流数据驱动的多层非线性动力学网络重构

Multilayer nonlinear dynamical network reconstruction from streaming data

现实世界中许多复杂的非线性动力学系统需要用多层网络来描述.如何从观测到的流数据中揭示多层非线性动力学网络结构的重构问题是对动力学系统研究的核心问题之一.虽然学者们提出了许多从静态数据中重构多层动力学网络结构的方法,但是它们很难从流数据中重构多层网络结构.由于该问题的困难性,截止目前,还没有适用于流数据的多层非线性动力学网络重构模型及其优化算法.针对此,本文提出流数据驱动的多层动力学网络重构框架,称为OMNR(online multilayer network reconstruction).OMNR首先建立了流数据驱动的在线多层非线性动力学网络重构模型,然后提出一种基于FTRL(follow-the-regularized-leader)的在线学习方法来优化该模型.OMNR每次只考虑一个事例来更新网络结构,非常适合处理流数据.而且,OMNR空间复杂度非常低,适合大数据任务.最后,在多层网络的Lorenz和R?ssler动力学系统上验证了OMNR可以有效地解决流数据驱动的多层动力学网络重构问题,填补了流数据驱动的多层非线性动力学网络重构技术的空白.

Many complex,real-world dynamic systems need to be described using multilayer networks.Reconstruction of the multilayer nonlinear dynamic network structure from the observed streaming data is one of the core issues of dynamic system research.Although many methods have been proposed to reconstruct multilayer nonlinear dynamic networks from static data,they cannot reconstruct the multilayer network from streaming data.Because of the complexity of the problem,there is no nonlinear dynamic network reconstruction model and its optimization algorithm suitable for streaming data.To resolve this limitation,in this paper,a streaming data-driven multilayer dynamic network reconstruction framework called online multilayer network reconstruction(OMNR)is proposed.OMNR first establishes an online multilayer nonlinear dynamics network reconstruction model for streaming data and then proposes an online learning method based on follow-the-regularized-leader to optimize the reconstruction model.It considers only one case at a time to update the network structure;this is suitable for processing streaming data.Moreover,the space complexity of OMNR is very low and suitable for big-data tasks.Finally,using the Lorenz and R?ssler dynamic systems of the multilayer network,it is verified that OMNR can solve the problem of multilayer dynamic network reconstruction driven by streaming data and fill the gap in the technology of multilayer nonlinear dynamic network reconstruction driven by streaming data.