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In a Networked Dynamical System (NDS), each node is a system whose dynamicsare coupled with the dynamics of neighboring nodes. The global dynamicsnaturally builds on this network of couplings and it is often excited by anoise input with nontrivial structure. The underlying network is unknown inmany applications and should be inferred from observed data. We assume: i)Partial observability -- time series data is only available over a subset ofthe nodes; ii) Input noise -- it is correlated across distinct nodes whiletemporally independent, i.e., it is spatially colored. We present a feasibilitycondition on the noise correlation structure wherein there exists a consistentnetwork inference estimator to recover the underlying fundamental dependenciesamong the observed nodes. Further, we describe a structure identificationalgorithm that exhibits competitive performance across distinct regimes ofnetwork connectivity, observability, and noise correlation.

Inferring the Graph of Networked Dynamical Systems under Partial Observability and Spatially Colored Noise