论文标题
与随机批处理方法进行相互作用粒子系统的长期行为和长期行为
Ergodicity and long-time behavior of the Random Batch Method for interacting particle systems
论文作者
论文摘要
我们研究了用于相互作用粒子系统的随机批处理方法的几何形状和长时间行为，该方法在最近的大型科学计算实验中表现出卓越的数值性能。我们表明，对于相互作用的粒子系统（IP）和随机批处理相互作用粒子系统（RB-ips），分布定律呈指数呈指数融合到它们各自的不变分布，并且收敛速率不取决于粒子$ n $的数量，时间步长$τ$用于批次划分或批次尺寸尺寸$ p $ $ p $。此外，IPS的不变分布与RB-ips之间的Wasserstein距离受$ O（\sqrtτ）$界定，这表明RB-ips可用于准确地对IPS的不变分布进行采样，并大大降低了计算成本。
We study the geometric ergodicity and the long time behavior of the Random Batch Method for interacting particle systems, which exhibits superior numerical performance in recent large-scale scientific computing experiments. We show that for both the interacting particle system (IPS) and the random batch interacting particle system (RB-IPS), the distribution laws converge to their respective invariant distributions exponentially, and the convergence rate does not depend on the number of particles $N$, the time step $τ$ for batch divisions or the batch size $p$. Moreover, the Wasserstein distance between the invariant distributions of the IPS and the RB-IPS is bounded by $O(\sqrtτ)$, showing that the RB-IPS can be used to sample the invariant distribution of the IPS accurately with greatly reduced computational cost.
