# UCNN: A Convolutional Strategy on Unstructured Mesh

arXiv: https://arxiv.org/abs/2101.05207 · HTML: https://mlsanity.com/paper/2101.05207/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 38 references that are in the map.
- First posted on arXiv 12 Jan 2021.

## Builds on (most cited first, 18 of 18)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [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)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting](https://mlsanity.com/paper/1506.04214/) (2015)
- [Image Super-Resolution Using Deep Convolutional Networks](https://mlsanity.com/paper/1501.00092/) (2014)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Geometric deep learning on graphs and manifolds using mixture model CNNs](https://mlsanity.com/paper/1611.08402/) (2016)
- [Diffusion-Convolutional Neural Networks](https://mlsanity.com/paper/1511.02136/) (2015)
- [A Survey of the Recent Architectures of Deep Convolutional Neural Networks](https://mlsanity.com/paper/1901.06032/) (2019)
- [SplineCNN: Fast Geometric Deep Learning with Continuous B-Spline Kernels](https://mlsanity.com/paper/1711.08920/) (2017)
- [Learning shape correspondence with anisotropic convolutional neural networks](https://mlsanity.com/paper/1605.06437/) (2016)
- [Recent progress in semantic image segmentation](https://mlsanity.com/paper/1809.10198/) (2018)

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

- [Generalised Latent Assimilation in Heterogeneous Reduced Spaces with Machine Learning Surrogate Models](https://mlsanity.com/paper/2204.03497/) (2022)
- [Learning Mappings in Mesh-based Simulations](https://mlsanity.com/paper/2506.12652/) (2025)

## Abstract (arXiv)

In machine learning for fluid mechanics, fully-connected neural network (FNN) only uses the local features for modelling, while the convolutional neural network (CNN) cannot be applied to data on structured/unstructured mesh. In order to overcome the limitations of FNN and CNN, the unstructured convolutional neural network (UCNN) is proposed, which aggregates and effectively exploits the features of neighbour nodes through the weight function. Adjoint vector modelling is taken as the task to study the performance of UCNN. The mapping function from flow-field features to adjoint vector is constructed through efficient parallel implementation on GPU. The modelling capability of UCNN is compared with that of FNN on validation set and in aerodynamic shape optimization at test case. The influence of mesh changing on the modelling capability of UCNN is further studied. The results indicate that UCNN is more accurate in modelling process.