Learning Dynamic Stability Landscapes in Synchronization Networks

The robustness of synchronization is typically characterized by scalar, per-node stability indices whose dependence on topology is studied via network science or graph neural networks (GNNs). We propose a novel upstream task, stability landscapes, which provide deeper insights into synchronization behavior and from which many such scalar indices can be derived. Crucially, we pioneer a graph-to-image prediction paradigm: learning image-like landscapes as per-node targets directly from graph topology, a formulation we are not aware of having been established elsewhere in the literature. To support this task, we release two datasets of 10,000 graphs each at 20 and 100 nodes with per-node landscape labels, based on a conceptual oscillator model, capturing power grid synchronization behavior. A GNN encodes topology and a CNN decoder renders per-node images, learned end-to-end with good in-distribution accuracy, generalizing across graph sizes and to realistic power grid topologies. This demonstrates that stability landscapes, while beyond the reach of conventional network science, are learnable from topology and open new avenues for moving beyond scalar stability indices in biology, neuroscience, and power grids.

Many natural and engineered systems, from power grids to the brain, consist of large numbers of interacting components that can fall into rhythmic, coordinated behavior called synchronization. Whether this synchronization is beneficial or harmful depends on the context: in power grids, it keeps the electricity flowing; in the brain, too much of it can trigger epileptic seizures. Either way, understanding how stable this synchronized state is when something goes wrong, say a sudden disturbance at one location in the network, is a question of practical importance. Traditionally, researchers summarize this stability by a single number per component, which gives a rough sense of how easily that component can be knocked out of sync. But a single number discards a lot of information. Researchers have therefore long used stability landscapes: pictures that show, for every possible disturbance at a given component, whether the system recovers or falls apart. These landscapes are far more informative, but computing them the conventional way is very expensive. We show that a machine learning model can learn to predict these landscape pictures directly from the wiring structure of the network, without running expensive simulations. To our knowledge, this is the first time images have been predicted as outputs for individual network components, a setup that may prove useful beyond synchronization, wherever a visual or spatial description of node behavior is more informative than a single number. The model looks at how components are connected and produces a landscape picture for each one, works well on networks it was trained on, and generalizes to larger networks and real power grid structures it has never seen before. This opens the door to fast, detailed stability assessments for complex networked systems across science and engineering.