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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.08336 |
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Table of Contents:
- 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 $O(τ^2 + 1/N)$ 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 $τ$ is the time step size and $N$ is the number of particles. Therefore, we improve the existing rate in discretization step size from $O(\sqrtτ)$ to $O(τ)$ in terms of the Wasserstein distance.