# SuperMeshing: A New Deep Learning Architecture for Increasing the Mesh Density of Metal Forming Stress Field with Attention Mechanism and Perceptual Features

arXiv: https://arxiv.org/abs/2104.09276 · HTML: https://mlsanity.com/paper/2104.09276/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 50 references that are in the map.
- First posted on arXiv 12 Mar 2021.

## Builds on (most cited first, 24 of 24)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [Perceptual Losses for Real-Time Style Transfer and Super-Resolution](https://mlsanity.com/paper/1603.08155/) (2016)
- [CBAM: Convolutional Block Attention Module](https://mlsanity.com/paper/1807.06521/) (2018)
- [Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network](https://mlsanity.com/paper/1609.04802/) (2016)
- [Image Super-Resolution Using Very Deep Residual Channel Attention Networks](https://mlsanity.com/paper/1807.02758/) (2018)
- [Real-Time Single Image and Video Super-Resolution Using an Efficient Sub-Pixel Convolutional Neural Network](https://mlsanity.com/paper/1609.05158/) (2016)
- [SqueezeNet: AlexNet-level accuracy with 50x fewer parameters and <0.5MB model size](https://mlsanity.com/paper/1602.07360/) (2016)
- [Recovering Realistic Texture in Image Super-resolution by Deep Spatial Feature Transform](https://mlsanity.com/paper/1804.02815/) (2018)
- [Learning Texture Transformer Network for Image Super-Resolution](https://mlsanity.com/paper/2006.04139/) (2020)
- [BAM: Bottleneck Attention Module](https://mlsanity.com/paper/1807.06514/) (2018)
- [Tell Me Where to Look: Guided Attention Inference Network](https://mlsanity.com/paper/1802.10171/) (2018)
- [Image Super-Resolution by Neural Texture Transfer](https://mlsanity.com/paper/1903.00834/) (2019)
- [MeshNet: Mesh Neural Network for 3D Shape Representation](https://mlsanity.com/paper/1811.11424/) (2018)
- [On Loss Functions for Deep Neural Networks in Classification](https://mlsanity.com/paper/1702.05659/) (2017)
- [TopologyGAN: Topology Optimization Using Generative Adversarial Networks Based on Physical Fields Over the Initial Domain](https://mlsanity.com/paper/2003.04685/) (2020)
- [A Novel Topology Optimization Approach using Conditional Deep Learning](https://mlsanity.com/paper/1901.04859/) (2019)
- [Minimax Optimal Estimation of KL Divergence for Continuous Distributions](https://mlsanity.com/paper/2002.11599/) (2020)
- [StressGAN: A Generative Deep Learning Model for 2D Stress Distribution Prediction](https://mlsanity.com/paper/2006.11376/) (2020)
- [A study on using image based machine learning methods to develop the surrogate models of stamp forming simulations](https://mlsanity.com/paper/2010.03370/) (2020)

## Abstract (arXiv)

In stress field analysis, the finite element analysis is a crucial approach, in which the mesh-density has a significant impact on the results. High mesh density usually contributes authentic to simulation results but costs more computing resources, leading to curtailing efficiency during the design process. To eliminate this drawback, we propose a new data-driven mesh-density boost model named SuperMeshingNet that strengthens the advantages of finite element analysis (FEA) with low mesh-density as inputs to the deep learning model, which consisting of Res-UNet architecture, to acquire high-density stress field instantaneously, shortening computing time and cost automatically. Moreover, the attention mechanism and the perceptual features are utilized, enhancing the performance of SuperMeshingNet. Compared to the baseline that applied the linear interpolation method, SuperMeshingNet achieves a prominent reduction in the mean squared error (MSE) and mean absolute error (MAE) on test data, which contains prior unseen cases. Based on the data set of metal forming, the comparable experiments are proceeded to demonstrate the high quality and superior precision of the reconstructed results generated by our model. The well-trained model can successfully show more excellent performance than the baseline and other methods on the multiple scaled mesh-density, including 2×, 4×, and 8×. With the refined result owning broaden scaling of mesh density and high precision, the FEA process can be accelerated with seldom cost on computation resources. We publicly share our work with full detail of implementation at https://github.com/zhenguonie/2021SuperMeshing2DMetalForming