# Global Stress Generation and Spatiotemporal Super-Resolution Physics-Informed Operator under Dynamic Loading for Two-Phase Random Materials

arXiv: https://arxiv.org/abs/2505.01438 · HTML: https://mlsanity.com/paper/2505.01438/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 35 references that are in the map.
- First posted on arXiv 26 Apr 2025.

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

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- [A Survey on Video Diffusion Models](https://mlsanity.com/paper/2310.10647/) (2023)
- [Upscale-A-Video: Temporal-Consistent Diffusion Model for Real-World Video Super-Resolution](https://mlsanity.com/paper/2312.06640/) (2023)
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- [Learning Trajectory-Aware Transformer for Video Super-Resolution](https://mlsanity.com/paper/2204.04216/) (2022)
- [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)
- [iSeeBetter: Spatio-temporal video super-resolution using recurrent generative back-projection networks](https://mlsanity.com/paper/2006.11161/) (2020)
- [Equilibrium Conserving Neural Operators for Super-Resolution Learning](https://mlsanity.com/paper/2504.13422/) (2025)

## Abstract (arXiv)

Material stress analysis is a critical aspect of material design and performance optimization. Under dynamic loading, the global stress evolution in materials exhibits complex spatiotemporal characteristics, especially in two-phase random materials (TRMs). Such kind of material failure is often associated with stress concentration, and the phase boundaries are key locations where stress concentration occurs. In practical engineering applications, the spatiotemporal resolution of acquired microstructural data and its dynamic stress evolution is often limited. This poses challenges for deep learning methods in generating high-resolution spatiotemporal stress fields, particularly for accurately capturing stress concentration regions. In this study, we propose a framework for global stress generation and spatiotemporal super-resolution in TRMs under dynamic loading. First, we introduce a diffusion model-based approach, named as Spatiotemporal Stress Diffusion (STS-diffusion), for generating global spatiotemporal stress data. This framework incorporates Space-Time U-Net (STU-net), and we systematically investigate the impact of different attention positions on model accuracy. Next, we develop a physics-informed network for spatiotemporal super-resolution, termed as Spatiotemporal Super-Resolution Physics-Informed Operator (ST-SRPINN). The proposed ST-SRPINN is an unsupervised learning method. The influence of data-driven and physics-informed loss function weights on model accuracy is explored in detail. Benefiting from physics-based constraints, ST-SRPINN requires only low-resolution stress field data during training and can upscale the spatiotemporal resolution of stress fields to arbitrary magnifications.