In a Networked Dynamical System (NDS), each node is a system whose dynamics are coupled with the dynamics of neighboring nodes. The global dynamics naturally builds on this network of couplings and it is often excited by a noise input with nontrivial structure. The underlying network is unknown in many applications and should be inferred from observed data. We assume: i) Partial observability -- time series data is only available over a subset of the nodes; ii) Input noise -- it is correlated across distinct nodes while temporally independent, i.e., it is spatially colored. We present a feasibility condition on the noise correlation structure wherein there exists a consistent network inference estimator to recover the underlying fundamental dependencies among the observed nodes. Further, we describe a structure identification algorithm that exhibits competitive performance across distinct regimes of network connectivity, observability, and noise correlation.

在网络化动力系统（NDS）中，每个节点是一个与相邻节点的动力学耦合的系统。我们提出了噪声相关性结构的可行性条件，其中存在一致的网络推断估计器以恢复观察节点之间的基本依赖关系。此外，我们描述了一种结构识别算法，该算法在网络连通性、可观测性和噪声相关性的不同情况下表现出竞争性能。

基于部分可观测和空间彩色噪声的网络动力系统推断