Entropy defense-by-restore: a GNN-empowered security and trust framework for meteorological cyber-physical-social systems

In meteorological Cyber–Physical–Social Systems (CPSSs), physical sensors, communication networks, and social interactions naturally form a heterogeneous graph–nodes denote weather sensors or human agents, and edges represent both data links and social ties. Graph Neural Networks (GNNs) are expressly designed for learning on these graph structures, making them a natural choice for node classification in CPSSs. Nonetheless, their sensitivity to adversarial perturbations–where even minute disturbances can lead to catastrophic performance degradation–poses a critical challenge for secure and trustworthy meteorological monitoring. In this Research Topic, we introduce **Entropy Defense**, a defense mechanism tailored to meteorological CPSS scenarios. We first extend the Kullback–Leibler divergence–well established for measuring distribution similarity–to assess structural distribution consistency among sensor–social nodes. Building on this, we define two complementary metrics, **feature similarity** and **structural similarity**, and pioneer the addition of new edges between vulnerable nodes to restore legitimate information flows while pruning malicious connections during GNN message passing. To validate our approach, we apply Entropy Defense to three representative GNN architectures and evaluate on four diverse GNN datasets. Experimental results demonstrate that Entropy Defense outperforms three state-of-the-art adversarial defenses in both classification accuracy and stability, offering a lightweight, scalable solution for robust, secure meteorological monitoring in CPSSs.