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---
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. |