---
frameworks:
  - pytorch
language:
  - en
license: gpl-3.0
tags:
  - OneScience
  - KNO
  - Koopman-operator
  - neural-operator
  - computational-fluid-dynamics
  - Navier-Stokes
tasks:
  - time-series-prediction
---
<p align="center">
  <strong>
    <span style="font-size: 30px;">KNO</span>
  </strong>
</p>

# Model Overview

KNO (Koopman Neural Operator) is a neural operator based on Koopman operator theory for learning the evolution of nonlinear dynamical systems. This model predicts Navier–Stokes time series on a two-dimensional regular grid, using the first 10 time steps to predict the subsequent 10 by default.

Paper: Koopman Neural Operator as a Mesh-free Solver of Non-linear Partial Differential Equations  
https://doi.org/10.1016/j.jcp.2024.113194

# Model Description

KNO uses an encoder to map historical physical fields into a latent Koopman space, learns an approximately linear evolution operator in the Fourier domain, and reconstructs future physical fields with a decoder. The model supports either linear or nonlinear latent-state propagation and performs multistep flow prediction autoregressively.

# Use Cases

| Use Case | Description |
| :---: | :--- |
| Flow-field time-series prediction | Predict future Navier–Stokes states from historical vorticity fields |
| Koopman operator research | Study approximately linear evolution of nonlinear dynamical systems in latent space |
| CFD surrogate modeling | Learn mappings from historical to future physical fields on regular grids |
| Pipeline validation | Validate training and inference using the bundled weights or a small-scale configuration |

# Usage

## 1. OneCode

Use the online OneCode environment for an intelligent, one-click AI for Science (AI4S) programming experience:

[Launch OneCode for one-click AI4S programming](https://web-2069360198568017922-iaaj.ksai.scnet.cn:58043/home)

## 2. Manual Setup

**Hardware Requirements**

- A GPU or DCU is recommended for training and inference.
- A CPU can be used for small-scale pipeline validation, but full training will be slow.
- DCU users must install DTK and a PyTorch environment compatible with the target cluster.

### Download the Model Package

```bash
modelscope download --model OneScience/KNO --local_dir ./KNO
cd KNO
```

### Set Up the Runtime Environment

**DCU Environment**

```bash
# Activate DTK and Conda first
conda create -n onescience311 python=3.11 -y
conda activate onescience311
pip install onescience[cfd-dcu] -i http://mirrors.onescience.ai:3141/pypi/simple/ --trusted-host mirrors.onescience.ai
```

**GPU Environment**

```bash
# Activate Conda first
conda create -n onescience311 python=3.11 -y libstdcxx-ng=12 libgcc-ng=12 gcc_linux-64=12 gxx_linux-64=12
conda activate onescience311
pip install onescience[cfd-gpu] -i http://mirrors.onescience.ai:3141/pypi/simple/ --trusted-host mirrors.onescience.ai
```

### Training Data

The model uses the standard Navier–Stokes dataset `NavierStokes_V1e-5_N1200_T20.mat`, in which the data variable `u` has shape `[1200, 64, 64, 20]`. Download the data with the following command and verify that the data path in `conf/config.yaml` is configured correctly:

```bash
modelscope download --dataset OneScience/cfd_benchmark data/ns/NavierStokes_V1e-5_N1200_T20.mat --local_dir ./data
```

### Training

```bash
python scripts/train.py
```

The default weights are saved to `weight/kno_navier_stokes.pt`.

### Model Weights

This repository provides weights trained on the standard Navier–Stokes dataset in the `weight/` directory.

### Inference, Evaluation, and Visualization

The model package includes weights for pipeline validation. After preparing the data, run:

```bash
python scripts/inference.py
```

The script loads `weight/kno_navier_stokes.pt` by default. Predicted tensors and visualizations are saved to the `result/` directory. Training and inference parameters can be modified in `conf/config.yaml`.

# Official OneScience Resources

| Platform | OneScience 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 |

# Citations and License

- Xiong, W. et al. Koopman Neural Operator as a Mesh-free Solver of Non-linear Partial Differential Equations. Journal of Computational Physics, 2024.
- Xiong, W. et al. KoopmanLab: Machine Learning for Solving Complex Physics Equations. APL Machine Learning, 2023.
- The model implementation is derived from KoopmanLab under the GPL-3.0 license. This model package retains the GPL-3.0 license and the corresponding source attribution.