Multi-resolution Graph Neural Networks for PDE Approximation

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