Learning Networked Dynamic System Models with Weak Form and Graph Neural Networks

This paper presents a framework for developing data-driven, control-oriented models of networked systems, i.e., systems that involve many interacting dynamic components. First, a general formulation named the weak latent dynamics model (wLDM) is developed for learning generic nonlinear dynamics with control. Leveraging the weak form, the wLDM enables more numerically stable and computationally efficient training, as well as more accurate prediction when compared to conventional methods such as neural ordinary differential equations. Building upon the wLDM, we propose the weak graph Koopman bilinear form model, which integrates geometric deep learning and Koopman theory to learn latent-space dynamics for networked systems, especially for challenging cases that have multiple timescales. The proposed methods are demonstrated on three examples of increasing complexity, from academic problems to an application of an electrified aircraft energy system, showing that they achieve superior predictive accuracy and training efficiency when compared to baseline models. Parametric studies provide insights into the effects of hyperparameters in the weak form. The proposed framework shows the capability to efficiently capture control-dependent dynamics in these systems, including stiff dynamics and multiphysics interactions, offering a promising direction for learning control-oriented models of complex networked systems.