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arXiv 2307.03491physics.soc-phmath.DS
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学习用于网络上扩散过程的可解释集体变量

Learning Interpretable Collective Variables for Spreading Processes on Networks

Zuse Institute Berlin(柏林齐泽研究所);FutureLab on Game Theory and Networks of Interacting Agents, Potsdam Institute for Climate Impact Research(波茨坦气候影响研究所博弈论与相互作用智能体网络未来实验室);Potsdam Institute for Climate Impact Research(波茨坦气候影响研究所);Complexity Science Department, Potsdam Institute for Climate Impact Research(波茨坦气候影响研究所复杂性科学系);Department of Mathematics, University of Bayreuth(拜罗伊特大学数学系)

Marvin Lücke, Stefanie Winkelmann, Jobst Heitzig, Nora Molkenthin, Péter Koltai

AI总结:

本文提出一种数据驱动方法,用于学习和理解网络上二元状态扩散过程的低维集体变量,通过四个不同网络示例验证了低维集体变量的存在。

摘要:

集体变量(CVs)是高维系统状态的低维投影。它们用于获取网络上过程复杂涌现动态行为的洞察。CVs与网络度量之间的关系尚未完全理解,其推导通常需要详细的动态系统和网络拓扑知识。本文提出了一种数据驱动的方法,用于算法学习和理解任意拓扑网络上二元状态扩散过程的CVs。我们通过四个示例网络:随机块模型、环形图、随机正则图和由Albert-Barabási模型生成的无标度网络展示了该方法。我们的结果提供了证据,表明即使在理论上尚未理解的情况下,低维CVs也存在。

英文摘要:

Collective variables (CVs) are low-dimensional projections of high-dimensional system states. They are used to gain insights into complex emergent dynamical behaviors of processes on networks. The relation between CVs and network measures is not well understood and its derivation typically requires detailed knowledge of both the dynamical system and the network topology. In this work, we present a data-driven method for algorithmically learning and understanding CVs for binary-state spreading processes on networks of arbitrary topology. We demonstrate our method using four example networks: the stochastic block model, a ring-shaped graph, a random regular graph, and a scale-free network generated by the Albert-Barabási model. Our results deliver evidence for the existence of low-dimensional CVs even in cases that are not yet understood theoretically.

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。

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