---
license: apache-2.0
language:
  - en
  - zh
tags:
  - OneScience
  - Kolmogorov-flow
  - computational-fluid-dynamics
  - turbulence
  - vorticity
  - neural-operator
  - FactFormer
frameworks:
  - NumPy
pretty_name: Kolmogorov Flow 2D Re1000
---
<p align="center">
  <strong>
    <span style="font-size: 30px;">Kolmogorov Flow 2D</span>
  </strong>
</p>

## Dataset Description

This dataset contains time series of single-channel vorticity fields obtained from numerical simulations of two-dimensional Kolmogorov Flow. It can be used for turbulence time-series forecasting, neural operator training, partial differential equation surrogate modeling, and long-horizon autoregressive forecasting.

The data describes scalar vorticity fields over a two-dimensional periodic domain. The dataset contains 120 trajectories, each with 320 frames, a spatial resolution of `256 x 256`, a data type of `float32`, and a Reynolds number of `Re = 1000`. The dataset has been adapted for `OneScience-Group/FactFormer`.

## Supported Tasks

| Scenario | Description |
|---|---|
| Multi-step flow field forecasting | Predict flow fields for multiple subsequent time steps from historical vorticity fields. |
| Autoregressive time-series modeling | Feed model outputs back into the input window for long-horizon rollouts. |
| Neural operator research | Compare operator architectures such as Transformer, FNO, UNO, and KNO. |
| Turbulence surrogate modeling | Learn the spatiotemporal evolution mappings produced by numerical solvers. |

## Dataset Format and Structure

The main data file is in NumPy `.npy` format:

```text
kf_2d_re1000_256_120seed.npy
```

The array shape is `[120, 320, 256, 256]`, with the dimensions representing trajectory, time, x-grid, and y-grid, respectively. The original file is approximately 9.38 GiB. On-demand access via `numpy.load(..., mmap_mode="r")` is recommended to avoid copying the entire array into memory.

The data contains only vorticity fields; it does not include velocity, pressure, forcing fields, or physical time-step information.

## How to Use the Dataset

Download the dataset:

```bash
hf download --dataset OneScience-Group/Kolmogorov_flow_2d --local-dir ./Kolmogorov_flow_2d
```

To use the dataset with FactFormer, set the data directory in `FactFormer/conf/config.yaml` to the download directory, and run:

```bash
cd FactFormer
python scripts/train.py
python scripts/inference.py
```

By default, FactFormer downsamples the spatial resolution to `128 x 128` and uses the first 10 frames to predict the subsequent 16 frames.

## 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

- Recommended model: `OneScience/FactFormer`.
- FactFormer: Liu-Schiaffini et al., *FactFormer: Factorized Transformer for Modeling Long-Range Dependencies in PDE Surrogate Modeling*.
- The documentation and supporting scripts in this repository are licensed under Apache-2.0. Before publicly distributing or redistributing the numerical data, verify its upstream source and licensing requirements.