A quantitative study on the approximation error and speed-up of the multi-scale MCMC (Monte Carlo Markov chain) method for molecular dynamics

The past two decades have borne remarkable progress in the application of the molecular dynamics method in a number of engineering problems. However, the computational efficiency is limited by the massive-atoms system, and the study of rare dynamically-relevant events is challenging at the timescale of molecular dynamics. In this work, a multi-scale molecular simulation algorithm is proposed with a novel toy model that can mimic the state transitions in extensive scenarios. The algorithm consists of two scales, including producing the realistic particle trajectory and probability transition matrix in the molecular dynamics scale and calculating the state distribution and residence time in the Monte Carlo scale. A new state definition is proposed to take the velocity direction into consideration, and different coarsening models are established in the spatial and time scales. The accuracy, efficiency, and robustness of our proposed multi-scale method have been validated, and the general applicability is also demonstrated by explaining two practical applications in the shale gas adsorption and protein folding problems respectively.