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Multi-resolution Graph Neural Networks for PDE Approximation

Wenzhuo Liu 1, 2 Mouadh Yagoubi 1 Marc Schoenauer 2 
2 TAU - TAckling the Underspecified
Inria Saclay - Ile de France, LISN - Laboratoire Interdisciplinaire des Sciences du Numérique
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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Submitted on : Thursday, November 25, 2021 - 9:43:32 AM
Last modification on : Wednesday, November 9, 2022 - 3:57:10 AM
Long-term archiving on: : Saturday, February 26, 2022 - 6:21:37 PM


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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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