Multiscale Neural Operators for Solving Time-Independent PDEs
Winfried Ripken Lisa Coiffard Felix Pieper Sebastian Dziadzio
Time-independent Partial Differential Equations (PDEs) on large meshes pose
significant challenges for data-driven neural PDE solvers. We introduce a novel
graph rewiring technique to tackle some of these challenges, such as
aggregating information across scales and on irregular meshes. Our proposed
approach bridges distant nodes, enhancing the global interaction capabilities
of GNNs. Our experiments on three datasets reveal that GNN-based methods set
new performance standards for time-independent PDEs on irregular meshes.
Finally, we show that our graph rewiring strategy boosts the performance of
baseline methods, achieving state-of-the-art results in one of the tasks.