Physics informed topology learning in networks of linear dynamical systems

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.

Efficient and passive learning of networked dynamical systems driven by non-white exogenous inputs

“…For any quantity β ∈ C, we use (β) and (β) to denote its real and imaginary components. We list the following result from [11] that enables consistent estimation of all edges in E (as described in Figure 1), using nodal state trajectories. Lemma 2.1 ( [11]).…”

“…We list the following result from [11] that enables consistent estimation of all edges in E (as described in Figure 1), using nodal state trajectories. Lemma 2.1 ( [11]). For i ∈ V of a well-posed networked LDS, the Wiener filter W i in Eq.…”

“…Continuous time LDS: Considering a fixed sampling time ∆T and a time-discretization function, the continuous time LDS can be converted to a discrete-time LDS with related frequency domainrepresentation [11]. The analysis will involve merging the error due to discretization with the finite sample analysis.…”

“…Very few works discuss learning such systems but are limited to the asymptotic regime (infinite sample limit). Examples include [9,10,11].…”

“…or white Gaussian noise, or that the exogenous inputs are observed [21,22]. On learning networked LDS with temporally correlated inputs (wide-sense stationary and cyclo-stationary) using state observations (not inputs), [11] presents a consistent algorithm using non-causal regression (Wiener filter) for exact recovery. Similarly, [23] recovers the underlying topology in networked LDS using the framework of directed mutual information.…”