Lai Pik-Yin
Department of Physics and Center for Complex Systems, National Central University, Chung-Li District, Taoyuan City 320, Taiwan, Republic of China.
Phys Rev E. 2017 Feb;95(2-1):022311. doi: 10.1103/PhysRevE.95.022311. Epub 2017 Feb 24.
Reconstructing network connection topology and interaction strengths solely from measurement of the dynamics of the nodes is a challenging inverse problem of broad applicability in various areas of science and engineering. For a discrete-time step network under noises whose noise-free dynamics is stationary, we derive general analytic results relating the weighted connection matrix of the network to the correlation functions obtained from time-series measurements of the nodes for networks with one-dimensional intrinsic node dynamics. Information about the intrinsic node dynamics and the noise strengths acting on the nodes can also be obtained. Based on these results, we develop a scheme that can reconstruct the above information of the network using only the time-series measurements of node dynamics as input. Reconstruction formulas for higher-dimensional node dynamics are also derived and illustrated with a two-dimensional node dynamics network system. Furthermore, we extend our results and obtain a reconstruction scheme even for the cases when the noise-free dynamics is periodic. We demonstrate that our method can give accurate reconstruction results for weighted directed networks with linear or nonlinear node dynamics of various connection topologies, and with linear or nonlinear couplings.
仅从节点动力学测量中重建网络连接拓扑和相互作用强度是一个具有挑战性的逆问题，在科学和工程的各个领域都有广泛的应用。对于处于噪声环境下的离散时间步网络，其无噪声动力学是平稳的，我们推导出了一般的解析结果，将网络的加权连接矩阵与从具有一维内在节点动力学的网络的节点时间序列测量中获得的相关函数联系起来。还可以获得有关内在节点动力学和作用于节点的噪声强度的信息。基于这些结果，我们开发了一种方案，该方案仅使用节点动力学的时间序列测量作为输入，就可以重建网络的上述信息。还推导了高维节点动力学的重建公式，并通过二维节点动力学网络系统进行了说明。此外，我们扩展了我们的结果，甚至在无噪声动力学是周期性的情况下也获得了一种重建方案。我们证明，对于具有各种连接拓扑、线性或非线性节点动力学以及线性或非线性耦合的加权有向网络，我们的方法可以给出准确的重建结果。
