KNO
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
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
modelscope download --model OneScience/KNO --local_dir ./KNO
cd KNO
Set Up the Runtime Environment
DCU Environment
# 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
# 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:
modelscope download --dataset OneScience/cfd_benchmark data/ns/NavierStokes_V1e-5_N1200_T20.mat --local_dir ./data
Training
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:
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.