On the mean-field limit of the Cucker-Smale model with Random Batch Method

Yuelin Wang; Yiwen Lin

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arXiv · 2407.21297

On the mean-field limit of the Cucker-Smale model with Random Batch Method

Yuelin Wang·Yiwen Lin

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Abstract

In this work, we focus on the mean-field limit of the Random Batch Method (RBM) for the Cucker-Smale model. Different from the classical mean-field limit analysis, the chaos in this model is imposed at discrete time and is propagated to discrete time flux. We approach separately the limits of the number of particles $N\to\infty$ and the discrete time interval $\tau\to 0$ with respect to the RBM, by using the flocking property of the Cucker-Smale model and the observation in combinatorics. The Wasserstein distance is used to quantify the difference between the approximation limit and the original mean-field limit. Also, we combine the RBM with generalized Polynomial Chaos (gPC) expansion and proposed the RBM-gPC method to approximate stochastic mean-field equations, which conserves positivity and momentum of the mean-field limit with random inputs.

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Yuelin Wang, Yiwen Lin. 2024-07-31. On the mean-field limit of the Cucker-Smale model with Random Batch Method. https://arxiv.org/abs/2407.21297

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