Computer simulation of liquids
Computer simulation of liquids
Bayesian Learning for Neural Networks
Bayesian Learning for Neural Networks
New Algorithms for Macromolecular Simulation (Lecture Notes in Computational Science and Engineering)
Monte Carlo Strategies in Scientific Computing
Monte Carlo Strategies in Scientific Computing
A comparison of generalized hybrid Monte Carlo methods with and without momentum flip
Journal of Computational Physics
A patch that imparts unconditional stability to explicit integrators for Langevin-like equations
Journal of Computational Physics
On the estimation and correction of discretization error in molecular dynamics averages
Applied Numerical Mathematics
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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.