# Predicting Stress in Two-phase Random Materials and Super-Resolution Method for Stress Images by Embedding Physical Information

arXiv: https://arxiv.org/abs/2504.18854 · HTML: https://mlsanity.com/paper/2504.18854/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 35 references that are in the map.
- First posted on arXiv 26 Apr 2025.

## Builds on (most cited first, 13 of 13)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network](https://mlsanity.com/paper/1609.04802/) (2016)
- [Attention U-Net: Learning Where to Look for the Pancreas](https://mlsanity.com/paper/1804.03999/) (2018)
- [Image Super-Resolution Using Deep Convolutional Networks](https://mlsanity.com/paper/1501.00092/) (2014)
- [Solving high-dimensional partial differential equations using deep learning](https://mlsanity.com/paper/1707.02568/) (2017)
- [Physics-informed neural network for ultrasound nondestructive quantification of surface breaking cracks](https://mlsanity.com/paper/2005.03596/) (2020)
- [Physics informed neural networks for continuum micromechanics](https://mlsanity.com/paper/2110.07374/) (2021)
- [A Physics-Guided Neural Network Framework for Elastic Plates: Comparison of Governing Equations-Based and Energy-Based Approaches](https://mlsanity.com/paper/2010.06050/) (2020)
- [A mixed formulation for physics-informed neural networks as a potential solver for engineering problems in heterogeneous domains: comparison with finite element method](https://mlsanity.com/paper/2206.13103/) (2022)
- [Stress field prediction in fiber-reinforced composite materials using a deep learning approach](https://mlsanity.com/paper/2111.05271/) (2021)
- [A nonlocal physics-informed deep learning framework using the peridynamic differential operator](https://mlsanity.com/paper/2006.00446/) (2020)
- [Microstructure reconstruction of 2D/3D random materials via diffusion-based deep generative models](https://mlsanity.com/paper/2311.17319/) (2023)
- [Data-Centric Mixed-Variable Bayesian Optimization For Materials Design](https://mlsanity.com/paper/1907.02577/) (2019)

## Abstract (arXiv)

Stress analysis is an important part of material design. For materials with complex microstructures, such as two-phase random materials (TRMs), material failure is often accompanied by stress concentration. Phase interfaces in two-phase materials are critical for stress concentration. Therefore, the prediction error of stress at phase boundaries is crucial. In practical engineering, the pixels of the obtained material microstructure images are limited, which limits the resolution of stress images generated by deep learning methods, making it difficult to observe stress concentration regions. Existing Image Super-Resolution (ISR) technologies are all based on data-driven supervised learning. However, stress images have natural physical constraints, which provide new ideas for new ISR technologies. In this study, we constructed a stress prediction framework for TRMs. First, the framework uses a proposed Multiple Compositions U-net (MC U-net) to predict stress in low-resolution material microstructures. By considering the phase interface information of the microstructure, the MC U-net effectively reduces the problem of excessive prediction errors at phase boundaries. Secondly, a Mixed Physics-Informed Neural Network (MPINN) based method for stress ISR (SRPINN) was proposed. By introducing the constraints of physical information, the new method does not require paired stress images for training and can increase the resolution of stress images to any multiple. This enables a multiscale analysis of the stress concentration regions at phase boundaries. Finally, we performed stress analysis on TRMs with different phase volume fractions and loading states through transfer learning. The results show the proposed stress prediction framework has satisfactory accuracy and generalization ability.