Mean field error estimate of the random batch method for large interacting particle system

2024/03/13 by Zhenyu Huang, Shi Jin, Huang, Zhenyu +3 · 1 citation
Agricultural and Biological Sciences · #Agriculture, Soil, Plant Science #FOS: Mathematics #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2403.08336

openalex publication_date 2024/03/13 · openalex created_date 2024/03/15 · openalex updated_date 2026/08/01

Abstract

The random batch method (RBM) proposed in [Jin et al., J. Comput. Phys., 400(2020), 108877] for large interacting particle systems is an efficient with linear complexity in particle numbers and highly scalable algorithm for N-particle interacting systems and their mean-field limits when N is large. We consider in this work the quantitative error estimate of RBM toward its mean-field limit, the Fokker-Planck equation. Under mild assumptions, we obtain a uniform-in-time O(τ² + 1/N) bound on the scaled relative entropy between the joint law of the random batch particles and the tensorized law at the mean-field limit, where τ is the time step size and N is the number of particles. Therefore, we improve the existing rate in discretization step size from O(√τ) to O(τ) in terms of the Wasserstein distance.

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