Fourier Neural Operator

This repository contains a PyTorch implementation of the following paper:

Fourier Neural Operator for Parametric Partial Differential Equations

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

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

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

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

Requirements

To install requirements for cpu, run the following command:

pip install -r requirements_cpu.txt

To install requirements for gpu, run the following command:

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