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

arXiv: https://arxiv.org/abs/2107.00090 · HTML: https://mlsanity.com/paper/2107.00090/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 99 references that are in the map.
- First posted on arXiv 4 Jun 2021.

## Builds on (most cited first, 27 of 27)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting](https://mlsanity.com/paper/1506.04214/) (2015)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [An Introduction to Convolutional Neural Networks](https://mlsanity.com/paper/1511.08458/) (2015)
- [Deep Learning on Graphs: A Survey](https://mlsanity.com/paper/1812.04202/) (2018)
- [Multipole Graph Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2006.09535/) (2020)
- [On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groups](https://mlsanity.com/paper/1802.03690/) (2018)
- [Harmonic Networks: Deep Translation and Rotation Equivariance](https://mlsanity.com/paper/1612.04642/) (2016)
- [Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Data](https://mlsanity.com/paper/2002.12880/) (2020)
- [Speeding-up Convolutional Neural Networks Using Fine-tuned CP-Decomposition](https://mlsanity.com/paper/1412.6553/) (2014)
- [Understanding Batch Normalization](https://mlsanity.com/paper/1806.02375/) (2018)
- [Convolutional neural networks with low-rank regularization](https://mlsanity.com/paper/1511.06067/) (2015)
- [Exploiting Cyclic Symmetry in Convolutional Neural Networks](https://mlsanity.com/paper/1602.02660/) (2016)
- [Semi-Implicit Graph Variational Auto-Encoders](https://mlsanity.com/paper/1908.07078/) (2019)
- [Geometric deep learning for computational mechanics Part I: Anisotropic Hyperelasticity](https://mlsanity.com/paper/2001.04292/) (2020)
- [Graph Attention Auto-Encoders](https://mlsanity.com/paper/1905.10715/) (2019)
- [GMLS-Nets: A framework for learning from unstructured data](https://mlsanity.com/paper/1909.05371/) (2019)
- [Rotation Equivariance and Invariance in Convolutional Neural Networks](https://mlsanity.com/paper/1805.12301/) (2018)
- [Inferring low-dimensional microstructure representations using convolutional neural networks](https://mlsanity.com/paper/1611.02764/) (2016)
- [Multiresolution Graph Attention Networks for Relevance Matching](https://mlsanity.com/paper/1902.10580/) (2019)

## Built on by (most cited first, 7 of 7)

- [Rewiring with Positional Encodings for Graph Neural Networks](https://mlsanity.com/paper/2201.12674/) (2022)
- [Modular machine learning-based elastoplasticity: generalization in the context of limited data](https://mlsanity.com/paper/2210.08343/) (2022)
- [A Microstructure-based Graph Neural Network for Accelerating Multiscale Simulations](https://mlsanity.com/paper/2402.13101/) (2024)
- [A heteroencoder architecture for prediction of failure locations in porous metals using variational inference](https://mlsanity.com/paper/2202.00078/) (2022)
- [Deep learning and multi-level featurization of graph representations of microstructural data](https://mlsanity.com/paper/2210.00854/) (2022)
- [Uncertainty Quantification of Graph Convolution Neural Network Models of Evolving Processes](https://mlsanity.com/paper/2402.11179/) (2024)
- [Equivariant graph convolutional neural networks for the representation of homogenized anisotropic microstructural mechanical response](https://mlsanity.com/paper/2404.17584/) (2024)

## Abstract (arXiv)

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.