Deep learning and multi-level featurization of graph representations of microstructural data

Newly developed graph neural networks (GNNs) [1-3], in particular convolutional graph neural networks, have been shown to be effective in a variety of classification and regression tasks. Recently they have been applied to physical problems [4, 5] where they can accommodate unstructured and hierarchical data naturally. Analogous to pixel-based convolutional neural networks (CNNs), "message passing" [6] graph convolutional neural networks (GCNNs) [7, 8] employ convolutional operations to achieve a compact parameter space by exploiting correlations in the data through connectivity defined by adjacency on the source discretization. Frankel et al. [9] and others [10-13] derive the information transmission graph directly from the connectivity of the discretization, computational grid or mesh based on the assumption the physical interactions are local. Some obvious advantages of applying convolutions to the discretization graph are that: general mesh data can be handled without interpolation to a structured grid, the discretization can be conformal to the microstructure, periodic boundary conditions can be handled without padding, and topological irregularities can be accommodated without approximations. In this approach the kernels and number of parameters are similar for a pre-selected reduction of the representation, e.g. based on the grains in a polycrystal [5], but the size of the adjacency can be prohibitive.