网络上动力系统的社团集成算法
Community Integration Algorithms (CIAs) for Dynamical Systems on Networks
摘要：
大规模网络过程的动力学是所有科学中重要现象的基础。大型网络模型的前向仿真通常在计算上是禁止的。然而，大多数网络都具有内在的社区结构。我们利用这些社区，并提出了一个快速的网络动态模拟算法。特别是，聚合节点接收的输入构成了数值模拟大规模网络动态的限制因素。我们开发社区整合算法（CIA），大大减少功能评估。我们得到了一个实质性的减少，从多项式线性计算复杂性。我们说明了我们的结果在多个应用程序，包括经典和高阶Kuramoto型系统的同步和Cucker-Smale系统表现出群集行为的合成以及现实世界的网络。数值比较和理论分析证实了该算法的鲁棒性和有效性。
英文摘要：
Dynamics of large-scale network processes underlies crucial phenomena ranging across all sciences. Forward simulation of large network models is often computationally prohibitive. Yet, most networks have intrinsic community structure. We exploit these communities and propose a fast simulation algorithm for network dynamics. In particular, aggregating the inputs a node receives constitutes the limiting factor in numerically simulating large-scale network dynamics. We develop community integration algorithms (CIAs) significantly reducing function-evaluations. We obtain a substantial reduction from polynomial to linear computational complexity. We illustrate our results in multiple applications including classical and higher-order Kuramoto-type systems for synchronisation and Cucker--Smale systems exhibiting flocking behaviour on synthetic as well as real-world networks. Numerical comparison and theoretical analysis confirm the robustness and efficiency of CIAs.
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。
