A GNN trained on two-node graphs provably extrapolates the first-order finite-volume scheme for the heat equation, and with symbolic regression it rediscovers the update rule and suggests higher-order corrections.
Battaglia, Razvan Pascanu, Matthew Lai, David Rezende, and Koray Kavukcuoglu
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Automated discovery of finite volume schemes using Graph Neural Networks
A GNN trained on two-node graphs provably extrapolates the first-order finite-volume scheme for the heat equation, and with symbolic regression it rediscovers the update rule and suggests higher-order corrections.