# Super-resolving 2D stress tensor field conserving equilibrium constraints using physics informed U-Net

arXiv: https://arxiv.org/abs/2206.01122 · HTML: https://mlsanity.com/paper/2206.01122/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 24 references that are in the map.
- First posted on arXiv 2 Jun 2022.

## Builds on (most cited first, 11 of 11)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network](https://mlsanity.com/paper/1609.04802/) (2016)
- [UNet++: A Nested U-Net Architecture for Medical Image Segmentation](https://mlsanity.com/paper/1807.10165/) (2018)
- [ESRGAN: Enhanced Super-Resolution Generative Adversarial Networks](https://mlsanity.com/paper/1809.00219/) (2018)
- [The relativistic discriminator: a key element missing from standard GAN](https://mlsanity.com/paper/1807.00734/) (2018)
- [RankSRGAN: Generative Adversarial Networks with Ranker for Image Super-Resolution](https://mlsanity.com/paper/1908.06382/) (2019)
- [Physics-Guided Machine Learning for Scientific Discovery: An Application in Simulating Lake Temperature Profiles](https://mlsanity.com/paper/2001.11086/) (2020)
- [Physics-guided Convolutional Neural Network (PhyCNN) for Data-driven Seismic Response Modeling](https://mlsanity.com/paper/1909.08118/) (2019)
- [StressGAN: A Generative Deep Learning Model for 2D Stress Distribution Prediction](https://mlsanity.com/paper/2006.11376/) (2020)

## Abstract (arXiv)

In a finite element analysis, using a large number of grids is important to obtain accurate results, but is a resource-consuming task. Aiming to real-time simulation and optimization, it is desired to obtain fine grid analysis results within a limited resource. This paper proposes a super-resolution method that predicts a stress tensor field in a high-resolution from low-resolution contour plots by utilizing a U-Net-based neural network which is called PI-UNet. In addition, the proposed model minimizes the residual of the equilibrium constraints so that it outputs a physically reasonable solution. The proposed network is trained with FEM results of simple shapes, and is validated with a complicated realistic shape to evaluate generalization capability. Although ESRGAN is a standard model for image super-resolution, the proposed U-Net based model outperforms ESRGAN model in the stress tensor prediction task.