docs(readme): update benchmark datasets documentation

- Remove "High-fidelity" descriptor from benchmark description
- Add paper reference link to DyMixOp framework description
- Update dataset table with detailed channel information and corrected PDE names
- Replace "Cahn-Hilliard + Reaction-Diffusion" with correct "Compressible Euler Curved Riemann Problem"
- Change "2D Burgers" to "Burgers" and "2D Navier-Stokes" to "Navier-Stokes"
- Add detailed channel descriptions including mathematical symbols for each dataset
- Correct spatial dimension description for 3dShallowWater as spherical coordinates
- Update 3dBrusselator description as 2D + 1D (Time) system
- Remove numpy from installation requirements
- Remove redundant Data Structure section
- Update NetCDF variable access method from dataset.variables.keys() to dataset.keys()

README.md

@@ -19,9 +19,9 @@ size_categories:
 
 # DyMixOp Benchmarks
 
-**High-fidelity benchmark datasets for evaluating neural operators on multi-scale spatiotemporal dynamical systems.**
+**Benchmark datasets for evaluating neural operators on multi-scale spatiotemporal dynamical systems.**
 
-Part of the **DyMixOp** (Dynamical Mixture of Operators) framework for learning complex PDE solutions.
+Part of the **DyMixOp** ([DyMixOp: A Neural Operator Designed from a Complex Dynamics Perspective with Local-Global Mixing for Solving PDEs](https://arxiv.org/abs/2508.13490)) framework for learning complex PDE solutions.
 
 [![License: MIT](https://img.shields.io/badge/License-MIT-yellow.svg)](https://opensource.org/licenses/MIT)
 [![Paper](https://img.shields.io/badge/arXiv-2508.13490-b31b1b.svg)](https://arxiv.org/abs/2508.13490)
@@ -31,13 +31,14 @@ Part of the **DyMixOp** (Dynamical Mixture of Operators) framework for learning
 
 | Dataset | PDE System | Spatial Dim | Resolution | Samples | Time Span | File Size | Key Parameters |
 |---------|------------|-------------|------------|---------|-----------|-----------|----------------|
-| [`1dKS`](./1dKS_1200x22x1x4096_dt1_t[100_120].mat) | Kuramoto-Sivashinsky | 1D | 4096 | 1,200 | t∈[100,120] | 845 MB | dt=1 |
-| [`2dBurgers`](./2dBurgers_1200x20x2x64x64_dt0.0025_t[0_0.5]_nu0.005.mat) | 2D Burgers | 2D | 64×64 | 1,200 | t∈[0,0.5] | 1.6 GB | ν=0.005, dt=0.0025 |
-| [`2dCE-CRP`](./2dCE-CRP_1430x21x5x128x128_dt0.05_t[0_1].nc) | Cahn-Hilliard + Reaction-Diffusion | 2D | 128×128 | 1,430 | t∈[0,1] | 9.6 GB | 5 channels, dt=0.05 |
-| [`2dDarcy`](./2dDarcy_5keys_2048x1x1x241x241.mat) | Darcy Flow | 2D | 241×241 | 2,048 | Steady-state | 3.7 GB | 5 permeability fields |
-| [`2dNS`](./2dNS_1200x20x1x64x64_dt1_t[10_30]_nu1e-05.mat) | 2D Navier-Stokes | 2D | 64×64 | 1,200 | t∈[10,30] | 2.2 GB | ν=1e-5, dt=1 |
-| [`3dBrusselator`](./3dBrusselator_1000x2x1x39x28x28_dt0.5_t[0_19].mat) | 3D Brusselator | 3D | 39×28×28 | 1,000 | t∈[0,19] | 478 MB | dt=0.5 |
-| [`3dShallowWater`](./3dShallowWater_1200x30x2x64x32.mat) | Shallow Water | 3D | 64×32 | 1,200 | 30 timesteps | 1.2 GB | 2 variables |
+| [`1dKS`](./1dKS_1200x22x1x4096_dt1_t[100_120].mat) | Kuramoto-Sivashinsky | 1D | 4096 | 1,200 | t∈[100,120] | 845 MB | 1 channel(Scalar $u$), dt=1 |
+| [`2dBurgers`](./2dBurgers_1200x20x2x64x64_dt0.0025_t[0_0.5]_nu0.005.mat) | Burgers | 2D | 64×64 | 1,200 | t∈[0,0.5] | 1.6 GB | 2 channel(X-Velocity $u$, Y-Velocity $v$), ν=0.005, dt=0.0025 |
+| [`2dCE-CRP`](./2dCE-CRP_1430x21x5x128x128_dt0.05_t[0_1].nc) | Compressible Euler Curved Riemann Problem | 2D | 128×128 | 1,430 | t∈[0,1] | 9.6 GB | 5 channels(Density $\rho$, X-Velocity $u$, Y-Velocity $v$, Pressure $p$, Energy $E$), dt=0.05 |
+| [`2dDarcy`](./2dDarcy_5keys_2048x1x1x241x241.mat) | Darcy Flow | 2D | 241×241 | 2,048 | Steady-state | 3.7 GB | 1 channel(Scalar $u$) |
+| [`2dNS`](./2dNS_1200x20x1x64x64_dt1_t[10_30]_nu1e-05.mat) | Navier-Stokes | 2D | 64×64 | 1,200 | t∈[10,30] | 2.2 GB | 1 channel(Vorticity $\omega$), ν=1e-5, dt=1 |
+| [`3dShallowWater`](./3dShallowWater_1200x30x2x64x32.mat) | Shallow Water | 3D (2D in Spherical) | 64×32 (Spherical) | 1,200 | 30 timesteps | 1.2 GB | 2 channels(Heigt $h$, Vorticity $\omega$) |
+| [`3dBrusselator`](./3dBrusselator_1000x2x1x39x28x28_dt0.5_t[0_19].mat) | Brusselator | 2D + 1D (Time) | 39×28×28 | 1,000 | t∈[0,19] | 478 MB | 1 channel(Spatiotemporal Trajectory of Concentration $u(x,y,t)$), dt=0.5|
+
 
 **Total: ~20GB across 7 benchmark datasets**
 
@@ -46,7 +47,7 @@ Part of the **DyMixOp** (Dynamical Mixture of Operators) framework for learning
 ### Installation
 
 ```bash
-pip install huggingface-hub numpy scipy
+pip install huggingface-hub scipy
 ```
 
 ### Direct Download
@@ -93,31 +94,15 @@ snapshot_download(
 {dimension}{system}_{samples}x{time_steps}x{channels}x{spatial_dims}_{params}.ext
 ```
 
-### Data Structure
-
-Most datasets are stored in MATLAB `.mat` format with the following structure:
-
-```python
-{
-    'u': array([...]),      # Solution fields (main data)
-    't': array([...]),      # Time coordinates
-    'x': array([...]),      # Spatial coordinates
-    'params': {...},        # System parameters
-    '__header__': bytes,    # MATLAB header
-    '__version__': str,     # MATLAB version
-    '__globals__': []       # Global variables
-}
-```
-
 ### NetCDF Format (2dCE-CRP)
 
-The Cahn-Hilliard dataset uses NetCDF format:
+The 2dCE-CRP dataset uses NetCDF format:
 
 ```python
 import netCDF4 as nc
 
 dataset = nc.Dataset('2dCE-CRP_1430x21x5x128x128_dt0.05_t[0_1].nc')
-print(dataset.variables.keys())  # View available variables
+print(dataset.keys())  # View available variables
 ```
 
 ## 🔬 Benchmark Applications