Physics Informed Topology Learning in Networks of Linear Dynamical Systems

TL;DR

This paper introduces a method using multivariate Wiener filtering to accurately reconstruct the influence topology in networks of linear dynamical systems, with applications to power, thermal, and consensus networks.

Contribution

It presents a novel algorithm for exact topology reconstruction in linear influence networks respecting flow conservation, validated through simulations and real-world experiments.

Findings

Exact topology recovery for flow-conserving networks

Effective in power, thermal, and consensus networks

Validated through simulations and real experiments

Abstract

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.