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fourier-neural-operator-0.9
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تبلیغات ما
مشتریان به طور فزاینده ای آنلاین هستند. تبلیغات می تواند به آنها کمک کند تا کسب و کار شما را پیدا کنند.
مشاهده بیشتر
تبلیغات ما
مشتریان به طور فزاینده ای آنلاین هستند. تبلیغات می تواند به آنها کمک کند تا کسب و کار شما را پیدا کنند.
مشاهده بیشترتوضیحات
Library and exemples to use the fourier neural operator
| ویژگی | مقدار |
|---|---|
| سیستم عامل | - |
| نام فایل | fourier-neural-operator-0.9 |
| نام | fourier-neural-operator |
| نسخه کتابخانه | 0.9 |
| نگهدارنده | [] |
| ایمیل نگهدارنده | [] |
| نویسنده | - |
| ایمیل نویسنده | - |
| آدرس صفحه اصلی | https://github.com/Forbu/fourier_neural_operator |
| آدرس اینترنتی | https://pypi.org/project/fourier-neural-operator/ |
| مجوز | - |
[](https://shields.io/)
# Fourier Neural Operator package
The original code and package come from : https://github.com/zongyi-li/fourier_neural_operator (the original author of the fourier neural operator paper).
We created some minor modification on the package to create a proper pip package using fourier neural operator.
You can install it using (after having download the repo)
```bash
python setup.py install
```
or simply using pypi :
```bash
pip install fourier-neural-operator
```
Then to create a fourier model with the pytorch framework, you can write :
```python
import fourier_neural_operator.fourier_2d as fourier_2d
model = fourier_2d.FNO2d(modes1=modes1, modes2=modes2, width=width, channel_input=3, output_channel=3)
```
You can also simply import fourier layer :
```python
from fourier_neural_operator.fourier_2d.layers.fourier_2d import SpectralConv2d
spectral_layer = SpectralConv2d(width, width, modes1, modes2)
```
The package is still under construction and modification will come for fourier_3d and 1d.
# Fourier Neural Operator explaination
This repository contains the code for the paper:
- [(FNO) Fourier Neural Operator for Parametric Partial Differential Equations](https://arxiv.org/abs/2010.08895)
In this work, we formulate a new neural operator by parameterizing the integral kernel directly in Fourier space, allowing for an expressive and efficient architecture.
We perform experiments on Burgers' equation, Darcy flow, and the Navier-Stokes equation (including the turbulent regime).
Our Fourier neural operator shows state-of-the-art performance compared to existing neural network methodologies and it is up to three orders of magnitude faster compared to traditional PDE solvers.
It follows from the previous works:
- [(GKN) Neural Operator: Graph Kernel Network for Partial Differential Equations](https://arxiv.org/abs/2003.03485)
- [(MGKN) Multipole Graph Neural Operator for Parametric Partial Differential Equations](https://arxiv.org/abs/2006.09535)
You can check the code in the exemples_paper/ directory.
## Requirements
- We have updated the files to support [PyTorch 1.8.0](https://pytorch.org/).
Pytorch 1.8.0 starts to support complex numbers and it has a new implementation of FFT.
As a result the code is about 30% faster.
- Previous version for [PyTorch 1.6.0](https://pytorch.org/) is avaiable at `FNO-torch.1.6`.
## Files
The code is in the form of simple scripts. Each script shall be stand-alone and directly runnable.
- `exemples_paper/fourier_1d_exemple.py` is the Fourier Neural Operator for 1D problem such as the (time-independent) Burgers equation discussed in Section 5.1 in the [paper](https://arxiv.org/pdf/2010.08895.pdf).
- `exemples_paper/fourier_2d_exemple.py` is the Fourier Neural Operator for 2D problem such as the Darcy Flow discussed in Section 5.2 in the [paper](https://arxiv.org/pdf/2010.08895.pdf).
- `exemples_paper/fourier_2d_time_exemple.py` is the Fourier Neural Operator for 2D problem such as the Navier-Stokes equation discussed in Section 5.3 in the [paper](https://arxiv.org/pdf/2010.08895.pdf), which uses a recurrent structure to propagates in time.
- `exemples_paper/fourier_3d_exemple.py` is the Fourier Neural Operator for 3D problem such as the Navier-Stokes equation discussed in Section 5.3 in the [paper](https://arxiv.org/pdf/2010.08895.pdf), which takes the 2D spatial + 1D temporal equation directly as a 3D problem
- The lowrank methods are similar. These scripts are the Lowrank neural operators for the corresponding settings.
- `data_generation` are the conventional solvers we used to generate the datasets for the Burgers equation, Darcy flow, and Navier-Stokes equation.
## Datasets
We provide the Burgers equation, Darcy flow, and Navier-Stokes equation datasets we used in the paper.
The data generation configuration can be found in the paper.
- [PDE datasets](https://drive.google.com/drive/folders/1UnbQh2WWc6knEHbLn-ZaXrKUZhp7pjt-?usp=sharing)
The datasets are given in the form of matlab file. They can be loaded with the scripts provided in utilities.py.
Each data file is loaded as a tensor. The first index is the samples; the rest of indices are the discretization.
For example,
- `Burgers_R10.mat` contains the dataset for the Burgers equation. It is of the shape [1000, 8192],
meaning it has 1000 training samples on a grid of 8192.
- `NavierStokes_V1e-3_N5000_T50.mat` contains the dataset for the 2D Navier-Stokes equation. It is of the shape [5000, 64, 64, 50],
meaning it has 5000 training samples on a grid of (64, 64) with 50 time steps.
We also provide the data generation scripts at `data_generation`.
## Models
Here are the pre-trained models. It can be evaluated using _eval.py_ or _super_resolution.py_.
- [models](https://drive.google.com/drive/folders/1swLA6yKR1f3PKdYSKhLqK4zfNjS9pt_U?usp=sharing)
## Citations
```
@misc{li2020fourier,
title={Fourier Neural Operator for Parametric Partial Differential Equations},
author={Zongyi Li and Nikola Kovachki and Kamyar Azizzadenesheli and Burigede Liu and Kaushik Bhattacharya and Andrew Stuart and Anima Anandkumar},
year={2020},
eprint={2010.08895},
archivePrefix={arXiv},
primaryClass={cs.LG}
}
@misc{li2020neural,
title={Neural Operator: Graph Kernel Network for Partial Differential Equations},
author={Zongyi Li and Nikola Kovachki and Kamyar Azizzadenesheli and Burigede Liu and Kaushik Bhattacharya and Andrew Stuart and Anima Anandkumar},
year={2020},
eprint={2003.03485},
archivePrefix={arXiv},
primaryClass={cs.LG}
}
```
## Future work
We are currently adding some new work to the repo :
- [ ] Factorized Fourier Neural Operator
- [ ] Conditioned Fourier Neural Operator
نحوه نصب
نصب پکیج whl fourier-neural-operator-0.9:
pip install fourier-neural-operator-0.9.whl
نصب پکیج tar.gz fourier-neural-operator-0.9:
pip install fourier-neural-operator-0.9.tar.gz