare for long range potentials and for mixed quantum-classical simulations. If\nthe noise is normally distributed we are able to modify the acceptance\nprobability by applying a penalty to the energy difference and thereby achieve\nexact sampling even with very strong noise. When one has to estimate the\nvariance we have an approximate formula, good in the limit of large number of\nindependent estimates. We argue that the penalty method is nearly optimal. We\nalso adapt an existing method by Kennedy and Kuti and compare to the penalty\nmethod on a one dimensional double well.",
"arxiv_id": "physics/9812035",
"authors": [
"D. M. Ceperley",
"M. Dewing"
],
"categories": [
"physics.comp-ph",
"physics.chem-ph"
],
"doi": "10.1063/1.478034",
"journal_ref": "J. Chem. Phys. 110, 9812 (1999)",
"title": "The Penalty Method for Random Walks with Uncertain Energies",
"url": "https://arxiv.org/abs/physics/9812035"
},
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