Random batch sum-of-Gaussians method for molecular dynamics simulations of particle systems

TL;DR

The paper introduces a scalable, efficient random batch sum-of-Gaussians method for molecular dynamics simulations that reduces computational costs and communication overhead while maintaining accuracy for long-range particle interactions.

Contribution

It presents a novel RBSOG method based on Gaussian decomposition and importance sampling, avoiding FFTs and enabling scalable simulations with theoretical guarantees.

Findings

Achieves O(N) computational complexity

Demonstrates high parallel efficiency in simulations

Accurately models long-range interactions in particle systems

Abstract

We develop an accurate, highly efficient and scalable random batch sum-of-Gaussians (RBSOG) method for molecular dynamics simulations of systems with long-range interactions. The idea of the RBSOG method is based on a sum-of-Gaussians decomposition of the Coulomb kernel, and then a random batch importance sampling on the Fourier space is employed for approximating the summation of the Fourier expansion of the Gaussians with large bandwidths (the long-range components). The importance sampling significantly reduces the computational cost, resulting in a scalable algorithm by avoiding the use of communication-intensive fast Fourier transform. Theoretical analysis is present to demonstrate the unbiasedness of the approximate force, the controllability of variance and the weak convergence of the algorithm. The resulting method has $\mathcal{O}(N)$ complexity with low communication latency. Accurate simulation results on both dynamical and equilibrium properties of benchmark problems are reported to illustrate the attractive performance of the method. Simulations on parallel computing are also performed to show the high parallel efficiency. The RBSOG method can be straightforwardly extended to more general interactions with long ranged kernels, and thus is promising to construct fast algorithms of a series of molecular dynamics methods for various interacting kernels.