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Conference Papers Year : 2021

Multi-resolution Graph Neural Networks for PDE Approximation

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Mouadh Yagoubi
  • Function : Author
Marc Schoenauer

Abstract

Deep Learning algorithms have recently received a growing interest to learn from examples of existing solutions and some accurate approximations of the solution of complex physical problems, in particular relying on Graph Neural Networks applied on a mesh of the domain at hand. On the other hand, state-of-the-art deep approaches of image processing use different resolutions to better handle the different scales of the images, thanks to pooling and up-scaling operations. But no such operators can be easily defined for Graph Convolutional Neural Networks (GCNN). This paper defines such operators based on meshes of different granularities. Multi-resolution GCNNs can then be defined. We propose the MGMI approach, as well as an architecture based on the famed U-Net. These approaches are experimentally validated on a diffusion problem, compared with projected CNN approach and the experiments witness their efficiency, as well as their generalization capabilities.
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Dates and versions

hal-03448278 , version 1 (25-11-2021)

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Wenzhuo Liu, Mouadh Yagoubi, Marc Schoenauer. Multi-resolution Graph Neural Networks for PDE Approximation. ICANN 2021 - 30th International Conference on Artificial Neural Networks, Sep 2021, Bratislava, Slovakia. pp.151-163, ⟨10.1007/978-3-030-86365-4_13⟩. ⟨hal-03448278⟩
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