# Hybrid machine-learned homogenization: Bayesian data mining and convolutional neural networks

arXiv: https://arxiv.org/abs/2302.12545 · HTML: https://mlsanity.com/paper/2302.12545/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 50 references that are in the map.
- First posted on arXiv 24 Feb 2023.

## Builds on (most cited first, 10 of 10)

- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Improved Regularization of Convolutional Neural Networks with Cutout](https://mlsanity.com/paper/1708.04552/) (2017)
- [An Introduction to Convolutional Neural Networks](https://mlsanity.com/paper/1511.08458/) (2015)
- [Bayesian Neural Networks: An Introduction and Survey](https://mlsanity.com/paper/2006.12024/) (2020)
- [Pooling Methods in Deep Neural Networks, a Review](https://mlsanity.com/paper/2009.07485/) (2020)
- [Quantifying Translation-Invariance in Convolutional Neural Networks](https://mlsanity.com/paper/1801.01450/) (2017)
- [Inferring low-dimensional microstructure representations using convolutional neural networks](https://mlsanity.com/paper/1611.02764/) (2016)
- [Data-Driven Microstructure Property Relations](https://mlsanity.com/paper/1903.10841/) (2019)
- [On the generation of periodic discrete structures with identical two-point correlation](https://mlsanity.com/paper/2002.01234/) (2020)

## Abstract (arXiv)

Beyond the generally deployed features for microstructure property prediction this study aims to improve the machine learned prediction by developing novel feature descriptors. Therefore, Bayesian infused data mining is conducted to acquire samples containing characteristics inexplicable to the current feature set, and suitable feature descriptors to describe these characteristics are proposed. The iterative development of feature descriptors resulted in 37 novel features, being able to reduce the prediction error by roughly one third. To further improve the predictive model, convolutional neural networks (Conv Nets) are deployed to generate auxiliary features in a supervised machine learning manner. The Conv Nets were able to outperform the feature based approach. A key ingredient for that is a newly proposed data augmentation scheme and the development of so-called deep inception modules. A combination of the feature based approach and the convolutional neural network leads to a hybrid neural network: A parallel deployment of the both neural network archetypes in a single model achieved a relative rooted mean squared error below 1%, more than halving the error compared to prior models operating on the same data. The hybrid neural network was found powerful enough to be extended to predict variable material parameters, from a low to high phase contrast, while allowing for arbitrary microstructure geometry at the same time.