Infrastructure networks, such as transportation networks and utility distribution systems, play an essential role in maintaining basic operations of a society. Ensuring their functionality, even under disruptive events, is crucial. In this context, reliability analysis plays a central role, yet it remains challenging because of the large size and complexity of the systems and the low probabilities associated with failure events. To address these issues, we develop a physics-informed neural network (PINN) to assess systems that are represented as a graph (i.e., an abstract object consisting of links and nodes). Training a neural network (NN) in advance facilitates rapid predictions of system states. The proposed PINN model is trained by utilizing the physical constraint that a target quantity (e.g., traffic flows and electricity) can be delivered only through neighboring links and nodes. By informing an NN of components’ dependence that is implied by network topology, we can expedite the training process and make the model less sensitive to network size. Moreover, by developing the PINN to make probabilistic predictions, we can quantify the uncertainty of the failure probability estimate and thereby avoid overconfidence. The proposed method is applied to transportation networks.

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