Reachability-Based Formal Verification of Graph Neural Networks with Node and Edge Features

2026-09-24

AI Summary

This study addresses the challenge of jointly performing formal verification on node and edge features for Graph Neural Network (GNN) models in power systems. By extending the NNV framework, this work introduces the GraphStar set to capture graph-structural uncertainty and designs algorithms for linear message-passing propagation and reliable ReLU nonlinearity approximation. Its core contribution lies in providing the first graph-aware robustness guarantees supporting joint node-edge perturbations, thereby overcoming the limitations of existing methods in verifying graph inputs. Experimental evaluations on power system tasks, including Power Flow (PF) and Optimal Power Flow (OPF), as well as standard benchmarks, demonstrate that the proposed approach yields tighter robustness bounds than CORA and effectively verifies edge-aware capabilities.

Abstract

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.

Problem

• Graph Neural Networks
• Formal Verification
• Reachability Analysis
• Power Systems
• Robustness Guarantees

Innovation

• GraphStar sets
• formal verification
• graph neural networks
• reachability analysis
• edge-aware robustness