Learning influence pathways of a network of dynamically related processes from observations is of considerable importance in many disciplines. In this article, influence networks of agents which interact dynamically via linear dependencies are considered. An algorithm for the reconstruction of the topology of interaction based on multivariate Wiener filtering is analyzed. It is shown that for a vast and important class of interactions, that respect flow conservation, the topology of the interactions can be exactly recovered. The class of problems where reconstruction is guaranteed to be exact includes power distribution networks, dynamic thermal networks and consensus networks. The efficacy of the approach is illustrated through simulation and experiments on consensus networks, IEEE power distribution networks and thermal dynamics of buildings.

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System identification of smart buildings is necessary for their optimal control and application in demand response. The thermal response of a building around an operating point can be modeled using a network of interconnected resistors with capacitors at each node/zone called RC network. The development of the RC network involves two phases: obtaining the network topology, and estimating thermal resistances and capacitance's. In this article, we present a provable method to reconstruct the interaction topology of thermal zones of a building solely from temperature measurements. We demonstrate that our learning algorithm accurately reconstructs the interaction topology for a 5 zone office building in EnergyPlus with real-world conditions. We show that our learning algorithm is able to recover the network structure in scenarios where prior research prove insufficient.

In this article, we present a new approach to reconstruct topology when latent nodes are present in the network. We show that the imaginary part of the inverse power spectral density matrix can be decomposed into the sum of a sparse and a low-rank matrix; the sparse matrix embeds information about the topology of a subgraph restricted to observed nodes. By exploiting the properties of the low-rank matrix, we reconstruct the edges among the observed nodes due to a directed path through a hidden node which could be a chain or a fork. With an assumption on the existence of at least one incoming and outgoing edge from a hidden node to distinct observed nodes and the number of hidden nodes, we reconstruct the exact topology of the generative graph with latent nodes.