在数据驱动下发现集体运动的随机动态方程
Arshed Nabeel1,2, Vivek Jadhav1, Danny Raj M3
1Center for Ecological Sciences, Indian Institute of Science, Bengaluru, India.
Physical biology
|June 27, 2023
概括
介面层聚合模型揭示了对对相互作用中的噪声诱导的顺序,以及高阶相互作用中的结合决定性/随机力. 数据驱动的方法揭示了从平均场理论中偏离的大小依赖的动态.
科学领域:
- 复杂的系统复杂的系统.
- 统计物理 统计物理
- 集体行为 集体行为
背景情况:
- 集群的宏观模型往往忽略了在中观尺度 (10-100个体) 中至关重要的随机性.
- 现有的中视镜模型通常缺乏空间组件,这限制了它们对现实世界群聚现象的适用性.
- 开发空间中观方程,特别是随机微分方程,在计算上具有挑战性.
研究的目的:
- 为集体运动的空间自行运动粒子 (SPP) 模型构建随机的介视描述.
- 为了研究相互作用顺序 (双向与更高顺序) 在群聚动态上的作用.
- 探索群体大小和相互作用参数对群体行为的影响.
主要方法:
- 采用一种新的数据驱动式方程学习方法来导出介面尺度方程.
- 分析了一个空间SPP模型,其中有不同的交互社区:k=1 (对式),k=2 (三元),以及所有邻居 (Vicsek-like).
- 研究了介面镜方程参数,群体大小,密度和相互作用半径之间的关系.
主要成果:
- 随机对交互导致由乘数噪声驱动的"噪声诱导的群体".
- 高阶相互作用 (k>1) 导致由确定性和随机性力量统治的集体秩序.
- 介面参数 - 种群大小关系偏离平均场预测,受密度和相互作用半径的影响.
结论:
- 突出介绍了中视镜描述对于理解群体系统的关键重要性.
- 展示了数据驱动式方程发现的力量,用于建模复杂系统.
- 提供了对噪音驱动现象和生物系统中大小依赖的集体行为的见解.
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