Merge pull request #26 from mesh-adaptation/mingrui_readme_1

update readme

README.md

@@ -1,18 +1,22 @@
 # Towards Universal Mesh Movement Networks
 
+This is the official code repository for the NeurIPS 2024 Spotlight paper [Toward Universal Mesh Movement Networks](https://arxiv.org/abs/2407.00382). 
+
+Additional information: [[Project page]](https://erizmr.github.io/UM2N/)
+
 <p align="center">
   <img src="./assets/UM2N_video_gif.gif" width="50%" height="50%" /><br>
   <em>UM2N(Universal Mesh Movement Networks) performs mesh adaptation for different PDEs and scenarios without re-training.</em>
 </p>
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+
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 <!-- <img width="100%" src="https://raw.githubusercontent.com/chunyang-w/chunyang-w.github.io/pic/202306231902481.webp"/> -->
 <!-- (Image source: [Star Trek: Official Site](https://intl.startrek.com/article/warp-drive-a-reality-could-be-soon)) -->
 
 
-<!-- ## Abstract:
-Solving complex Partial Differential Equations (PDEs) accurately and efficiently is an essential and challenging problem in all scientific and engineering disciplines. Mesh movement methods provide the capability to improve the accuracy of the numerical solution without increasing the overall mesh degree of freedom count. Conventional sophisticated mesh movement methods are extremely expensive and struggle to handle scenarios with complex boundary geometries. However, existing learning-based methods require re-training from scratch given a different PDE type or boundary geometry, which limits their applicability, and also often suffer from robustness issues in the form of inverted elements. In this paper, we introduce the Universal Mesh Movement Network (UM2N), which -- once trained -- can be applied in a non-intrusive, zero-shot manner to move meshes with different size distributions and structures, for solvers applicable to different PDE types and boundary geometries. UM2N consists of a Graph Transformer (GT) encoder for extracting features and a Graph Attention Network (GAT) based decoder for moving the mesh. We evaluate our method on advection and Navier-Stokes based examples, as well as a real-world tsunami simulation case. Our method outperforms existing learning-based mesh movement methods in terms of the benchmarks described above. In comparison to the conventional sophisticated Monge-Ampère PDE-solver based method, our approach not only significantly accelerates mesh movement, but also proves effective in scenarios where the conventional method fails. -->
 
-## 🔎 About this project:
-This is the official code repository for the NeurIPS 2024 Spotlight paper [Toward Universal Mesh Movement Networks](https://arxiv.org/abs/2407.00382). [[Project page]](https://erizmr.github.io/UM2N/)
+## 🔎 Abstract
 
 Solving complex Partial Differential Equations (PDEs) accurately and efficiently is an essential and challenging problem in all scientific and engineering disciplines. Mesh movement methods provide the capability to improve the accuracy of the numerical solution without increasing the overall mesh degree of freedom count. Conventional sophisticated mesh movement methods are extremely expensive and struggle to handle scenarios with complex boundary geometries. However, existing learning-based methods require re-training from scratch given a different PDE type or boundary geometry, which limits their applicability, and also often suffer from robustness issues in the form of inverted elements. In this paper, we introduce the Universal Mesh Movement Network (UM2N), which -- once trained -- can be applied in a non-intrusive, zero-shot manner to move meshes with different size distributions and structures, for solvers applicable to different PDE types and boundary geometries. UM2N consists of a Graph Transformer (GT) encoder for extracting features and a Graph Attention Network (GAT) based decoder for moving the mesh. We evaluate our method on advection and Navier-Stokes based examples, as well as a real-world tsunami simulation case. Our method outperforms existing learning-based mesh movement methods in terms of the benchmarks described above. In comparison to the conventional sophisticated Monge-Ampère PDE-solver based method, our approach not only significantly accelerates mesh movement, but also proves effective in scenarios where the conventional method fails.
 <!-- In the famous TV series Star Trek, the starship Enterprise is able to travel
@@ -168,14 +172,14 @@ The documentation is generated by Sphinx. To build the documentation, under the
 └── README.md (Project summary and useful information)
 ```
 
-## Useful thing: delete plot directory
+<!-- ## Useful thing: delete plot directory
 
 ```
 find ./ -type d -name "plot" -exec rm -rf {} +
 
 tensorboard --logdir=path/to/your/logs
 ```
 
-<!-- ## 🖖🏼 At last ...
+## 🖖🏼 At last ...
 
 Live long and prosper!   -->