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| Natura: | Preprint |
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2024
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| Accesso online: | https://arxiv.org/abs/2403.08336 |
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| _version_ | 1866914713050284032 |
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| author | Huang, Zhenyu Jin, Shi Li, Lei |
| author_facet | Huang, Zhenyu Jin, Shi Li, Lei |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_08336 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Mean field error estimate of the random batch method for large interacting particle system Huang, Zhenyu Jin, Shi Li, Lei Numerical Analysis 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. |
| title | Mean field error estimate of the random batch method for large interacting particle system |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2403.08336 |