Name
Abstract | ||
|---|---|---|
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. |
Year | DOI | Venue |
|---|---|---|
2014 | 10.1137/130932740 | SIAM JOURNAL ON SCIENTIFIC COMPUTING |
Keywords | Field | DocType |
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 | Order of accuracy,Mathematical optimization,Markov chain Monte Carlo,Hybrid Monte Carlo,Integrator,Curse of dimensionality,Gaussian,Boosting (machine learning),Verlet integration,Mathematics | Journal |
Volume | Issue | ISSN |
36 | 4 | 1064-8275 |
Citations | PageRank | References |
11 | 1.48 | 4 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| S. Blanes | 1 | 42 | 10.47 |
| Fernando Casas | 2 | 74 | 18.30 |
| J. M. Sanz-Serna | 3 | 156 | 63.96 |