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Fourier-Neural-Operator

★ 36 Open GitHub ↗

Implementation of Fourier Neural Operator using PyTorch

// repository documentation

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# Fourier Neural Operator

[![PyTorch](https://img.shields.io/badge/PyTorch-2.1.0-red.svg)](https://pytorch.org/)
[![Python](https://img.shields.io/badge/Python-3.8.0-blue.svg)](https://www.python.org/)
[![Google Colab](https://img.shields.io/badge/Google%20Colab-Open%20In%20Colab-yellow.svg)](https://colab.research.google.com/drive/15ztLOeiNlLfpwnqhw-Q1btFOAwybXjfL?usp=sharing)
![alpha](https://img.shields.io/badge/alpha-0.1.0-orange.svg)

This repository contains a PyTorch implementation of the following paper:

> [**Fourier Neural Operator for Parametric Partial Differential Equations**](https://arxiv.org/abs/2010.08895)

## Navier-Stokes equations

This repository contains a code for data generation to solve Navier-Stokes equations using spectral method. The Navier-Stokes equations are given by

$$
\begin{align*}
\partial_t w(x,t) + u(x,t) \cdot \nabla w(x,t) &= \nu \Delta w(x,t) + f(x)\\
\nabla \cdot u(x,t) &= 0\\
w(x,0) &= w_0(x)
\end{align*}
$$

![Navier-Stokes prediction](https://raw.githubusercontent.com/abelsr/Fourier-Neural-Operator/main/</src/FNO_NavierStokes_super_resolution512_model64.gif>)

also, it is included a Jupyter notebook to train and test the model using the data generated by the previous code.

## Heat equation

This repository contains a jupyter notebook to solve heat equation using spectral method. The heat equation is given by

$$
\begin{align*}
\frac{\partial u}{\partial t} - \alpha \nabla^2 u &= 0\\
\end{align*}
$$

![Heat Equation prediction](https://raw.githubusercontent.com/abelsr/Fourier-Neural-Operator/main/</src/HeatEquation2D_FNO.gif>)

## Requirements

To install requirements for cpu, run the following command:

```setup
pip install -r requirements_cpu.txt
```

To install requirements for gpu, run the following command:

```setup
pip install -r requirements_gpu.txt
```

Also if you prefer install by yourself, you can install the following packages:

- `torch`
- `matplotlib`
- `numpy`
- `scipy`
- `tqdm`
- `h5py`

Fourier-Neural-Operator

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