Graph Neural Networks to Simulate Flexible Pavement Responses Using Three-Dimensional Finite Element Analysis Data

Abstract

The significant computational costs and efforts required for accurate three-dimensional (3D) finite element (FE) pavement response calculations necessitate an expedited approach. This study proposes a graph neural network (GNN)-based simulator for the modeling of 3D pavement structural responses under tire loading. The GNN model was trained using 240 simulations of 3D pavement FE data of flexible pavement structures. The simulator represented the state of pavement structure meshes in FE analysis at any given timestep as a graph, with FE nodes encoded as graph nodes and mesh edges as graph edges. The dynamic behaviors of pavement FEs were computed via learned message-passing between two graphs within two continuous timesteps. The one-step mean squared error (MSE) and rollout MSE were used as evaluation metrics for the GNN model. The results showed that, given an initial state of FE responses, the model could perform accurate one-step predictions, extending to trajectory predictions with one-step MSE as low as $1.21\times {10}^{-8}$ and rollout MSE around $4.55\times {10}^{-5}$ . The prediction framework is efficient; it requires a week of model training but only a mere 5 min of prediction for each single case. This a contrast to traditional 3D FE analyses that can span hours to weeks for a single case. The hyperparameters, including the number of message-passing steps M and the number of historical timesteps C, were established as 10 and 1, respectively, based on model performance and computation time. It was also observed that data normalization before training could significantly reduce model simulation noise.