Multi-Scale Message Passing Neural PDE Solvers

Léonard Equer; T. Konstantin Rusch; Siddhartha Mishra

Multi-Scale Message Passing Neural PDE Solvers

Machine Learning 2023-02-08 v1 Numerical Analysis Numerical Analysis Machine Learning

Authors: Léonard Equer , T. Konstantin Rusch , Siddhartha Mishra

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.

Keywords

partial differential equations molecular communication parallel algorithm

Cite

@article{arxiv.2302.03580,
  title  = {Multi-Scale Message Passing Neural PDE Solvers},
  author = {Léonard Equer and T. Konstantin Rusch and Siddhartha Mishra},
  journal= {arXiv preprint arXiv:2302.03580},
  year   = {2023}
}

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