一种新的具有随机批处理策略的避碰模型
A new collision avoidance model with random batch resolution strategy
摘要：
人群仿真的研究具有重要而广泛的应用价值。主要的困难是如何用一个简单的规则来引导所有的粒子，特别是当粒子很多的时候。本文首先提出了一个基于Agent的二维避碰模型，该模型是一个$N$ -粒子牛顿系统。设计了碰撞相互作用力、即将发生的相互作用力和跟随相互作用力，从而可以将粒子引导到各自的目的地而不会发生碰撞。提出的基于代理的模型，然后扩展到相应的平均场极限模型作为$N\to\infty$。其次，注意，直接模拟$N$ -粒子牛顿系统是非常耗时的，因为计算复杂性是$\mathcal{O}(N^2)$阶。与此相反，我们提出了一种有效的混合分辨率策略，以减少计算复杂性。它是随机批处理方法（Shi Jin，Lei Li，and Jian-Guo Liu.相互作用粒子系统的随机批处理方法。Journal of Computational Physics，400：108877，2020.）和基于局部粒子牛顿体系的方法。由于这种混合分辨率策略，计算复杂性降低到$\mathcal{O}(N)$。最后，各种测试，以显示我们的碰撞避免模型和混合解决策略的鲁棒性和效率。
英文摘要：
Research on crowd simulation has important and wide range of applications. The main difficulty is how to lead all particles with a same and simple rule, especially when particles are numerous. In this paper, we firstly propose a two dimensional agent-based collision avoidance model, which is a $N$-particles Newtonian system. The collision interaction force, imminent interaction force and following interaction force are designed, so that particles can be guided to their respective destinations without collisions. The proposed agent-based model is then extended to the corresponding mean field limit model as $N\to\infty$. Secondly, notice that direct simulation of the $N$-particles Newtonian system is very time-consuming, since the computational complexity is of order $\mathcal{O}(N^2)$. In contrast, we propose an efficient hybrid resolution strategy to reduce the computational complexity. It is a combination of the Random Batch method (Shi Jin, Lei Li, and Jian-Guo Liu. Random batch methods (RBM) for interacting particle systems. Journal of Computational Physics, 400:108877, 2020.) and the method based on local particles Newtonian system. Thanks to this hybrid resolution strategy, the computational complexity is reduced to $\mathcal{O}(N)$. Finally, various tests are presented to show robustness and efficiency of our collision avoidance model and the hybrid resolution strategy.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
