Multi-Scale Message Passing Neural PDE Solvers

Léonard Equer, T. Konstantin Rusch, Siddhartha Mishra

Keywords: Graph neural network (GNN), Partial Differential Equation (PDE), Message-Passing, Multi-scale, Long Expressive Memory (LEM), Gradient Gating (G^2)

Abstract: 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.