Multi-Scale Message Passing Neural PDE Solvers
This work addresses the challenge of efficiently solving complex PDEs for computational science and engineering, representing an incremental improvement with a novel method for a known bottleneck.
The authors tackled the problem of solving time-dependent PDEs by proposing a multi-scale message passing neural network algorithm, which outperformed baselines on a PDE with varying spatial and temporal scales.
We propose a novel multi-scale message passing neural network algorithm for learning the solutions of time-dependent PDEs. Our algorithm possesses both temporal and spatial multi-scale resolution features by incorporating multi-scale sequence models and graph gating modules in the encoder and processor, respectively. Benchmark numerical experiments are presented to demonstrate that the proposed algorithm outperforms baselines, particularly on a PDE with a range of spatial and temporal scales.