Random batch sum-of-Gaussians method for molecular dynamics simulation of particle systems in the NPT ensemble

TL;DR

This paper introduces RBSOG, a novel scalable method for molecular dynamics in the NPT ensemble that reduces variance and computational cost while accurately capturing pressure and structural properties.

Contribution

The paper develops a new random batch sum-of-Gaussians approach with measure-recalibration for efficient, unbiased pressure estimation in large-scale NPT molecular dynamics simulations.

Findings

Achieves about 10x speedup over particle-particle particle-mesh methods.

Reduces variance by 4x compared to existing random batch Ewald methods.

Maintains accuracy in structural and dynamical observables across various systems.

Abstract

In this work, we develop a random batch sum-of-Gaussians (RBSOG) method for molecular dynamics simulations of charged systems in the isothermal-isobaric (NPT) ensemble. We introduce an SOG splitting of the pressure-related $1/r^3$ kernel, yielding a smooth short-/long-range decomposition for instantaneous pressure evaluation. The long-range part is treated in Fourier space by random-batch importance sampling. Because the radial and non-radial pressure components favor different proposals, direct sampling either increases structure-factor evaluations and communication or leads to substantial variance inflation. To address this tradeoff, we introduce a measure-recalibration strategy that reuses Fourier modes drawn from the radial proposal and corrects them for the non-radial target, producing an unbiased pressure estimator with significantly reduced variance and negligible extra cost. The resulting method mitigates pressure artifacts caused by cutoff discontinuities in traditional Ewald-based treatments while preserving near-optimal $O(N)$ complexity. We provide theoretical evidence on pressure decomposition error, consistency of stochastic approximation, and convergence of RBSOG-based MD. Numerical experiments on bulk water, LiTFSI ionic liquids, and DPPC membranes show that RBSOG accurately reproduces key structural and dynamical observables with small batch sizes ($P\sim 100$). In large-scale benchmarks up to $10^7$ atoms on $2048$ CPU cores, RBSOG achieves about an order-of-magnitude speedup over particle-particle particle-mesh in electrostatic calculations for NPT simulations, together with a consistent $4\times$ variance reduction relative to random batch Ewald and excellent weak/strong scalability. Overall, RBSOG provides a practical and scalable route to reduce time-to-solution and communication cost in large-scale NPT simulations.