论文标题
部分可观测时空混沌系统的无模型预测
Error Analysis of Time-Discrete Random Batch Method for Interacting Particle Systems and Associated Mean-Field Limits
论文作者
论文摘要
随机批处理方法提供了一种有效的算法，用于计算相互作用粒子的规范集合的统计特性。在这项工作中，我们研究了完全离散的随机批次方法的错误估计，尤其是在近似不变分布方面。使用三角形不平等框架，我们表明该方法的长期错误为$ O（\sqrtτ + e^{--λt}）$，其中$τ$是时间步骤，$λ$是不取决于时间步长$τ$或粒子数量或粒子$ n $ n $ n $ n $ n of的收敛速率。我们的结果也适用于McKean-Vlasov过程，这是相互作用粒子系统的平均场限制，作为粒子数量$ n \ rightarrow \ infty $。
The random batch method provides an efficient algorithm for computing statistical properties of a canonical ensemble of interacting particles. In this work, we study the error estimates of the fully discrete random batch method, especially in terms of approximating the invariant distribution. Using a triangle inequality framework, we show that the long-time error of the method is $O(\sqrtτ + e^{-λt})$, where $τ$ is the time step and $λ$ is the convergence rate which does not depend on the time step $τ$ or the number of particles $N$. Our results also apply to the McKean-Vlasov process, which is the mean-field limit of the interacting particle system as the number of particles $N\rightarrow\infty$.
