Research On Network Reconstruction Algorithms Based On Differential Equations

Network reconstruction, also known as network inference, means to infer the interactions between nodes from measured data. Network topology not only helps understand the inner mechanism, but also benefits to predict or change the dynamic behavior.This thesis explores the network reconstruction algorithms based on differential equations. The main contributions of this thesis are summarized as follows:1. For a special kind of linear networked systems, where all nodes are observable while only parts of nodes can be controlled directly by external inputs, we propose a dynamical structure function based reconstruction algorithm, in which a unique system structure can be obtained from time-series data and steady-state data regardless of the controllability. Specifically, the topological relationship among nodes with input are first obtained via dynamical structure function; and then, the in?uences from the nodes with input to the nodes without are deduced from the transfer function; finally,a convex optimization algorithm is proposed to infer the full structure of the network.Simulations show that our algorithm has higher reconstruction precision than convex programming algorithm. Compared with the classic system realization, our algorithm can be applied to uncontrollable linear systems.2. We propose a reconstruction algorithm, which combines information theory and differential equations, to reconstruct the network structure with steady-state data.Firstly the algorithm calculates the mutual information between any two nodes. Secondly, according to mutual information values, links are chosen for each node by multiple regression. Considering of the sparsity and nonuniform nature in actual networks,the in-degree of each node is determined by a criterion. Simulations show that, compared with the NIR algorithm and convex programming algorithm, which are based on differential equations, our algorithm has wider application range, lower computational complexity and higher reconstruction precision.