isuarez/pde_collection

PDE Collection

This dataset contains numerical solutions of canonical Partial Differential Equations (PDEs) generated with the 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.

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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.

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License

Released under the MIT License --- free to use, modify, and share with attribution.