GNN-based physics surrogate for predicting PDE solutions
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We introduce a surrogate for the approximation of elastic and hyper-elastic stationary mechanics problems based on graph neural networks (GNNs) trained with mesh-based ground-truth simulations. Our GNNs are an extension of MeshGraphNets [1] to time-independent problems. The latter are particularly challenging because they require fast propagation of the information throughout the domain. The improved MeshGraphNets guarantee the immediate propagation of information between points in the domain that are far apart. This is achieved by 1) augmenting the baseline network with nonlocal connections, or 2) training the network hierarchically, in a multi-grid manner. In this presentation, we show the results of numerical tests for two-dimensional problems characterized by changing domains, materials, and boundary conditions. The prediction accuracy of our results illustrates the ability of the surrogate to generalize to unseen scenarios.
