  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.
