# Predicting Transonic Flowfields in Non-Homogeneous Unstructured Grids Using Autoencoder Graph Convolutional Networks

arXiv: https://arxiv.org/abs/2405.04396 · HTML: https://mlsanity.com/paper/2405.04396/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 47 references that are in the map.
- First posted on arXiv 7 May 2024.

## Builds on (most cited first, 14 of 14)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Convolutional Networks on Graphs for Learning Molecular Fingerprints](https://mlsanity.com/paper/1509.09292/) (2015)
- [Adversarial Attacks on Neural Networks for Graph Data](https://mlsanity.com/paper/1805.07984/) (2018)
- [A Survey of Convolutional Neural Networks: Analysis, Applications, and Prospects](https://mlsanity.com/paper/2004.02806/) (2020)
- [Deep Learning on Graphs: A Survey](https://mlsanity.com/paper/1812.04202/) (2018)
- [Recent Advances in Convolutional Neural Networks](https://mlsanity.com/paper/1512.07108/) (2015)
- [GRAM: Graph-based Attention Model for Healthcare Representation Learning](https://mlsanity.com/paper/1611.07012/) (2016)
- [DeepInf: Social Influence Prediction with Deep Learning](https://mlsanity.com/paper/1807.05560/) (2018)
- [Graph Convolutional Neural Networks for Body Force Prediction](https://mlsanity.com/paper/2012.02232/) (2020)

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

- [Text2PDE: Latent Diffusion Models for Accessible Physics Simulation](https://mlsanity.com/paper/2410.01153/) (2024)
- [Towards aerodynamic surrogate modeling based on β-variational autoencoders](https://mlsanity.com/paper/2408.04969/) (2024)

## Abstract (arXiv)

This paper focuses on addressing challenges posed by non-homogeneous unstructured grids, commonly used in Computational Fluid Dynamics (CFD). Their prevalence in CFD scenarios has motivated the exploration of innovative approaches for generating reduced-order models. The core of our approach centers on geometric deep learning, specifically the utilization of graph convolutional network (GCN). The novel Autoencoder GCN architecture enhances prediction accuracy by propagating information to distant nodes and emphasizing influential points. This architecture, with GCN layers and encoding/decoding modules, reduces dimensionality based on pressure-gradient values. The autoencoder structure improves the network capability to identify key features, contributing to a more robust and accurate predictive model. To validate the proposed methodology, we analyzed two different test cases: wing-only model and wing--body configuration. Precise reconstruction of steady-state distributed quantities within a two-dimensional parametric space underscores the reliability and versatility of the implemented approach.