Superscalability of the random batch Ewald method

Abstract

Coulomb interaction, following an inverse-square force-law, quantifies the amount of force between two stationary and electrically charged particles. The long-range nature of Coulomb interactions poses a major challenge to molecular dynamics simulations, which are major tools for problems at the nano-/micro-scale. Various algorithms are developed to calculate the pairwise Coulomb interactions to a linear scale, but poor scalability limits the size of simulated systems. Here, we use an efficient molecular dynamics algorithm with the random batch Ewald method on all-atom systems where the complete Fourier components in the Coulomb interaction are replaced by randomly selected mini-batches. By simulating the N-body systems up to 108 particles using 10 000 central processing unit cores, we show that this algorithm furnishes O(N) complexity, almost perfect scalability, and an order of magnitude faster computational speed when compared to the existing state-of-the-art algorithms. Further examinations of our algorithm on distinct systems, including pure water, a micro-phase separated electrolyte, and a protein solution, demonstrate that the spatiotemporal information on all time and length scales investigated and thermodynamic quantities derived from our algorithm are in perfect agreement with those obtained from the existing algorithms. Therefore, our algorithm provides a promising solution on scalability of computing the Coulomb interaction. It is particularly useful and cost-effective to simulate ultra-large systems, which is either impossible or very costly to conduct using existing algorithms, and thus will be beneficial to a broad range of problems at nano-/micro-scales.

Improved random batch Ewald method in molecular dynamics simulations

“…For the long-range force, owing to the random batch idea in the Fourier space, a serial importance sampling procedure and a global broadcast operation seems to be required at each MD step. We note that this cost can be significantly reduced by using parallel sampling strategy [36]. The samples and the positions of particles are packaged into 512-bit vectors when the structure factors ρ(k) are evaluated using the local atoms of each MPI rank.…”

“…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].…”

“…This procedure is independently repeated for three times. A highly efficient parallel strategy for the importance sampling under NVT/NPT ensemble is also developed [36]. The MD simulations can then be performed via the random mini-batch approach with this importance sampling strategy.…”

“…In recent years, stochastic algorithms emerge gradually and furnish an important bridge linking traditional methods and modern massive high-performance computing, lifting both efficiency and scalability [36,37]. For electrostatic interactions, the random batch Ewald (RBE) method proposed recently [38,36], has presented its tremendous potential to overcome the scalability issues for deterministic algorithms such as particle-mesh Ewald. The RBE method is based on the Ewald summation.…”

“…It avoids the use of the FFT by employing a random mini-batch importance sampling strategy on the Fourier components to approximate the force and pressure contributions from the long-range part. 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.…”