Mesh-based graph convolutional neural networks for modeling materials with microstructure

TL;DR

This paper introduces a graph convolutional neural network that directly models microstructure evolution in materials, offering advantages over traditional pixel-based and feature-based models in terms of simplicity, flexibility, and invariance.

Contribution

The paper presents a novel mesh-based graph convolutional neural network that operates directly on microstructure data without segmentation, enhancing modeling capabilities for materials with complex microstructures.

Findings

Outperforms traditional pixel-based CNNs in microstructure prediction

Maintains rotational invariance in microstructure modeling

Works efficiently on unstructured grid data

Abstract

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.