# A heteroencoder architecture for prediction of failure locations in porous metals using variational inference

arXiv: https://arxiv.org/abs/2202.00078 · HTML: https://mlsanity.com/paper/2202.00078/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 55 references that are in the map.
- First posted on arXiv 31 Jan 2022.

## Builds on (most cited first, 15 of 15)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [Generating Sentences from a Continuous Space](https://mlsanity.com/paper/1511.06349/) (2015)
- [A systematic study of the class imbalance problem in convolutional neural networks](https://mlsanity.com/paper/1710.05381/) (2017)
- [Stochastic Gradient Descent as Approximate Bayesian Inference](https://mlsanity.com/paper/1704.04289/) (2017)
- [Monte Carlo Gradient Estimation in Machine Learning](https://mlsanity.com/paper/1906.10652/) (2019)
- [Bayesian Deep Convolutional Encoder-Decoder Networks for Surrogate Modeling and Uncertainty Quantification](https://mlsanity.com/paper/1801.06879/) (2018)
- [Flipout: Efficient Pseudo-Independent Weight Perturbations on Mini-Batches](https://mlsanity.com/paper/1803.04386/) (2018)
- [Stress Field Prediction in Cantilevered Structures Using Convolutional Neural Networks](https://mlsanity.com/paper/1808.08914/) (2018)
- [Machine learning materials physics: Multi-resolution neural networks learn the free energy and nonlinear elastic response of evolving microstructures](https://mlsanity.com/paper/2001.01575/) (2019)
- [Bayesian neural networks for weak solution of PDEs with uncertainty quantification](https://mlsanity.com/paper/2101.04879/) (2021)
- [Mesh-based graph convolutional neural networks for modeling materials with microstructure](https://mlsanity.com/paper/2107.00090/) (2021)
- [Scale bridging materials physics: Active learning workflows and integrable deep neural networks for free energy function representations in alloys](https://mlsanity.com/paper/2002.02305/) (2020)

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

- [Geometric deep learning for computational mechanics Part II: Graph embedding for interpretable multiscale plasticity](https://mlsanity.com/paper/2208.00246/) (2022)
- [Single- to multi-fidelity history-dependent learning with uncertainty quantification and disentanglement: application to data-driven constitutive modeling](https://mlsanity.com/paper/2507.13416/) (2025)

## Abstract (arXiv)

In this work we employ an encoder-decoder convolutional neural network to predict the failure locations of porous metal tension specimens based only on their initial porosities. The process we model is complex, with a progression from initial void nucleation, to saturation, and ultimately failure. The objective of predicting failure locations presents an extreme case of class imbalance since most of the material in the specimens do not fail. In response to this challenge, we develop and demonstrate the effectiveness of data- and loss-based regularization methods. Since there is considerable sensitivity of the failure location to the particular configuration of voids, we also use variational inference to provide uncertainties for the neural network predictions. We connect the deterministic and Bayesian convolutional neural networks at a theoretical level to explain how variational inference regularizes the training and predictions. We demonstrate that the resulting predicted variances are effective in ranking the locations that are most likely to fail in any given specimen.