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

arXiv: https://arxiv.org/abs/2210.00854 · HTML: https://mlsanity.com/paper/2210.00854/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 64 references that are in the map.
- First posted on arXiv 29 Sep 2022.

## Builds on (most cited first, 25 of 25)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Hierarchical Graph Representation Learning with Differentiable Pooling](https://mlsanity.com/paper/1806.08804/) (2018)
- [Graph U-Nets](https://mlsanity.com/paper/1905.05178/) (2019)
- [Representation Learning on Graphs: Methods and Applications](https://mlsanity.com/paper/1709.05584/) (2017)
- [Evaluating the visualization of what a Deep Neural Network has learned](https://mlsanity.com/paper/1509.06321/) (2015)
- [Understanding Neural Networks Through Deep Visualization](https://mlsanity.com/paper/1506.06579/) (2015)
- [A Survey on Neural Network Interpretability](https://mlsanity.com/paper/2012.14261/) (2020)
- [Model-Agnostic Interpretability of Machine Learning](https://mlsanity.com/paper/1606.05386/) (2016)
- [Graph Neural Networks with convolutional ARMA filters](https://mlsanity.com/paper/1901.01343/) (2019)
- [Benchmarking and Survey of Explanation Methods for Black Box Models](https://mlsanity.com/paper/2102.13076/) (2021)
- [Understanding Pooling in Graph Neural Networks](https://mlsanity.com/paper/2110.05292/) (2021)
- [Geometric deep learning for computational mechanics Part I: Anisotropic Hyperelasticity](https://mlsanity.com/paper/2001.04292/) (2020)
- [GNN-Surrogate: A Hierarchical and Adaptive Graph Neural Network for Parameter Space Exploration of Unstructured-Mesh Ocean Simulations](https://mlsanity.com/paper/2202.08956/) (2022)
- [Graph Convolutional Neural Networks for Body Force Prediction](https://mlsanity.com/paper/2012.02232/) (2020)
- [Mesh-based graph convolutional neural networks for modeling materials with microstructure](https://mlsanity.com/paper/2107.00090/) (2021)
- [Learning the nonlinear dynamics of soft mechanical metamaterials with graph networks](https://mlsanity.com/paper/2202.13775/) (2022)
- [Deeply learning molecular structure-property relationships using attention- and gate-augmented graph convolutional network](https://mlsanity.com/paper/1805.10988/) (2018)

## Built on by (most cited first, 2 of 2)

- [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)

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.