Multi-Scale Message Passing Neural PDE Solvers

L\'eonard Equer; Siddhartha Mishra; T. Konstantin Rusch

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Multi-Scale Message Passing Neural PDE Solvers

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arxiv 2302.03580 v1 pith:4IBPSCOK submitted 2023-02-07 cs.LG cs.NAmath.NAstat.ML

Multi-Scale Message Passing Neural PDE Solvers

L\'eonard Equer , T. Konstantin Rusch , Siddhartha Mishra This is my paper

classification cs.LG cs.NAmath.NAstat.ML

keywords multi-scalealgorithmmessageneuralpassingspatialtemporalbaselines

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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.

Multi-Scale Message Passing Neural PDE Solvers

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