Structural Inference of Networked Dynamical Systems with Universal Differential Equations
This work addresses the challenge of modeling complex networked systems in fields like biology and engineering, but it is incremental as it builds on existing Universal Differential Equation methods.
The paper tackled the problem of inferring the intrinsic physics, graphical structure, and coupling physics of networked dynamical systems from nodal state observations, using Universal Differential Equations to approximate unknown dynamics with neural networks or known terms. The result demonstrated effectiveness in predicting future states and inferring system behavior on varied network topologies, applied to canonical nonlinear coupled oscillators.
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.