GSHMC swMATH ID: 2631 Software Authors: Akhmatskaya, Elena; Reich, Sebastian Description: 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. Homepage: http://www.sciencedirect.com/science/article/pii/S0021999108000533 Related Software: NUTS; Gromacs; Stan; UCI-ml; CODA; PyMC; JAGS; CVODE; SUNDIALS; BUGS; PRMLT; MCMCglmm; Mcmcpack; WinBUGS; RODAS; EnKF; ProtoMol; SQPlab; LINCS Cited in: 18 Documents Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year GSHMC: An efficient method for molecular simulation. Zbl 1148.82316Akhmatskaya, Elena; Reich, Sebastian 2008 all top 5 Cited by 20 Authors 9 Akhmatskaya, Elena 7 Bou-Rabee, Nawaf M. 5 Reich, Sebastian 5 Sanz-Serna, Jesús María 3 Fernández-Pendás, Mario 3 Vanden-Eijnden, Eric 2 Escribano, Bruno 2 Radivojević, Tijana 1 Arizumi, Nana 1 Azpiroz, Jon M. 1 Bond, Stephen D. 1 Campos, Cédric Martínez 1 Donev, Aleksandar 1 Leimkuhler, Benedict J. 1 Lelièvre, Tony 1 Mujika, Jon I. 1 Nagar, Lorenzo 1 Rousset, Mathias 1 Schuh, Katharina 1 Stoltz, Gabriel all top 5 Cited in 10 Serials 9 Journal of Computational Physics 1 Communications on Pure and Applied Mathematics 1 Mathematics of Computation 1 Applied Numerical Mathematics 1 Electronic Journal of Probability 1 Central European Journal of Mathematics 1 Multiscale Modeling & Simulation 1 Acta Numerica 1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 1 Statistics and Computing all top 5 Cited in 8 Fields 16 Numerical analysis (65-XX) 8 Probability theory and stochastic processes (60-XX) 8 Statistical mechanics, structure of matter (82-XX) 1 Partial differential equations (35-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Statistics (62-XX) 1 Mechanics of particles and systems (70-XX) 1 Biology and other natural sciences (92-XX) Citations by Year