# Adapting U-Net for linear elastic stress estimation in polycrystal Zr microstructures

arXiv: https://arxiv.org/abs/2303.08541 · HTML: https://mlsanity.com/paper/2303.08541/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 29 references that are in the map.
- First posted on arXiv 15 Mar 2023.

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

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Fully Convolutional Networks for Semantic Segmentation](https://mlsanity.com/paper/1411.4038/) (2014)
- [Visualizing the Loss Landscape of Neural Nets](https://mlsanity.com/paper/1712.09913/) (2017)
- [Approximating Continuous Functions by ReLU Nets of Minimal Width](https://mlsanity.com/paper/1710.11278/) (2017)
- [AutoGAN: Neural Architecture Search for Generative Adversarial Networks](https://mlsanity.com/paper/1908.03835/) (2019)
- [Building high accuracy emulators for scientific simulations with deep neural architecture search](https://mlsanity.com/paper/2001.08055/) (2020)
- [Physics-informed Convolutional Neural Networks for Temperature Field Prediction of Heat Source Layout without Labeled Data](https://mlsanity.com/paper/2109.12482/) (2021)
- [Stress Field Prediction in Cantilevered Structures Using Convolutional Neural Networks](https://mlsanity.com/paper/1808.08914/) (2018)

## Built on by (most cited first, 1 of 1)

- [Auto-Regressive U-Net for Full-Field Prediction of Shrinkage-Induced Damage in Concrete](https://mlsanity.com/paper/2509.20507/) (2025)

## Abstract (arXiv)

A variant of the U-Net convolutional neural network architecture is proposed to estimate linear elastic compatibility stresses in a-Zr (hcp) polycrystalline grain structures. Training data was generated using VGrain software with a regularity alpha of 0.73 and uniform random orientation for the grain structures and ABAQUS to evaluate the stress welds using the finite element method. The initial dataset contains 200 samples with 20 held from training for validation. The network gives speedups of around 200x to 6000x using a CPU or GPU, with signifcant memory savings, compared to finite element analysis with a modest reduction in accuracy of up to 10%. Network performance is not correlated with grain structure regularity or texture, showing generalisation of the network beyond the training set to arbitrary Zr crystal structures. Performance when trained with 200 and 400 samples was measured, finding an improvement in accuracy of approximately 10% when the size of the dataset was doubled.