Dynamical networks are versatile models that can describe a variety of behaviours such as synchronisation and feedback. However, applying these models in real world contexts is difficult as prior information pertaining to the connectivity structure or local dynamics is often unknown and must be inferred from time series observations of network states. Additionally, the influence of coupling interactions between nodes further complicates the isolation of local node dynamics. Given the architectural similarities between dynamical networks and recurrent neural networks (RNN), we propose a network inference method based on the backpropagation through time (BPTT) algorithm commonly used to train recurrent neural networks. This method aims to simultaneously infer both the connectivity structure and local node dynamics purely from observation of node states. 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 dynamical network based on the previously constructed local models until convergence is achieved. This method was found to be succesful in identifying the connectivity structure for coupled networks of Lorenz, Chua and FitzHugh-Nagumo oscillators. Freerun prediction performance with the resulting local models and weights was found to be comparable to the true system with noisy initial conditions. The method is also extended to non-conventional network couplings such as asymmetric negative coupling.

翻译：动力网络是能够描述同步和反馈等多种行为的通用模型。然而，将这些模型应用于现实场景存在困难，因为关于连接结构或局部动力学的先验信息通常未知，必须通过网络状态的时间序列观测加以推断。此外，节点间耦合相互作用的影响进一步增加了隔离局部节点动力学的复杂性。鉴于动力网络与循环神经网络（RNN）在架构上的相似性，我们提出一种基于常用于训练循环神经网络的时间反向传播（BPTT）算法的网络推断方法。该方法旨在仅从节点状态的观测中同时推断连接结构和局部节点动力学。首先利用神经网络构建局部节点动力学的近似，再与改进的BPTT算法交替进行：基于先前构建的局部模型，通过最小化动力网络的预测误差回归相应的网络权重，直至收敛。研究发现，该方法能成功识别洛伦兹、蔡氏和菲茨休-纳古莫振荡器耦合网络的连接结构。利用所得局部模型和权重进行自由运行预测时，其性能与带有噪声初始条件的真实系统相当。该方法还可扩展至非传统网络耦合，例如非对称负耦合。