用图像化方法学习同步网络的动态稳定性，揭示传统指标无法捕捉的系统行为。
Learning Dynamic Stability Landscapes in Synchronization Networks
- 将图结构直接映射为节点级稳定性图像，开创图到图像预测新范式。
- 在20和100节点的仿真数据上实现高精度端到端学习，跨规模泛化良好。
- 适用于电力系统、神经科学等领域，推动从单一指标向全局稳定分析演进。
同步网络的鲁棒性通常通过节点级的标量稳定性指标来刻画，其与拓扑结构的关系常通过网络科学或图神经网络（GNN）研究。本文提出一项新型上游任务——学习稳定性景观，可提供对同步行为更深入的理解，并从中推导出多种标量指标。关键创新在于首次建立图到图像的预测范式：直接从图拓扑学习节点级图像化的稳定性景观，这一形式在现有文献中尚未见报道。为此，我们构建了两个各含10,000张图的数据集（分别对应20和100个节点），基于概念振荡器模型生成，模拟电力系统同步行为并标注每节点的景观标签。采用GNN编码拓扑，CNN解码生成图像，实现端到端训练，在分布内表现优异，且能跨图规模推广至真实电力网拓扑。结果表明，尽管传统网络科学难以触及，稳定性景观仍可从拓扑中学习，为生物学、神经科学及电力系统等领域突破标量稳定性指标局限开辟新路径。
原文摘要 · Abstract (English)
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, learning 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.
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