  Predicting the evolution of a representative sample of a material with
microstructure is a fundamental problem in homogenization. In this work we
propose a graph convolutional neural network that utilizes the discretized
representation of the initial microstructure directly, without segmentation or
clustering. Compared to feature-based and pixel-based convolutional neural
network models, the proposed method has a number of advantages: (a) it is deep
in that it does not require featurization but can benefit from it, (b) it has a
simple implementation with standard convolutional filters and layers, (c) it
works natively on unstructured and structured grid data without interpolation
(unlike pixel-based convolutional neural networks), and (d) it preserves
rotational invariance like other graph-based convolutional neural networks. We
demonstrate the performance of the proposed network and compare it to
traditional pixel-based convolution neural network models and feature-based
graph convolutional neural networks on multiple large datasets.
