Numerical Integrators for the Hybrid Monte Carlo Method
We construct numerical integrators for Hamiltonian problems that may advantageously replace the standard Verlet time-stepper within Hybrid Monte Carlo and related simulations. Past attempts have often aimed at boosting the order of accuracy of the integrator and/or reducing the size of its error con...
| Authors: | , , |
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| Format: | article |
| Publication Date: | 2014 |
| Country: | España |
| Institution: | Universitat Politècnica de València (UPV) |
| Repository: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Language: | English |
| OAI Identifier: | oai:riunet.upv.es:10251/62802 |
| Online Access: | https://riunet.upv.es/handle/10251/62802 |
| Access Level: | Open access |
| Keyword: | Hybrid Monte Carlo method Markov Chain Monte Carlo Acceptance probability Hamiltonian dynamics Reversibility Volume preservation Symplectic integrators Verlet method Split-step integrator Stability Error constant Molecular dynamics MATEMATICA APLICADA Métodos numéricos y aplicaciones médicas e industriales 35393 / D - Máster universitario en seguridad nuclear y protección radiológica 2307 |
| Summary: | We construct numerical integrators for Hamiltonian problems that may advantageously replace the standard Verlet time-stepper within Hybrid Monte Carlo and related simulations. Past attempts have often aimed at boosting the order of accuracy of the integrator and/or reducing the size of its error constants; order and error constant are relevant concepts in the limit of vanishing step-length. We propose an alternative methodology based on the performance of the integrator when sampling from Gaussian distributions with not necessarily small step-lengths. We construct new splitting formulae that require two, three, or four force evaluations per time-step. Limited, proof-of-concept numerical experiments suggest that the new integrators may provide an improvement on the efficiency of the standard Verlet method, especially in problems with high dimensionality. |
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