# Recurrent U-Net-Based Graph Neural Network (RUGNN) for Accurate Deformation Predictions in Sheet Material Forming

arXiv: https://arxiv.org/abs/2507.11547 · HTML: https://mlsanity.com/paper/2507.11547/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 45 references that are in the map.
- First posted on arXiv 10 Jul 2025.

## Builds on (most cited first, 21 of 21)

- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Graph networks as learnable physics engines for inference and control](https://mlsanity.com/paper/1806.01242/) (2018)
- [Physics-informed graph neural Galerkin networks: A unified framework for solving PDE-governed forward and inverse problems](https://mlsanity.com/paper/2107.12146/) (2021)
- [MultiScale MeshGraphNets](https://mlsanity.com/paper/2210.00612/) (2022)
- [Everything is Connected: Graph Neural Networks](https://mlsanity.com/paper/2301.08210/) (2023)
- [Learning rigid dynamics with face interaction graph networks](https://mlsanity.com/paper/2212.03574/) (2022)
- [MAgNET: A Graph U-Net Architecture for Mesh-Based Simulations](https://mlsanity.com/paper/2211.00713/) (2022)
- [Deep Learning in Deterministic Computational Mechanics](https://mlsanity.com/paper/2309.15421/) (2023)
- [ST-UNet: A Spatio-Temporal U-Network for Graph-structured Time Series Modeling](https://mlsanity.com/paper/1903.05631/) (2019)
- [Geometric Deep Learning for Computer-Aided Design: A Survey](https://mlsanity.com/paper/2402.17695/) (2024)
- [A review of graph neural network applications in mechanics-related domains](https://mlsanity.com/paper/2407.11060/) (2024)
- [Learning rigid-body simulators over implicit shapes for large-scale scenes and vision](https://mlsanity.com/paper/2405.14045/) (2024)
- [Towards Fast Simulation of Environmental Fluid Mechanics with Multi-Scale Graph Neural Networks](https://mlsanity.com/paper/2205.02637/) (2022)
- [On the use of graph neural networks and shape-function-based gradient computation in the deep energy method](https://mlsanity.com/paper/2207.07216/) (2022)
- [A Review of Machine Learning Methods Applied to Structural Dynamics and Vibroacoustic](https://mlsanity.com/paper/2204.06362/) (2022)
- [Physics-Encoded Graph Neural Networks for Deformation Prediction under Contact](https://mlsanity.com/paper/2402.03466/) (2024)
- [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)
- [Rapid feasibility assessment of components formed through hot stamping: A deep learning approach](https://mlsanity.com/paper/2104.13199/) (2021)

## Built on by (most cited first, 1 of 1)

- [Mask-Morph Graph U-Net: A Generalisable Mesh-Based Surrogate for Crashworthiness Field Prediction under Large Geometric Variation](https://mlsanity.com/paper/2605.15231/) (2026)

## Abstract (arXiv)

In recent years, various artificial intelligence-based surrogate models have been proposed to provide rapid manufacturability predictions of material forming processes. However, traditional AI-based surrogate models, typically built with scalar or image-based neural networks, are limited in their ability to capture complex 3D spatial relationships and to operate in a permutation-invariant manner. To overcome these issues, emerging graph-based surrogate models are developed using graph neural networks. This study developed a new graph neural network surrogate model named Recurrent U Net-based Graph Neural Network (RUGNN). The RUGNN model can achieve accurate predictions of sheet material deformation fields across multiple forming timesteps. The RUGNN model incorporates Gated Recurrent Units (GRUs) to model temporal dynamics and a U-Net inspired graph-based downsample/upsample mechanism to handle spatial long-range dependencies. A novel 'node-to-surface' contact representation method was proposed, offering significant improvements in computational efficiency for large-scale contact interactions. The RUGNN model was validated using a cold forming case study and a more complex hot forming case study using aluminium alloys. Results demonstrate that the RUGNN model provides accurate deformation predictions closely matching ground truth FE simulations and outperforming several baseline GNN architectures. Model tuning was also performed to identify suitable hyperparameters, training strategies, and input feature representations. These results demonstrate that RUGNN is a reliable approach to support sheet material forming design by enabling accurate manufacturability predictions.