# From Structured to Unstructured:A Comparative Analysis of Computer Vision and Graph Models in solving Mesh-based PDEs

arXiv: https://arxiv.org/abs/2406.00081 · HTML: https://mlsanity.com/paper/2406.00081/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 22 references that are in the map.
- First posted on arXiv 31 May 2024.

## Builds on (most cited first, 17 of 17)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [Training data-efficient image transformers & distillation through attention](https://mlsanity.com/paper/2012.12877/) (2020)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [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)
- [Graph U-Nets](https://mlsanity.com/paper/1905.05178/) (2019)
- [PDEBENCH: An Extensive Benchmark for Scientific Machine Learning](https://mlsanity.com/paper/2210.07182/) (2022)
- [Message Passing Neural PDE Solvers](https://mlsanity.com/paper/2202.03376/) (2022)
- [Transformer for Partial Differential Equations' Operator Learning](https://mlsanity.com/paper/2205.13671/) (2022)
- [Sustainable AI: Environmental Implications, Challenges and Opportunities](https://mlsanity.com/paper/2111.00364/) (2021)
- [Convolutional Neural Operators for robust and accurate learning of PDEs](https://mlsanity.com/paper/2302.01178/) (2023)
- [Efficient Learning of Mesh-Based Physical Simulation with BSMS-GNN](https://mlsanity.com/paper/2210.02573/) (2022)
- [Multiscale Neural Operators for Solving Time-Independent PDEs](https://mlsanity.com/paper/2311.05964/) (2023)
- [Dataset of a parameterized U-bend flow for Deep Learning Applications](https://mlsanity.com/paper/2305.05216/) (2023)
- [DADO -- Low-Cost Query Strategies for Deep Active Design Optimization](https://mlsanity.com/paper/2307.04536/) (2023)
- [Enhancing Multi-Objective Optimization through Machine Learning-Supported Multiphysics Simulation](https://mlsanity.com/paper/2309.13179/) (2023)

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

- [Machine learning for modelling unstructured grid data in computational physics: a review](https://mlsanity.com/paper/2502.09346/) (2025)

## Abstract (arXiv)

This article investigates the application of computer vision and graph-based models in solving mesh-based partial differential equations within high-performance computing environments. Focusing on structured, graded structured, and unstructured meshes, the study compares the performance and computational efficiency of three computer vision-based models against three graph-based models across three data-sets. The research aims to identify the most suitable models for different mesh topographies, particularly highlighting the exploration of graded meshes, a less studied area. Results demonstrate that computer vision-based models, notably U-Net, outperform the graph models in prediction performance and efficiency in two (structured and graded) out of three mesh topographies. The study also reveals the unexpected effectiveness of computer vision-based models in handling unstructured meshes, suggesting a potential shift in methodological approaches for data-driven partial differential equation learning. The article underscores deep learning as a viable and potentially sustainable way to enhance traditional high-performance computing methods, advocating for informed model selection based on the topography of the mesh.