---
license: other
#User-Defined Tags
tags:
  - BENO
  - CFD
  - neural operator
language:
  - en
  - zh
---
<p align="center">
  <strong>
    <span style="font-size: 30px;">BENO</span>
  </strong>
</p>

## Dataset Description

The BENO dataset originates from the ICLR 2024 paper *BENO: Boundary-Embedded Neural Operators for Elliptic PDEs* and is designed for solving elliptic partial differential equations under complex boundary conditions. The data contains random boundary geometries with four, three, two, one, or no corners, all standardized to a `32 x 32` grid resolution.

Paper: [BENO: Boundary-Embedded Neural Operators for Elliptic PDEs](https://proceedings.iclr.cc/paper_files/paper/2024/file/218ca0d92e6ed8f9db00621e103dc70c-Paper-Conference.pdf)

## Supported Tasks

| Scenario | Description |
|---|---|
| Elliptic PDE solving | Predict the solution field from the boundary conditions and the right-hand side of the equation. |
| Boundary-condition research | Compare solution performance under Dirichlet and Neumann boundary conditions. |
| Geometry generalization evaluation | Evaluate model generalization across different random boundary shapes. |
| Neural operator research | Provide standardized training and evaluation data for operator models such as BENO. |

## Dataset Format and Structure

The data is organized by boundary condition:

```text
data/
  Dirichlet/
  Neumann/
```

Each boundary-condition category contains the following six configurations: `N32_0c`, `N32_1c`, `N32_2c`, `N32_3c`, `N32_4c`, and `N32_mix`. Each configuration contains 1,000 `float64` samples:

| File | shape | Description |
|---|---|---|
| `BC_<prefix>_all.npy` | `[1000, 128, 4]` | Boundary coordinates, boundary values, and boundary features. |
| `RHS_<prefix>_all.npy` | `[1000, 1024, 4]` | Coordinates, source terms, and cell states on a 32×32 grid. |
| `SOL_<prefix>_all.npy` | `[1000, 1024, 1]` | Elliptic PDE solution fields. |

## How to Use the Dataset

This dataset has been adapted for the `OneScience-Group/BENO` model. Download the dataset and model:

```bash
hf download --dataset OneScience-Group/beno --local-dir ./data
```

## Official OneScience Information

| Platform | OneScience Main Repository | Skills Repository |
|---|---|---|
| Gitee | https://gitee.com/onescience-ai/onescience | https://gitee.com/onescience-ai/oneskills |
| GitHub | https://github.com/onescience-ai/OneScience | https://github.com/onescience-ai/oneskills |

## Citation and License

- Original BENO paper: [BENO: Boundary-embedded Neural Operators for Elliptic PDEs](https://openreview.net/forum?id=ZZTkLDRmkg)
- This dataset has been organized and converted from the original BENO dataset. Its use must comply with the licensing requirements published by the original project.