  In many cutting-edge applications, high-fidelity computational models prove
to be too slow for practical use and are therefore replaced by much faster
surrogate models. Recently, deep learning techniques have increasingly been
utilized to accelerate such predictions. To enable learning on
large-dimensional and complex data, specific neural network architectures have
been developed, including convolutional and graph neural networks. In this
work, we present a novel encoder-decoder geometric deep learning framework
called MAgNET, which extends the well-known convolutional neural networks to
accommodate arbitrary graph-structured data. MAgNET consists of innovative
Multichannel Aggregation (MAg) layers and graph pooling/unpooling layers,
forming a graph U-Net architecture that is analogous to convolutional U-Nets.
We demonstrate the predictive capabilities of MAgNET in surrogate modeling for
non-linear finite element simulations in the mechanics of solids.
