Multiparticle moves in acceptance rate optimized monte carlo

Abstract

Molecular Dynamics (MD) and Monte Carlo (MC) based simulation methods are widely used to investigate molecular and nanoscale structures and processes. While the investigation of systems in MD simulations is limited by very small time steps, MC methods are often stifled by low acceptance rates for moves that significantly perturb the system. In many Metropolis MC methods with hard potentials, the acceptance rate drops exponentially with the number of uncorrelated, simultaneously proposed moves. In this work, we discuss a multiparticle Acceptance Rate Optimized Monte Carlo approach (AROMoCa) to construct collective moves with near unit acceptance probability, while preserving detailed balance even for large step sizes. After an illustration of the protocol, we demonstrate that AROMoCa significantly accelerates MC simulations in four model systems in comparison to standard MC methods. AROMoCa can be applied to all MC simulations where a gradient of the potential is available and can help to significantly speed up molecular simulations.

Monte-Carlo Simulations of Soft Matter Using SIMONA: A Review of Recent Applications

“…Two methods for MC move generation are provided in SIMONA: the Generic Metropolis MC [31] and AROMoCa [5]. The total rates of states (Γ) moving from a point p-p′, Γ(p → p′) must be equal to the backwards rate Γ(p′ → p) to satisfy the detailed balance condition.…”

“…The selection is made from a uniform and random distribution equation to choose a random coefficient. Finally, the moves with large forces and probabilities are evaluated by the acceptance criteria [5] (further details are in Ref. [5]).…”

“…Methods with a force-biased move construction, using an energy estimator to increase the MC simulation efficiency, are suitable to generate moves with many degrees of freedom. Examples are forced bias MC [3,4] and AROMoCa (Acceptance Rate Optimized Monte-Carlo) approach [5], which is a generic MC protocol that has been proven to be effective compared with generic MC methods.…”