| Issue |
ESAIM: M2AN
Volume 59, Number 1, January-February 2025
|
|
|---|---|---|
| Page(s) | 265 - 289 | |
| DOI | https://doi.org/10.1051/m2an/2024071 | |
| Published online | 08 January 2025 | |
Mean field error estimate of the random batch method for large interacting particle system
1
School of Mathematical Sciences, Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai 200240, P.R. China
2
School of Mathematical Sciences, Institute of Natural Sciences, MOE-LSC, Shanghai Jiao Tong University, Shanghai 200240, P.R. China
3
Shanghai Artificial Intelligence Laboratory, Shanghai, P.R. China
* Corresponding author: zhenyuhuang@sjtu.edu.cn
Received:
13
March
2024
Accepted:
5
September
2024
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.
Mathematics Subject Classification: 60H10 / 65C20 / 65C35
Key words: Relative entropy / random batch method / interacting particle system / propagation of chaos
© The authors. Published by EDP Sciences, SMAI 2025
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