Mean field error estimate of the random batch method for large interacting particle system
<|reference_start|>Mean field error estimate of the random batch method for large interacting particle system: 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 $O(\tau^2 + 1/N)$ 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 $\tau$ is the time step size and $N$ is the number of particles. Therefore, we improve the existing rate in discretization step size from $O(\sqrt{\tau})$ to $O(\tau)$ in terms of the Wasserstein distance.<|reference_end|>
@article{huang2024mean,
    title={Mean field error estimate of the random batch method for large
  interacting particle system},
    author={Zhenyu Huang, Shi Jin, and Lei Li},
    journal={arXiv preprint arXiv:2403.08336},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.08336},
    primaryClass={math.NA cs.NA}
}