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Multiple-time-stepping generalized hybrid Monte Carlo methods
- Performance of the generalized shadow hybrid Monte Carlo (GSHMC) method [1], which proved to be superior in sampling efficiency over its predecessors [2-4], molecular dynamics and hybrid Monte Carlo, can be further improved by combining it with multi-time-stepping (MTS) and mollification of slow forces. We demonstrate that the comparatively simple modifications of the method not only lead to better performance of GSHMC itself but also allow for beating the best performed methods, which use the similar force splitting schemes. In addition we show that the same ideas can be successfully applied to the conventional generalized hybrid Monte Carlo method (GHMC). The resulting methods, MTS-GHMC and MTS-GSHMC, provide accurate reproduction of thermodynamic and dynamical properties, exact temperature control during simulation and computational robustness and efficiency. MTS-GHMC uses a generalized momentum update to achieve weak stochastic stabilization to the molecular dynamics (MD) integrator. MTS-GSHMC adds the use of a shadow (modified)Performance of the generalized shadow hybrid Monte Carlo (GSHMC) method [1], which proved to be superior in sampling efficiency over its predecessors [2-4], molecular dynamics and hybrid Monte Carlo, can be further improved by combining it with multi-time-stepping (MTS) and mollification of slow forces. We demonstrate that the comparatively simple modifications of the method not only lead to better performance of GSHMC itself but also allow for beating the best performed methods, which use the similar force splitting schemes. In addition we show that the same ideas can be successfully applied to the conventional generalized hybrid Monte Carlo method (GHMC). The resulting methods, MTS-GHMC and MTS-GSHMC, provide accurate reproduction of thermodynamic and dynamical properties, exact temperature control during simulation and computational robustness and efficiency. MTS-GHMC uses a generalized momentum update to achieve weak stochastic stabilization to the molecular dynamics (MD) integrator. MTS-GSHMC adds the use of a shadow (modified) Hamiltonian to filter the MD trajectories in the HMC scheme. We introduce a new shadow Hamiltonian formulation adapted to force-splitting methods. The use of such Hamiltonians improves the acceptance rate of trajectories and has a strong impact on the sampling efficiency of the method. Both methods were implemented in the open-source MD package ProtoMol and were tested on a water and a protein systems. Results were compared to those obtained using a Langevin Molly (LM) method [5] on the same systems. The test results demonstrate the superiority of the new methods over LM in terms of stability, accuracy and sampling efficiency. This suggests that putting the MTS approach in the framework of hybrid Monte Carlo and using the natural stochasticity offered by the generalized hybrid Monte Carlo lead to improving stability of MTS and allow for achieving larger step sizes in the simulation of complex systems.…
Author details: | Bruno Escribano, Elena Akhmatskaya, Sebastian ReichORCiDGND, Jon M. Azpiroz |
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DOI: | https://doi.org/10.1016/j.jcp.2014.08.052 |
ISSN: | 0021-9991 |
ISSN: | 1090-2716 |
Title of parent work (English): | Journal of computational physics |
Publisher: | Elsevier |
Place of publishing: | San Diego |
Publication type: | Article |
Language: | English |
Year of first publication: | 2015 |
Publication year: | 2015 |
Release date: | 2017/03/27 |
Tag: | Force splitting; Generalized hybrid Monte Carlo; Modified Hamiltonians; Molecular dynamics; Mollification |
Volume: | 280 |
Number of pages: | 20 |
First page: | 1 |
Last Page: | 20 |
Funding institution: | MICINN [MTM2011-24766]; Basque Government through the BERC program; Spanish Ministry of Economy and Competitiveness MINECO: BCAM Severo Ochoa excellence accreditation [SEV-2013-0323]; Spanish Ministry of Education for funding through a FPU fellowship [AP2009-1514]; Fujitsu Laboratories of Europe U.K. |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
Peer review: | Referiert |