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---
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license: mit
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tags:
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- pde
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- physics
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- numerical-simulation
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pretty_name: PDE Collection
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task_categories:
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- other
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---
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# PDE Collection
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This dataset contains numerical solutions of canonical **Partial
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Differential Equations (PDEs)** generated with the
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[ines-lang/pde-solver](https://github.com/ines-lang/pde-solver).\
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It provides standardized datasets for benchmarking PDE solvers, machine
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learning surrogates, and physics-informed methods.
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------------------------------------------------------------------------
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## Dataset Structure
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When running the solver locally, the directory structure is organized by
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**dimension first** (e.g., `1D/`, `2D/`, `3D/`), then by PDE type and
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initial condition (IC).
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However, on Hugging Face the datasets follow a slightly different
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organization: files are grouped by **PDE type first**, then by
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dimension.\
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This difference ensures consistency when browsing multiple PDE datasets.
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### Example Hugging Face structure for a PDE dataset:
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pde/
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├── 1D/
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│ └── ic/
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│ ├── dataset.h5
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│ ├── metadata.json
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│ └── plots/
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│ └── variable0.000_channel_0.png # Example visualization for 1D
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├── 2D/
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│ └── ...
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### File descriptions:
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- **`dataset.h5`**: HDF5 file with the PDE solution data
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(multi-dimensional arrays over space and time).
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- **`metadata.json`**: Describes PDE type, dimensionality, ICs, BCs,
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solver method, and parameters.
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- **`plots/`**: Folder with quick-look PNG visualizations of generated
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seeds for inspection.
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-----------------------------------------------------
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## Applications
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This dataset supports research and education in scientific computing and machine learning:
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- **Benchmarking**: Standardized data for evaluating PDE solvers and surrogate models.
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- **Machine Learning**: Training physics-informed and reduced-order models for dynamical systems.
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- **Reproducibility**: Consistent metadata and structure enable reliable comparisons across studies.
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- **Extensibility**: Easily adapted to new PDEs, parameter regimes, or boundary conditions.
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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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------------------------------------------------------------------------
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## License
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Released under the **MIT License** --- free to use, modify, and share
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with attribution. |
