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Community integration algorithms (CIAs) for dynamical systems on networks
Journal of Computational Physics ( IF 4.1 ) Pub Date : 2022-08-08 , DOI: 10.1016/j.jcp.2022.111524
Tobias Böhle , Mechthild Thalhammer , Christian Kuehn

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.



中文翻译:

网络上动态系统的社区集成算法 (CIA)

大规模网络过程的动力学是所有科学领域的关键现象的基础。大型网络模型的前向模拟通常在计算上是令人望而却步的。然而,大多数网络都有内在的社区结构。我们利用这些社区并提出了一种用于网络动态的快速模拟算法。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。我们开发社区集成算法 (CIA),显着减少功能评估。我们从多项式到线性计算复杂度大幅降低。我们在多种应用中展示了我们的结果,包括用于同步的经典和高阶 Kuramoto 型系统,以及在合成网络和真实网络上表现出集群行为的 Cucker-Smale 系统。数值比较和理论分析证实了中央情报局的稳健性和效率。

更新日期:2022-08-08
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