Appendix of M2N: Mesh Movement Networks for PDESolvers AAdditional Model Details

Global Feature Extractor As mentioned in the paper, the global feature extractor GFE()is composed of 3 modules: GFE(Mn) = GAP(Conv(Sample(Mn))). The sampling module Sample()is implemented by the built-in interpolation interface in Firedrake[Rathgeber et al., 2016], with sampling density 32x32. The convolutional block contains 4 convolutional layers. The SELU [Klambauer et al., 2017] activation function is used to increase the representation capability of the model. The output tensor from the convolutional block is then fed into a Global Average Pooling (GAP) layer to get a mesh resolution invariant global feature embedding En.