Physics Informed Topology Learning in Networks of Linear Dynamical Systems
This work addresses the challenge of reconstructing interaction topologies in dynamic networks, which is important for applications like power systems and building thermal management, but it appears incremental as it builds on existing filtering methods with specific constraints.
The paper tackles the problem of learning influence pathways in networks of linear dynamical systems by analyzing an algorithm based on multivariate Wiener filtering, showing that exact topology recovery is possible for interactions respecting flow conservation, such as in power distribution and consensus networks, with efficacy demonstrated through simulations and experiments.
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.