  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.
