GSHMC: An efficient method for molecular simulation. The hybrid Monte Carlo (HMC) method is a popular and rigorous method for sampling from a canonical ensemble. The HMC method is based on classical molecular dynamics simulations combined with a Metropolis acceptance criterion and a momentum resampling step. While the HMC method completely resamples the momentum after each Monte Carlo step, the generalized hybrid Monte Carlo (GHMC) method can be implemented with a partial momentum refreshment step. This property seems desirable for keeping some of the dynamic information throughout the sampling process similar to stochastic Langevin and Brownian dynamics simulations. It is, however, ultimate to the success of the GHMC method that the rejection rate in the molecular dynamics part is kept at a minimum. Otherwise an undesirable Zitterbewegung in the Monte Carlo samples is observed. In this paper, we describe a method to achieve very low rejection rates by using a modified energy, which is preserved to high-order along molecular dynamics trajectories. The modified energy is based on backward error results for symplectic time-stepping methods. The proposed generalized shadow hybrid Monte Carlo (GSHMC) method is applicable to NVT as well as NPT ensemble simulations.

References in zbMATH (referenced in 16 articles , 1 standard article )

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  1. Radivojević, Tijana; Akhmatskaya, Elena: Modified Hamiltonian Monte Carlo for Bayesian inference (2020)
  2. Bou-Rabee, Nawaf; Sanz-Serna, J. M.: Geometric integrators and the Hamiltonian Monte Carlo method (2018)
  3. Radivojević, Tijana; Fernández-Pendás, Mario; Sanz-Serna, Jesús María; Akhmatskaya, Elena: Multi-stage splitting integrators for sampling with modified Hamiltonian Monte Carlo methods (2018)
  4. Fernández-Pendás, Mario; Akhmatskaya, Elena; Sanz-Serna, J. M.: Adaptive multi-stage integrators for optimal energy conservation in molecular simulations (2016)
  5. Campos, Cédric M.; Sanz-Serna, J. M.: Extra chance generalized hybrid Monte Carlo (2015)
  6. Escribano, Bruno; Akhmatskaya, Elena; Reich, Sebastian; Azpiroz, Jon M.: Multiple-time-stepping generalized hybrid Monte Carlo methods (2015)
  7. Bou-Rabee, Nawaf; Donev, Aleksandar; Vanden-Eijnden, Eric: Metropolis integration schemes for self-adjoint diffusions (2014)
  8. Escribano, Bruno; Akhmatskaya, Elena; Mujika, Jon I.: Combining stochastic and deterministic approaches within high efficiency molecular simulations (2013)
  9. Arizumi, Nana; Bond, Stephen D.: On the estimation and correction of discretization error in molecular dynamics averages (2012)
  10. Bou-Rabee, Nawaf; Vanden-Eijnden, Eric: A patch that imparts unconditional stability to explicit integrators for Langevin-like equations (2012)
  11. Lelièvre, Tony; Rousset, Mathias; Stoltz, Gabriel: Langevin dynamics with constraints and computation of free energy differences (2012)
  12. Bou-Rabee, Nawaf; Vanden-Eijnden, Eric: Pathwise accuracy and ergodicity of metropolized integrators for SDEs (2010)
  13. Akhmatskaya, Elena; Bou-Rabee, Nawaf; Reich, Sebastian: A comparison of generalized hybrid Monte Carlo methods with and without momentum flip (2009)
  14. Akhmatskaya, Elena; Bou-Rabee, Nawaf; Reich, Sebastian: Erratum to “A comparison of generalized hybrid Monte Carlo methods with and without momentum flip” (2009)
  15. Leimkuhler, Benedict; Reich, Sebastian: A Metropolis adjusted Nosé-Hoover thermostat (2009)
  16. Akhmatskaya, Elena; Reich, Sebastian: GSHMC: An efficient method for molecular simulation (2008)