Physics-Aware Random Walk Fingerprints for Scalable Power Grid Graph Classification

Graph neural networks (GNNs) have become a prominent approach for developing fast, topology-aware surrogates in electric power systems, supporting tasks such as power flow (PF) analysis, optimal power flow (OPF) estimation, and cascading failure analysis (CFA). Despite this growing use, formally verifying GNN-based models remains challenging, with existing methods limited in scope. We extend the neural network verification (NNV) framework to graph-structured inputs through GraphStar sets, a generalization of Star sets that captures uncertainty over both node and edge features. This extension enables the propagation of linear message-passing operations and the sound approximation of ReLU nonlinearities for GNN architectures, including graph convolutional network (GCN) and graph isomorphism network with edge features (GINE) layers. We evaluate GNNV across three power system tasks, PF, OPF, and CFA, on the IEEE-24, IEEE-39, and IEEE-118 test cases, as well as two standard graph classification benchmarks, ENZYMES and PROTEINS. Our results show that GNNV provides tighter robustness guarantees than CORA on graph classification models with ReLU-based activations and, for the first time, delivers edge-aware robustness guarantees for GINE-based PF and OPF models under joint node and edge perturbations.

Solving the alternating current power flow equations in real time is essential for secure grid operation, yet classical Newton-Raphson solvers can be slow under stressed conditions. Existing graph neural networks for power flow are typically trained on a single system and often degrade on different systems. We present PowerModelsGAT-AI, a physics-informed graph attention network that predicts bus voltages and generator injections. The model uses bus-type-aware masking to handle different bus types and balances multiple loss terms, including a power-mismatch penalty, using learned weights. We evaluate the model on 14 benchmark systems (4 to 6,470 buses) and train a unified model on 13 of these under N-2 (two-branch outage) conditions, achieving an average normalized mean absolute error of 0.89% for voltage magnitudes and R^2 > 0.99 for voltage angles. We also show continual learning: when adapting a base model to a new 1,354-bus system, standard fine-tuning causes severe forgetting with error increases exceeding 1000% on base systems, while our experience replay and elastic weight consolidation strategy keeps error increases below 2% and in some cases improves base-system performance. Interpretability analysis shows that learned attention weights correlate with physical branch parameters (susceptance: r = 0.38; thermal limits: r = 0.22), and feature importance analysis supports that the model captures established power flow relationships.

Modern power systems face growing operational complexity driven by the integration of renewable energy sources, decentralization, and the need for real-time decision-making across a wide range of timescales. Addressing these challenges traditionally relies on model-based methods that, while accurate, can be too slow for operational demands. Machine learning (ML) has therefore emerged as a faster, data-driven alternative. As grid topology plays a central role in power system operation, graph machine learning (GML) methods offer a natural framework for incorporating topological dependencies as an inductive bias. We survey nearly 800 papers at the intersection of GML and power systems, covering forecasting, state estimation, optimization, control, fault diagnosis, and cybersecurity. Power systems constitute an unusually rich benchmark setting for GML, as they combine hard physical constraints, multi-scale dynamics, safety-critical requirements, and scarce labeled data within a single, well-defined domain. Conversely, power systems can benefit from utilizing GML to complement classical solvers, as GML provide scalable, topology-aware approximations with promising generalization and computational efficiency. We identify open challenges, including limited real-world deployment and the need for interpretable models in safety-critical settings. Despite the rapidly growing number of publications, standardized benchmarks and open datasets remain scarce, leaving many results difficult to reproduce and undermining the long-term scientific credibility of the field. We further derive a structured requirements catalog for ML-ready power grid benchmarks, intended to guide future dataset development and improve reproducibility across studies. We call on the community to prioritize dedicated benchmark studies and the release of open datasets and models.