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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

Léonard Equer , T. Konstantin Rusch , Siddhartha Mishra This is my paper · ORCID
classification cs.LGcs.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.

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Cited by 1 Pith paper

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  1. A Deep Learning approach for parametrized and time dependent Partial Differential Equations using Dimensionality Reduction and Neural ODEs

    cs.LG 2025-02 conditional novelty 5.0 of 10

    An autoencoder plus latent neural ODE, trained with teacher forcing and autoregressive rollouts, beats several published neural PDE surrogates on benchmark equations while using fewer parameters and faster inference.

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