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

TL;DR

This paper introduces a deep learning approach that uses multi-level featurization of graph representations of microstructural data to improve predictions of material responses, offering interpretability and efficiency over traditional methods.

Contribution

It develops a novel method for deep learning on reduced graph representations of microstructure data, enhancing interpretability and computational efficiency.

Findings

Outperforms CNNs on native discretizations in three physical examples.

Reduces graph complexity while maintaining prediction accuracy.

Provides interpretable features linked to microstructural regions.

Abstract

Many material response functions depend strongly on microstructure, such as inhomogeneities in phase or orientation. Homogenization presents the task of predicting the mean response of a sample of the microstructure to external loading for use in subgrid models and structure-property explorations. Although many microstructural fields have obvious segmentations, learning directly from the graph induced by the segmentation can be difficult because this representation does not encode all the information of the full field. We develop a means of deep learning of hidden features on the reduced graph given the native discretization and a segmentation of the initial input field. The features are associated with regions represented as nodes on the reduced graph. This reduced representation is then the basis for the subsequent multi-level/scale graph convolutional network model. There are a number of advantages of reducing the graph before fully processing with convolutional layers it, such as interpretable features and efficiency on large meshes. We demonstrate the performance of the proposed network relative to convolutional neural networks operating directly on the native discretization of the data using three physical exemplars.