Structural Inference of Networked Dynamical Systems with Universal Differential Equations

TL;DR

This paper introduces a method using Universal Differential Equations to infer the physics, network structure, and coupling dynamics of complex networked systems from observational data, demonstrated on nonlinear oscillators.

Contribution

It presents a novel framework combining neural networks and known physics to infer system components and structure in networked dynamical systems.

Findings

Effective inference of system physics and network topology.

Accurate future state predictions for complex networks.

Applicable to nonlinear coupled oscillators.

Abstract

Networked dynamical systems are common throughout science in engineering; e.g., biological networks, reaction networks, power systems, and the like. For many such systems, nonlinearity drives populations of identical (or near-identical) units to exhibit a wide range of nontrivial behaviors, such as the emergence of coherent structures (e.g., waves and patterns) or otherwise notable dynamics (e.g., synchrony and chaos). In this work, we seek to infer (i) the intrinsic physics of a base unit of a population, (ii) the underlying graphical structure shared between units, and (iii) the coupling physics of a given networked dynamical system given observations of nodal states. These tasks are formulated around the notion of the Universal Differential Equation, whereby unknown dynamical systems can be approximated with neural networks, mathematical terms known a priori (albeit with unknown parameterizations), or combinations of the two. We demonstrate the value of these inference tasks by investigating not only future state predictions but also the inference of system behavior on varied network topologies. The effectiveness and utility of these methods is shown with their application to canonical networked nonlinear coupled oscillators.