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

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 $O({\tau }^2+1/N)$ 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.

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Cited by in corpus (1)

• On the Mean-Field limit of diffusive games through the master equation: $L^{\infty }$ estimates and extreme value behavior