A Backpropagation Algorithm for Inferring Disentagled Nodal Dynamics and Connectivity Structure of Dynamical Networks

Abstract

Dynamical networks are versatile models that describe a variety of behaviours such as synchronisation and feedback in networks of coupled dynamical components. However, applying these models in real systems is difficult as prior information of the connectivity structure or local dynamics is often unknown and must be inferred from node state observations. Additionally, the influence of coupling interactions complicates the isolation of local node dynamics. Given the architectural similarities between dynamical networks and recurrent neural networks (RNNs), we propose a network inference method based on the backpropagation through time (BPTT) algorithm used to train RNNs. This method aims to simultaneously infer both the connectivity structure and isolated local node dynamics from node state observations. An approximation of local node dynamics is first constructed using a neural network. This is alternated with an adapted BPTT algorithm to regress corresponding network weights by minimising prediction errors of the network based on the previously constructed local models until convergence. This method was successful in identifying the connectivity structure for coupled networks of chaotic oscillators. Freerun prediction performance with the resulting local models and weights was comparable to the true system with noisy initial conditions. The method is also extended to asymmetric negative coupling.