# PhySRNet: Physics informed super-resolution network for application in computational solid mechanics

arXiv: https://arxiv.org/abs/2206.15457 · HTML: https://mlsanity.com/paper/2206.15457/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 53 references that are in the map.
- First posted on arXiv 30 Jun 2022.

## Builds on (most cited first, 20 of 20)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Residual Dense Network for Image Super-Resolution](https://mlsanity.com/paper/1802.08797/) (2018)
- [Deep Laplacian Pyramid Networks for Fast and Accurate Super-Resolution](https://mlsanity.com/paper/1704.03915/) (2017)
- [Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10561/) (2017)
- [Recurrent Back-Projection Network for Video Super-Resolution](https://mlsanity.com/paper/1903.10128/) (2019)
- [Understanding and mitigating gradient pathologies in physics-informed neural networks](https://mlsanity.com/paper/2001.04536/) (2020)
- [Multi-Objective Loss Balancing for Physics-Informed Deep Learning](https://mlsanity.com/paper/2110.09813/) (2021)
- [Physics informed deep learning for computational elastodynamics without labeled data](https://mlsanity.com/paper/2006.08472/) (2020)
- [MeshfreeFlowNet: A Physics-Constrained Deep Continuous Space-Time Super-Resolution Framework](https://mlsanity.com/paper/2005.01463/) (2020)
- [Machine learning in cardiovascular flows modeling: Predicting arterial blood pressure from non-invasive 4D flow MRI data using physics-informed neural networks](https://mlsanity.com/paper/1905.04817/) (2019)
- [Physics-informed deep learning for incompressible laminar flows](https://mlsanity.com/paper/2002.10558/) (2020)
- [Machine learning for metal additive manufacturing: Predicting temperature and melt pool fluid dynamics using physics-informed neural networks](https://mlsanity.com/paper/2008.13547/) (2020)
- [Physics-Informed Neural Networks for Nonhomogeneous Material Identification in Elasticity Imaging](https://mlsanity.com/paper/2009.04525/) (2020)
- [Turbulence Enrichment using Physics-informed Generative Adversarial Networks](https://mlsanity.com/paper/2003.01907/) (2020)
- [Physics-informed neural networks for modeling rate- and temperature-dependent plasticity](https://mlsanity.com/paper/2201.08363/) (2022)
- [A comparative study of physics-informed neural network models for learning unknown dynamics and constitutive relations](https://mlsanity.com/paper/1904.04058/) (2019)
- [Using Physics-Informed Super-Resolution Generative Adversarial Networks for Subgrid Modeling in Turbulent Reactive Flows](https://mlsanity.com/paper/1911.11380/) (2019)
- [Machine Learning-Accelerated Computational Solid Mechanics: Application to Linear Elasticity](https://mlsanity.com/paper/2112.08676/) (2021)
- [Predicting Peak Stresses In Microstructured Materials Using Convolutional Encoder-Decoder Learning](https://mlsanity.com/paper/2201.00722/) (2022)

## Built on by (most cited first, 7 of 7)

- [Physics-Informed Computer Vision: A Review and Perspectives](https://mlsanity.com/paper/2305.18035/) (2023)
- [Physics-Guided, Physics-Informed, and Physics-Encoded Neural Networks in Scientific Computing](https://mlsanity.com/paper/2211.07377/) (2022)
- [Spatio-Temporal Super-Resolution of Dynamical Systems using Physics-Informed Deep-Learning](https://mlsanity.com/paper/2212.04457/) (2022)
- [Redefining Super-Resolution: Fine-mesh PDE predictions without classical simulations](https://mlsanity.com/paper/2311.09740/) (2023)
- [A Deep Learning Framework for Solving Hyperbolic Partial Differential Equations: Part I](https://mlsanity.com/paper/2307.04121/) (2023)
- [An Operator Learning Framework for Spatiotemporal Super-resolution of Scientific Simulations](https://mlsanity.com/paper/2311.02328/) (2023)
- [Downscaling Neural Network for Coastal Simulations](https://mlsanity.com/paper/2408.16553/) (2024)

## Abstract (arXiv)

Traditional approaches based on finite element analyses have been successfully used to predict the macro-scale behavior of heterogeneous materials (composites, multicomponent alloys, and polycrystals) widely used in industrial applications. However, this necessitates the mesh size to be smaller than the characteristic length scale of the microstructural heterogeneities in the material leading to computationally expensive and time-consuming calculations. The recent advances in deep learning based image super-resolution (SR) algorithms open up a promising avenue to tackle this computational challenge by enabling researchers to enhance the spatio-temporal resolution of data obtained from coarse mesh simulations. However, technical challenges still remain in developing a high-fidelity SR model for application to computational solid mechanics, especially for materials undergoing large deformation. This work aims at developing a physics-informed deep learning based super-resolution framework (PhySRNet) which enables reconstruction of high-resolution deformation fields (displacement and stress) from their low-resolution counterparts without requiring high-resolution labeled data. We design a synthetic case study to illustrate the effectiveness of the proposed framework and demonstrate that the super-resolved fields match the accuracy of an advanced numerical solver running at 400 times the coarse mesh resolution while simultaneously satisfying the (highly nonlinear) governing laws. The approach opens the door to applying machine learning and traditional numerical approaches in tandem to reduce computational complexity accelerate scientific discovery and engineering design.