# A GNN-Based False Data Detection Scheme for Smart Grids
## 1 Introduction  
The Internet of Things (IoT) is boosting the progress of Cyber Physical Systems (CPSs), which build a complex communication system on top of physical processes [1] by integrating information flowing between several interconnected sensors and controllers. Smart grids, as an example of CPSs, also deploy a large number of sensors, measurement devices, and controllers on top of the power network. Sensors collect grid data and transmit them over the network to the control center, which gives instructions to the controllers in the power network for critical tasks based on the collected data [2]. Due to the high level of integration between communication systems and physical systems in CPSs, cyber attacks against communication systems can not only affect the operation of communication systems, but can also have a serious impact on physical systems, leading to serious consequences such as grid failure [3]. The smart grid integrates the cutting-edge information and communication technology (ICT) to achieve real-time surveillance, optimization, and the control of power supply and demand, improving the efficiency, reliability, and flexibility of the power system. By applying advanced sensors and devices at key nodes, such as substations, transmission lines, and user terminals, IoT technology has achieved real-time data collection and human-computer interaction. These apparatuses are able to gather real-time data and transmitthem to a central processing system for analysis and processing through a communication network, providing real-time status of the power system for staff and allowing timely decision-making on potential issues. The application of IoT technology has improved the real-time monitoring capability of smart grids, allowing them to predict system failures, quickly alert users of emergencies, and automatically adjust grid configurations to maintain power supply stability. For example, in Figure 1, the communication system contains three control centers \(X_{1}\), \(X_{2}\), and \(X_{3}\), and the power system contains two generators \(Y_{2}\) and \(Y_{3}\) and two power relay nodes \(Y_{1}\) and \(Y_{4}\). If \(X_{2}\) in the communication system fails by a network attack, it will cause \(Y_{2}\) generators in the power system to stop working, and the corresponding two relay nodes \(Y_{1}\) and \(Y_{4}\) in the power system will also fail, which in turn will lead to the failure of \(X_{1}\) and \(X_{3}\) in the communication system according to the cascading failure in the coupling network, which may eventually lead to the collapse of the entire power system. For example, in 2019, malicious attacks against hydroelectric centers caused nationwide power outages in Venezuela [4]. Therefore, ensuring cybersecurity in the smart grid is critical to national security. Deep learning (DL), thanks to its powerful data abstraction capabilities, is able to extract potential connections between anomalies and data in communication systems. Thus, deep learning is extensively utilized for anomaly detection in Cyber-Physical Systems (CPSs) [2; 5; 6]. Given the nature of the Industrial Internet of Things (IIoT), in which devices are interconnected, it is appropriate to use a graph to represent the spatial relationships between devices. Traditional deep learning models are mainly devised to manage data with Euclidean structures, encompassing texts and images, which can not effectively capture the spatial information within more intricate non-Euclidean structures. By contrast, GNN enhances deep neural networks by incorporating both network structures and node features, which allows it to effectively handle graph-structured data. This makes a GNN particularly well-suited for anomaly detection in smart grids, utilizing spatial information. For example, in [7], the weather data obtained from sensor measurements are processed to measure the possibility of power outages through a graph neural network.