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Multi-resolution Graph Neural Networks for PDE Approximation

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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https://hal.archives-ouvertes.fr/hal-03448278
Contributor : Wenzhuo Liu Connect in order to contact the contributor
Submitted on : Thursday, November 25, 2021 - 9:43:32 AM
Last modification on : Saturday, November 27, 2021 - 3:43:33 AM

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Wenzhuo Liu, Mouadh Yagoubi, Marc Schoenauer. Multi-resolution Graph Neural Networks for PDE Approximation. Artificial Neural Networks and Machine Learning – ICANN 2021, 12893, Springer International Publishing, pp.151-163, 2021, Lecture Notes in Computer Science, ⟨10.1007/978-3-030-86365-4_13⟩. ⟨hal-03448278⟩

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