Year: 2024
Type: article
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.
DOI: 10.1051/m2an/2024071
Authors: Zhenyu Huang, Shi Jin, Lei Li
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid:
OpenAlex ID: W4402889588