矩信息力重缩放用于随机批量朗之万动力学

中文摘要 AI 辅助

随机批量方法通过用随机力估计器替代全相互作用求和来加速分子动力学模拟。然而，在朗之万模拟中，随机批量力误差可能导致人为加热，并扭曲平衡态和动力学可观测量，尤其是在小批量尺寸或弱恒温器耦合下。此外，这些误差的大小可能因粒子而异。我们引入了用于随机批量列表（Mi-RBL）和随机批量Ewald（Mi-RBE）方法的矩信息力重缩放。在当前批量采样之前，每个粒子采样力强度的滞后平均值设定一个各向同性增益，从而在不改变方向的情况下改变随机批量力的幅度。正式的有限时间分析量化了偏差-方差权衡，稳态动能温度误差的估计预测了动能误差随时间步长和恒温器摩擦的缩放关系。在共存、二元混合物和电解质测试中，Mi-RBL和Mi-RBE减少了动能误差，并更接近地再现了参考解的均方位移、径向分布函数和电荷密度分布。Mi-RBE还将动能误差随时间步长的增长率降低了一半以上，并保留了预测的恒温器摩擦依赖性。测试的重缩放强度随批量尺寸增大而减小，粒子级更新在固定批量尺寸下保持O(N)复杂度。

英文摘要

Random-batch methods accelerate molecular dynamics by replacing full interaction sums with stochastic force estimators. In Langevin simulations, however, random-batch force errors can cause artificial heating and distort equilibrium and dynamical observables, especially for small batch sizes or under weak thermostat coupling. Moreover, the magnitude of these errors can vary across particles. We introduce moment-informed force rescaling for random-batch list (Mi-RBL) and random-batch Ewald (Mi-RBE) methods. A lagged average of each particle's sampled-force intensity sets an isotropic gain before the current batch is sampled, changing the random-batch force magnitude without changing its direction. The formal finite-time analysis quantifies the bias--variance tradeoff, and an estimate of the steady-state kinetic-temperature error predicts the scaling of the kinetic error with time step and thermostat friction. In the coexistence, binary-mixture, and electrolyte tests, Mi-RBL and Mi-RBE reduce kinetic errors and more closely reproduce the mean-square displacement, radial distribution function, and charge density profiles of the reference solutions. Mi-RBE also reduces the growth rate of the kinetic error with the time step by more than half and retains the predicted dependence on thermostat friction. The tested rescaling strength decreases with increasing batch size, and the particlewise update retains $O(N)$ complexity for fixed batch size.

发表机构

• School of Mathematical Sciences, Shanghai Jiao Tong University（上海交大数学科学学院）
• National University of Singapore（新加坡国立大学）
• SOG AI-Technology Co. Ltd.（商汤科技）

机构由 AI 辅助整理，请以论文原文为准。