Update README.md

README.md

@@ -1,14 +1,12 @@
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-license: mit
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-
 # Multiphysics Bench
 
-From Multiphysics Bench: Benchmarking and Investigating Scientific Machine Learning for Multiphysics PDEs
+Dataset: [huggingface.co/datasets/Indulge-Bai/Multiphysics_Bench ](https://huggingface.co/datasets/Indulge-Bai/Multiphysics_Bench)
+
+Paper: [Multiphysics Bench: Benchmarking and Investigating Scientific Machine Learning for Multiphysics PDEs](https://arxiv.org/abs/2505.17575)
 
 We propose the first general multiphysics benchmark dataset that encompasses six canonical coupled scenarios across domains such as electromagnetics, heat transfer, fluid flow, solid mechanics, pressure acoustics, and mass transport. This benchmark features the most comprehensive coupling types, the most diverse PDEs, and the largest data scale.
 
-![image](https://anonymous.4open.science/r/MultiphysicsBench/assets/intro.jpg)
+![image](./assets/intro.jpg)
 
 ---
 
@@ -16,7 +14,7 @@ We propose the first general multiphysics benchmark dataset that encompasses six
 
 ## 1. Dataset Download
 
-Please visit the link [huggingface.co/datasets/Indulge-Bai/Multiphysics_Bench ](https://huggingface.co/datasets/Indulge-Bai/Multiphysics_Bench ) to download the dataset (you will obtain `training.tar.gz` and `testing.tar.gz` separately). Extract the files to get the following directory structure:
+Please visit the link [huggingface.co/datasets/Indulge-Bai/Multiphysics_Bench ](https://huggingface.co/datasets/Indulge-Bai/Multiphysics_Bench) to download the dataset (you will obtain `training.tar.gz` and `testing.tar.gz` separately). Extract the files to get the following directory structure:
 
 Run the preprocessing code to convert the training and testing datasets into normalized tensor format. The final directory structure will look like this:
 
@@ -51,7 +49,7 @@ folder_path = snapshot_download(
 
 This dataset contains simulations of the Wave Equation and Heat Conduction Equation. This coupling mechanism underpins various applications, including thermal management in electronic components (e.g., microprocessors), inductive heating (e.g., welding and metal processing), biomedical technologies (e.g., photothermal therapy), and aerospace engineering (e.g., radiative heating of satellite surfaces).
 
-<img src="https://anonymous.4open.science/r/MultiphysicsBench/assets/problem_pic/TEheat_Data.png" width="40%" />
+<img src="./assets/TEheat_Data.png" width="50%" />
 
 
 **How to use**
@@ -79,7 +77,7 @@ DataProcessing/data_generate/TE_heat/parm2matrix_TE_heat.m
 
 This dataset contains simulations of the Navier–Stokes Equations and Heat Balance Equation. Thermo-Fluid coupling is essential in the design and optimization of systems such as electronic cooling (e.g., chip heat dissipation), energy systems (e.g., nuclear reactor cooling), and precision thermal control in manufacturing.
 
-<img src="https://anonymous.4open.science/r/MultiphysicsBench/assets/problem_pic/NSheat_Data.png" width="30%" />
+<img src="./assets/NSheat_Data.png" width="52%" />
 
 
 **How to use**
@@ -109,7 +107,7 @@ DataProcessing/data_generate/NS_heat/parm2matrix_NS_heat.m
 
 This dataset simulates the Navier–Stokes Equations and Current Continuity Equation. This coupling is foundational to applications such as micropumps and micromixers in microfluidic systems.
 
-<img src="https://anonymous.4open.science/r/MultiphysicsBench/assets/problem_pic/Eflow_Data.png" width="30%" />
+<img src="./assets/Eflow_Data.png" width="50%" />
 
 **How to use**
 
@@ -138,7 +136,7 @@ DataProcessing/data_generate/E_flow/parm2matrix_E_flow.m
 
 This dataset simulates Ampère’s Law, Continuity Equation, Navier–Stokes Equations, and Lorentz Force. This model finds extensive application in electromagnetic pumps, plasma confinement devices (e.g., tokamaks), astrophysical phenomena, and pollutant transport modeling.
 
-<img src="https://anonymous.4open.science/r/MultiphysicsBench/assets/problem_pic/MHD_Data.png" width="30%" />
+<img src="./assets/MHD_Data.png" width="50%" />
 
 
 **How to use**
@@ -159,8 +157,7 @@ This dataset simulates Ampère’s Law, Continuity Equation, Navier–Stokes Equ
 
 The dataset generation code is located at:  
 
-```
-DataProcessing/data_generate/MHD/main_MHD.m
+```DataProcessing/data_generate/MHD/main_MHD.m
 DataProcessing/data_generate/MHD/parm2matrix_MHD.m
 ```
 
@@ -170,7 +167,7 @@ DataProcessing/data_generate/MHD/parm2matrix_MHD.m
 
 This dataset simulates the Acoustic Wave Equation and Structural Vibration Equation. The input is the spatial material density (1 channel). The outputs comprise the acoustic pressure field (2 channels), stress components (6 channels), and structural displacements (4 channels), for a total of **12 output channels**.
 
-<img src="https://anonymous.4open.science/r/MultiphysicsBench/assets/problem_pic/VA_Data.png" width="30%" />
+<img src="./assets/VA_Data.png" width="50%" />
 
 
 **How to use**
@@ -210,7 +207,7 @@ DataProcessing/data_generate/VA/parm2matrix_VA.m
 
 This dataset contains simulations based on Darcy’s Law and the Convection–Diffusion Equation. The input includes the source term `Sc` and the initial state of the system at time `t0` (concentration and velocity), totaling **4 channels**. The output consists of the predicted concentration and velocity fields across **10 future time steps**, resulting in **30 channels in total**.
 
-<img src="https://anonymous.4open.science/r/MultiphysicsBench/assets/problem_pic/Elder_Data.gif" width="30%" />
+<img src="./assets/Elder_Data.gif" width="50%" />
 
 
 **How to use**
@@ -255,3 +252,16 @@ For **DeepONet** and **PINNs**, navigate to the corresponding problem directory
 For **FNO**, please refer to the official documentation at [FNO]([http://www.xxx.com](https://github.com/NeuralOperator/neuraloperator)).
 
 For **DiffusionPDE**, please refer to the official documentation at [DiffusionPDE](https://github.com/jhhuangchloe/DiffusionPDE).
+
+
+### Citing
+If you find our dataset or code useful for your research, please cite our paper.
+
+```
+@article{yang2025multiphysics,
+      title={Multiphysics Bench: Benchmarking and Investigating Scientific Machine Learning for Multiphysics PDEs}, 
+      author={Changfan Yang and Lichen Bai and Yinpeng Wang and Shufei Zhang and Zeke Xie},
+      year={2025},
+      journal={arXiv preprint arXiv:2505.17575},
+}
+```