Physics informed topology learning in networks of linear dynamical systems

Learning influence pathways in 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 includes physical systems with flow conservation, the topology of the interactions can be exactly recovered, even for colored exogenous inputs. The efficacy of the approach is illustrated through simulation and experiments on multiple important networks, including consensus networks, IEEE power networks and EnergyPlus based simulation of thermal dynamics of buildings.