Separable shadow hybrid Monte Carlo method

Hybrid Monte Carlo (HMC) is a rigorous sampling method that uses molecular dynamics as a global Monte Carlo move. The acceptance rate of HMC decays exponentially with system size. The Shadow Hybrid Monte Carlo (SHMC) was previously introduced to overcome this performance degradation by sampling instead from the shadow Hamiltonian defined for MD when using a symplectic integrator. We show that SHMC’s performance is limited by the need to generate momenta for the MD step from a non-separable shadow Hamiltonian. We introduce the Separable Shadow Hybrid Monte Carlo (S2HMC) method, based on a separable formulation of the shadow Hamiltonian, which allows efficient generation of momenta. Through analysis and numerical experiments we show that S2HMC consistently gives a speedup greater than 2 over HMC for systems with more than 4,000 atoms. By comparison, using a 500 fs MD trajectory with SHMC gave a maximum speedup of only 1.62 over HMC. S2HMC has the additional advantage of not requiring any user parameters beyond those of HMC. The increased efficiency of SHMC methods is a compromise with the standard deviation of reweighted observables. We provide analysis and guidelines for determining the optimal values. The implementation of S2HMC and the optimal SHMC presented here are available in the open source program ProtoMol. All experimental details have been archived at http://www.nd.edu/ ~lcls/papers/SwHI06a/. ∗Corresponding author: [email protected]