Response flow graph neural network for capacitated network reliability analysis

Capacitated network reliability (CNR) analysis is essential for computing the reliability of diverse networks. The NP-hard nature of CNR problems makes exact solutions through exhaustive permutations impractical for many real-world engineering networks. In this research, a new graph-based neural network termed the response flow graph neural network (RFGNN) is developed to address CNR problems. The innovation of the proposed method comprises three key components. Firstly, an iteration equation is proposed to update network link weights by identifying nodes where flow is obstructed during propagation. Secondly, a novel expression is developed to amalgamate local neighborhood information for each node by incorporating the updated link weights, culminating in the creation of the RFGNN. Thirdly, an adaptive framework is developed to improve the prediction accuracy of the RFGNN in solving CNR problems. Several CNR problems are presented to assess the efficacy of the developed method. The results unequivocally demonstrate the effectiveness of the developed method. Furthermore, the RFGNN exhibits remarkable computational accuracy when estimating CNRs across various sub-networks once it is appropriately constructed from the original network. This represents a capability that conventional non-machine learning methods typically struggle to attain.