Random-batch list algorithm for short-range molecular dynamics simulations

Abstract

We propose a fast method for the calculation of short-range interactions in molecular dynamics simulations. The so-called random-batch list method is a stochastic version of the classical neighbor-list method to avoid the construction of a full Verlet list, which introduces two-level neighbor lists for each particle such that the neighboring particles are located in core and shell regions, respectively. Direct interactions are performed in the core region. For the shell zone, we employ a random batch of interacting particles to reduce the number of interaction pairs. The error estimate of the algorithm is provided. We investigate the Lennard-Jones fluid by molecular dynamics simulations and show that this novel method can significantly accelerate the simulations with a factor of several fold without loss of the accuracy. This method is simple to implement, can be well combined with any linked cell methods to further speed up and scale up the simulation systems, and can be straightforwardly extended to other interactions, such as Ewald short-range part, and thus it is promising for large-scale molecular dynamics simulations.

Improved random batch Ewald method in molecular dynamics simulations

“…The RBL is an extension of the original random batch method [41] by dividing the region into a core-shell structure and constructing the minibatch for particles in the shell region. This idea works well for the LJ potential [40], and in this paper we demonstrate its further extension in the IRBE method for a united scheme of the non-bonded interactions is effective. We present the accuracy and stability analysis of the IRBE method.…”

“…Another remark is that the IRBE method brings in an additional variance in the force term, leading to the numerical heating effect. Therefore, at the moment, this method is not suitable for long time simulations under the microcanonical ensembles, similar to the previous work [38,40]. One shall develop an appropriate symplectic scheme for the time integration of the equations of motion, which remains an open problem for our stochastic algorithms.…”

“…The RBE has shown its superscalibility in large-scale all-atom simulations [36], resulting in that the evaluation of short-range non-bonded interactions becomes the most timeconsuming part [39]. To reduce the calculation for short-range interactions and save CPU memory in the original RBE method, we introduce the RBL algorithm, first proposed for pure LJ fluid systems [40].…”

“…The central particle then interacts with the batch particles with a rescaled strength. This idea is demonstrated that the average interacting neighbors of each particle are significantly reduced, and the accuracy is maintained by resolving the kernel singularity issue for the LJ systems [40].…”

“…Since its superior speedup in the Fourier space, it is pointed out [36,39] that the short-range part becomes the bottleneck of the MD simulations, and a further acceleration requires a high-efficient treatment of the short-range contributions of the non-bonded force, including the LJ and the real part of the Ewald splitting. For this purpose, in this paper we propose an improved RBE (IRBE) method employing the random batch list (RBL) scheme [40] to accelerate the short-range calculation under the RBE framework. Basically, the RBL does the random batch in the real space, resulting in a significant reduction in the number of neighbors for each particle.…”