# Topology-Agnostic Graph U-Nets for Scalar Field Prediction on Unstructured Meshes

arXiv: https://arxiv.org/abs/2410.06406 · HTML: https://mlsanity.com/paper/2410.06406/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 57 references that are in the map.
- First posted on arXiv 8 Oct 2024.

## Builds on (most cited first, 25 of 25)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [PointConv: Deep Convolutional Networks on 3D Point Clouds](https://mlsanity.com/paper/1811.07246/) (2018)
- [DeepGCNs: Can GCNs Go as Deep as CNNs?](https://mlsanity.com/paper/1904.03751/) (2019)
- [Graph U-Nets](https://mlsanity.com/paper/1905.05178/) (2019)
- [PairNorm: Tackling Oversmoothing in GNNs](https://mlsanity.com/paper/1909.12223/) (2019)
- [DeeperGCN: All You Need to Train Deeper GCNs](https://mlsanity.com/paper/2006.07739/) (2020)
- [Escape from Cells: Deep Kd-Networks for the Recognition of 3D Point Cloud Models](https://mlsanity.com/paper/1704.01222/) (2017)
- [Towards Sparse Hierarchical Graph Classifiers](https://mlsanity.com/paper/1811.01287/) (2018)
- [BRepNet: A topological message passing system for solid models](https://mlsanity.com/paper/2104.00706/) (2021)
- [A Point-Cloud Deep Learning Framework for Prediction of Fluid Flow Fields on Irregular Geometries](https://mlsanity.com/paper/2010.09469/) (2020)
- [Implicit Neural Spatial Representations for Time-dependent PDEs](https://mlsanity.com/paper/2210.00124/) (2022)
- [MAgNet: Mesh Agnostic Neural PDE Solver](https://mlsanity.com/paper/2210.05495/) (2022)
- [MAgNET: A Graph U-Net Architecture for Mesh-Based Simulations](https://mlsanity.com/paper/2211.00713/) (2022)
- [Towards Reusable Surrogate Models: Graph-Based Transfer Learning on Trusses](https://mlsanity.com/paper/2109.02689/) (2021)
- [Deep Surrogate for Direct Time Fluid Dynamics](https://mlsanity.com/paper/2112.10296/) (2021)
- [VIRL: Volume-Informed Representation Learning towards Few-shot Manufacturability Estimation](https://mlsanity.com/paper/2406.12286/) (2024)
- [Automating Style Analysis and Visualization With Explainable AI -- Case Studies on Brand Recognition](https://mlsanity.com/paper/2306.03021/) (2023)

## Built on by (most cited first, 2 of 2)

- [FLARE: Fast Low-rank Attention Routing Engine](https://mlsanity.com/paper/2508.12594/) (2025)
- [Attention to Detail: Fine-Scale Feature Preservation-Oriented Geometric Pre-training for AI-Driven Surrogate Modeling](https://mlsanity.com/paper/2504.20110/) (2025)

## Abstract (arXiv)

Machine-learned surrogate models to accelerate lengthy computer simulations are becoming increasingly important as engineers look to streamline the product design cycle. In many cases, these approaches offer the ability to predict relevant quantities throughout a geometry, but place constraints on the form of the input data. In a world of diverse data types, a preferred approach would not restrict the input to a particular structure. In this paper, we propose Topology-Agnostic Graph U-Net (TAG U-Net), a graph convolutional network that can be trained to input any mesh or graph structure and output a prediction of a target scalar field at each node. The model constructs coarsened versions of each input graph and performs a set of convolution and pooling operations to predict the node-wise outputs on the original graph. By training on a diverse set of shapes, the model can make strong predictions, even for shapes unlike those seen during training. A 3-D additive manufacturing dataset is presented, containing Laser Powder Bed Fusion simulation results for thousands of parts. The model is demonstrated on this dataset, and it performs well, predicting both 2-D and 3-D scalar fields with a median R-squared > 0.85 on test geometries. Code and datasets are available online.