# MAgNET: A Graph U-Net Architecture for Mesh-Based Simulations

arXiv: https://arxiv.org/abs/2211.00713 · HTML: https://mlsanity.com/paper/2211.00713/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 84 references that are in the map.
- First posted on arXiv 1 Nov 2022.

## Builds on (most cited first, 30 of 36)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [3D U-Net: Learning Dense Volumetric Segmentation from Sparse Annotation](https://mlsanity.com/paper/1606.06650/) (2016)
- [Spatial Temporal Graph Convolutional Networks for Skeleton-Based Action Recognition](https://mlsanity.com/paper/1801.07455/) (2018)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [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)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
- [Self-Attention Graph Pooling](https://mlsanity.com/paper/1904.08082/) (2019)
- [Semantic Graph Convolutional Networks for 3D Human Pose Regression](https://mlsanity.com/paper/1904.03345/) (2019)
- [PhyGeoNet: Physics-Informed Geometry-Adaptive Convolutional Neural Networks for Solving Parameterized Steady-State PDEs on Irregular Domain](https://mlsanity.com/paper/2004.13145/) (2020)
- [An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications](https://mlsanity.com/paper/1908.10407/) (2019)
- [Physics-informed graph neural Galerkin networks: A unified framework for solving PDE-governed forward and inverse problems](https://mlsanity.com/paper/2107.12146/) (2021)
- [Graph Coarsening with Neural Networks](https://mlsanity.com/paper/2102.01350/) (2021)
- [Geometric deep learning for computational mechanics Part I: Anisotropic Hyperelasticity](https://mlsanity.com/paper/2001.04292/) (2020)
- [Physics informed neural networks for continuum micromechanics](https://mlsanity.com/paper/2110.07374/) (2021)
- [CFDNet: a deep learning-based accelerator for fluid simulations](https://mlsanity.com/paper/2005.04485/) (2020)
- [Deep Learning for Reduced Order Modelling and Efficient Temporal Evolution of Fluid Simulations](https://mlsanity.com/paper/2107.04556/) (2021)
- [Simulation of hyperelastic materials in real-time using Deep Learning](https://mlsanity.com/paper/1904.06197/) (2019)
- [Physics-informed Convolutional Neural Networks for Temperature Field Prediction of Heat Source Layout without Labeled Data](https://mlsanity.com/paper/2109.12482/) (2021)
- [NN-EUCLID: deep-learning hyperelasticity without stress data](https://mlsanity.com/paper/2205.06664/) (2022)
- [Three-dimensional convolutional neural network (3D-CNN) for heterogeneous material homogenization](https://mlsanity.com/paper/2002.07600/) (2020)
- [Clique pooling for graph classification](https://mlsanity.com/paper/1904.00374/) (2019)
- [Finite electro-elasticity with physics-augmented neural networks](https://mlsanity.com/paper/2206.05139/) (2022)
- [Probabilistic Deep Learning for Real-Time Large Deformation Simulations](https://mlsanity.com/paper/2111.01867/) (2021)
- [Neural Extended Kalman Filters for Learning and Predicting Dynamics of Structural Systems](https://mlsanity.com/paper/2210.04165/) (2022)

## Built on by (most cited first, 26 of 26)

- [A review of graph neural network applications in mechanics-related domains](https://mlsanity.com/paper/2407.11060/) (2024)
- [Mesh-based Super-Resolution of Fluid Flows with Multiscale Graph Neural Networks](https://mlsanity.com/paper/2409.07769/) (2024)
- [Interpretable A-posteriori Error Indication for Graph Neural Network Surrogate Models](https://mlsanity.com/paper/2311.07548/) (2023)
- [Convolution, aggregation and attention based deep neural networks for accelerating simulations in mechanics](https://mlsanity.com/paper/2212.01386/) (2022)
- [Artificial Intelligence in Materials Science and Engineering: Current Landscape, Key Challenges, and Future Trajectorie](https://mlsanity.com/paper/2601.12554/) (2026)
- [A graph neural network surrogate model for mesh-based crashworthiness prediction of vehicle panel components](https://mlsanity.com/paper/2503.17386/) (2025)
- [A hybrid numerical methodology coupling Reduced Order Modeling and Graph Neural Networks for non-parametric geometries: applications to structural dynamics problems](https://mlsanity.com/paper/2406.02615/) (2024)
- [LatticeGraphNet: A two-scale graph neural operator for simulating lattice structures](https://mlsanity.com/paper/2402.01045/) (2024)
- [Scalable and Consistent Graph Neural Networks for Distributed Mesh-based Data-driven Modeling](https://mlsanity.com/paper/2410.01657/) (2024)
- [Topology-Agnostic Graph U-Nets for Scalar Field Prediction on Unstructured Meshes](https://mlsanity.com/paper/2410.06406/) (2024)
- [Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems](https://mlsanity.com/paper/2505.18857/) (2025)
- [FIGNN: Feature-Specific Interpretability for Graph Neural Network Surrogate Models](https://mlsanity.com/paper/2506.11398/) (2025)
- [Learning Nonlinear Finite Element Solution Operators using Multilayer Perceptrons and Energy Minimization](https://mlsanity.com/paper/2412.04596/) (2024)
- [Recurrent U-Net-Based Graph Neural Network (RUGNN) for Accurate Deformation Predictions in Sheet Material Forming](https://mlsanity.com/paper/2507.11547/) (2025)
- [Multi-Stage Graph Neural Networks for Data-Driven Prediction of Natural Convection in Enclosed Cavities](https://mlsanity.com/paper/2509.06041/) (2025)
- [Graph Network-based Structural Simulator: Graph Neural Networks for Structural Dynamics](https://mlsanity.com/paper/2510.25683/) (2025)
- [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)
- [Learning-Based Finite Element Methods Modeling for Complex Mechanical Systems](https://mlsanity.com/paper/2409.00160/) (2024)
- [Predicting Wall Thickness Changes in Cold Forging Processes: An Integrated FEM and Neural Network approach](https://mlsanity.com/paper/2411.13366/) (2024)
- [Machine learning surrogate models of many-body dispersion interactions in polymer melts](https://mlsanity.com/paper/2503.15149/) (2025)
- [Learning Deformable Body Interactions With Adaptive Spatial Tokenization](https://mlsanity.com/paper/2507.13707/) (2025)
- [Adaptive Fusion Graph Network for 3D Strain Field Prediction in Solid Rocket Motor Grains](https://mlsanity.com/paper/2512.23443/) (2025)
- [Deep Wave Network for Modeling Multi-Scale Physical Dynamics](https://mlsanity.com/paper/2605.04198/) (2026)
- [NSPOD: Accelerating Krylov solvers via DeepONet-learned POD subspaces](https://mlsanity.com/paper/2605.07828/) (2026)
- [HyperShape: Hyperelasticity Across Diverse Shapes](https://mlsanity.com/paper/2608.09938/) (2026)
- [Generalizing Soft Tissue Deformation and Force Prediction Across Material Stiffness and Geometry](https://mlsanity.com/paper/2608.20967/) (2026)

## Abstract (arXiv)

In many cutting-edge applications, high-fidelity computational models prove to be too slow for practical use and are therefore replaced by much faster surrogate models. Recently, deep learning techniques have increasingly been utilized to accelerate such predictions. To enable learning on large-dimensional and complex data, specific neural network architectures have been developed, including convolutional and graph neural networks. In this work, we present a novel encoder-decoder geometric deep learning framework called MAgNET, which extends the well-known convolutional neural networks to accommodate arbitrary graph-structured data. MAgNET consists of innovative Multichannel Aggregation (MAg) layers and graph pooling/unpooling layers, forming a graph U-Net architecture that is analogous to convolutional U-Nets. We demonstrate the predictive capabilities of MAgNET in surrogate modeling for non-linear finite element simulations in the mechanics of solids.