New Hybrid Monte Carlo Methods for Efficient Sampling:from Physics to Biology and Statistics

Abstract

We introduce a class of novel hybrid methods for detailed simulations of large complex systems in p hysics, biology, materials science and statistics. These generalized shadow Hybrid Monte Carlo (GSHMC) methods combine the advantages of stochastic and deterministic simulati on techniques. They utilize a partial momentum update to retain some of the dynamical information, employ modified Hamiltonians 1-3) to overcome exponential performance degradation with the system’s size and make use of multi-scale natur e of complex systems. Variants of GSHMCs were developed for atomistic simulation, particle simulation and stati stics: GSHMC (thermodynamically consistent implementation of constant-temperature molecular dynamics), MTS-GSHMC (multiple-time-stepping GSHMC), meso-GSHMC (Metropolis corrected dissipative particle dynamics (DPD) metho d), and a generalized shadow Hamiltonian Monte Carlo, GSHmMC, (a GSHMC for statistical simulations). All of these are compatible with other enhanced sampling techniques and suitable for massively parallel computing allowing for a ran ge of multi-level parallel strategies. A brief description of the GSHMC approach, examples of its application on high performance computer s and comparison with other existing techniques are given . Our approach is shown to resolve such problems as resonance instabilities of the MTS methods and non-preservati on of thermodynamic equilibrium properties in DPD, and to outperform known methods in sampling efficiency by an order of magnitude.