updated README with correct Data Structure

README.md

@@ -9,31 +9,63 @@ task_categories:
   - other
 ---
 
+# PDE Collection
+
+This dataset contains numerical solutions of canonical **Partial
+Differential Equations (PDEs)** generated with the
+[ines-lang/pde-solver](https://github.com/ines-lang/pde-solver).\
+It provides standardized datasets for benchmarking PDE solvers, machine
+learning surrogates, and physics-informed methods.
+
+------------------------------------------------------------------------
+
 ## Dataset Structure
 
-When you run the code from [ines-lang/pde-solver](https://github.com/ines-lang/pde-solver), it automatically generates a directory structure based on the **selected PDE** and **initial condition (IC)**.
+When running the solver locally, the directory structure is organized by
+**dimension first** (e.g., `1D/`, `2D/`, `3D/`), then by PDE type and
+initial condition (IC).
 
-This folder structure matches the format in which this dataset is organized and shared here.
+However, on Hugging Face the datasets follow a slightly different
+organization: files are grouped by **PDE type first**, then by
+dimension.\
+This difference ensures consistency when browsing multiple PDE datasets.
 
-### Example structure for a 1D PDE dataset:
+### Example Hugging Face structure for a PDE dataset:
 
-```
-1D/
-├── pde/
-│   └── ic/
-│       ├── dataset.h5
-│       ├── metadata.json
-│       └── plots/
-│           └── seed_i.png  # for 1D
-```
+    pde/
+    ├── 1D/
+    │   └── ic/
+    │       ├── dataset.h5
+    │       ├── metadata.json
+    │       └── plots/
+    │           └── variable0.000_channel_0.png  # Example visualization for 1D
+    ├── 2D/
+    │   └── ...
 
 ### File descriptions:
-- **`dataset.h5`**: Contains the full dataset with the generated PDE solution data.
-- **`metadata.json`**: Describes the PDE type, initial conditions, and solver parameters.
-- **`plots/`**: Contains sample visualizations for each generated seed.
 
----
+-   **`dataset.h5`**: HDF5 file with the PDE solution data
+    (multi-dimensional arrays over space and time).
+-   **`metadata.json`**: Describes PDE type, dimensionality, ICs, BCs,
+    solver method, and parameters.
+-   **`plots/`**: Folder with quick-look PNG visualizations of generated
+    seeds for inspection.
 
-You can extend this structure to other PDEs and dimensions (e.g., `2D/`, `3D/`) following the same hierarchy.
+-----------------------------------------------------
+## Applications
 
----
+This dataset supports research and education in scientific computing and machine learning:  
+
+- **Benchmarking**: Standardized data for evaluating PDE solvers and surrogate models.  
+- **Machine Learning**: Training physics-informed and reduced-order models for dynamical systems.  
+- **Reproducibility**: Consistent metadata and structure enable reliable comparisons across studies.  
+- **Extensibility**: Easily adapted to new PDEs, parameter regimes, or boundary conditions.  
+
+By combining reproducible datasets with rich metadata, this resource bridges **numerical analysis and modern ML**, providing a foundation for standardized benchmarks in data-driven PDE modeling.
+
+------------------------------------------------------------------------
+
+## License
+
+Released under the **MIT License** --- free to use, modify, and share
+with attribution.