---
license: mit
tags:
  - pde
  - physics
  - numerical-simulation
pretty_name: PDE Collection
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.

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## Dataset Structure

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).

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 Hugging Face structure for a PDE dataset:

    pde/
    ├── 1D/
    │   └── ic/
    │       ├── dataset.h5
    │       ├── metadata.json
    │       └── plots/
    │           └── variable0.000_channel_0.png  # Example visualization for 1D
    ├── 2D/
    │   └── ...

### File descriptions:

-   **`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.

-----------------------------------------------------
## 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.