Predicting Dynamic Stability Landscapes in Synchronization Networks

The robustness of synchronization is a central theme of the study of dynamical systems on networks. Typically one attempts to define a single stability index that characterizes the robustness of individual nodes to a class of perturbations. The dependence of a stability index on topology and system parameters can then be studied using network science or GNNs. Here we propose a novel upstream task, Stability Landscapes, that allows deriving many downstream stability indices. To support this task, we release two computationally intensive datasets of 10,000 graphs each at 20 and 100 nodes with per-node landscape labels. The dynamics are given by a conceptual oscillator model that captures aspects of the synchronization behavior of power grids. A compact graph neural network with a CNN decoder predicts these landscapes with about 85\% SSIM in distribution and 67\% under a 20 to 100 size shift, and 65\%-73\% SSIM when going from the 100 node ensemble to realistic power grid topologies with 100-400 nodes. This demonstrates that while basin landscapes are not suitable for study with conventional methods of network science, they are amenable to machine learning methods. This suggests that there is considerable potential in the study of complex networked systems across biology, neuroscience, and power grids, to move beyond scalar stability indices.