Learning Dynamic Stability Landscapes in Synchronization Networks

Spatio-temporal graph neural networks (STGNNs) are widely used for short-term forecasting in dynamic physical systems such as traffic and weather. However, the prevailing evaluation practice uses real world benchmark data sets in a single domain with a single fixed holdout splits, making it difficult to compare architectures across different dynamical regimes. We introduce ChaosNetBench (CNB), a synthetic benchmark dataset and evaluation framework for studying STGNN performance under controlled multidimensional chaotic dynamics. CNB is built on a lattice of coupled standard maps with independently tunable local chaos ($K$), coupling strength ($\varepsilon$), and system size ($N$), providing known topology and known dynamics across 96 system instances and 9{,}600 trajectories. We introduce chaos indicators, evaluation metrics and a protocol to analyze and compare the capacity of STGNN architectures to deal with different levels of local and global chaos. We illustrate the usage of the framework by analyzing 13 architectures (5 STGNNs and 8 non-graph baselines). The results reveal a regime dependent transition in which non-graph baselines (TCN, N-BEATS, iTransformer) remain competitive when there is low local chaos, while STGNNs (e.g., Graph WaveNet, D2STGNN, STAEformer) are generally more resilient to higher levels of local and global chaos. CNB provides a practical, reusable testbed for systematically comparing and analyzing the capacity of STGNN architectures to handle different levels of local and global chaos.

Collective behavior arises when locally interacting units produce coordinated global organization, from synchronization in dynamical systems to task-relevant information flow on graphs. The central challenge is not only to explain how collective behavior emerges, but to design local interaction rules that can produce desired global organization and generalize across graphs, dynamics and tasks.To address this challenge, we introduce the Swarm-Inspired Emergent Synchronizer (SIES), a graph-dynamical framework that learns generalizable local-interaction laws for controllable collective organization. Each node is an agent-like dynamical unit with a state and task cue, and signed source-target-conditioned attention acts as an adaptive coupling term inside an explicit evolution model. Therefore, SIES combines an explicit dynamical engine with local agent intelligence, similar to biological swarms. For synchronization control, SIES learns a generalizable coupling operator that produces prescribed synchronization patterns for CDSs across untrained network scales, target phase relations, and intrinsic node dynamics without retraining. The learned operator also reaches gait-related modes faster than three oscillator baselines and generalizes synchronization-driven locomotion to simulated multi-legged robots of different scales and a physical hexapod after leg disablement. For graph representation learning, SIES applies the same signed interaction principle to message passing and achieves the highest performance among the compared methods on heterophilous node-classification benchmarks. Together, these results position SIES as a generalizable and learnable graph-dynamical interaction framework with promise for synchronization control, adaptive robot coordination, and heterophilous graph representation learning.

Utilities increasingly rely on planning and operational tools to cope with the increased penetrations of distributed energy resources, yet the lack of realistic, openly available datasets remains a major barrier for benchmarking and comparison. Traditional test feeders, and recently proposed large-scale synthetic networks alleviate this issue but are typically based on heuristic rules and do not learn directly from data. This paper proposes a generative framework based on Generative Adversarial Networks (GANs) to create power distribution network layouts using image-based representations. The model is trained on rasterised views of distribution systems and can operate in two modes: an unconditional configuration that learns layout patterns from the training dataset, and conditional configurations that incorporate geographical context such as street maps and the spatial distribution of consumers. The methodology includes dataset preparation from Geographic Information System (GIS) sources, GAN architecture design, and the analysis of training stability and image resolution. Results from three representative cases show that the proposed approach can reproduce the topologies of low (LV), medium (MV) and high voltage (HV) feeders and align generated layouts with underlying geographical structures. At the same time, the study reveals limitations related to training stability, resolution-dependent artefacts and limits, and the absence of explicit electrical constraints. The proposed framework constitutes a data-driven complement to existing synthetic network generation methods, and could be applied to propose distribution network layouts for the electrification of new areas. This would require future extensions towards power flow, electrically validated models.