Fourier Neural Operators (FNO) in JAX

Neural Operators are mappings between (discretized) function spaces, like from the IC of a PDE to its solution at a later point in time. FNOs do so by employing a spectral convolution that allows for multiscale properties. Let's code a simple example in JAX: https://github.com/Ceyron/machine-lea...

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Timestamps:
00:00 Intro
01:09 What are Neural Operators?
03:11 About FNOs and their multiscale property
05:05 About Spectral Convolutions
09:17 A "Fourier Layer"
10:18 Stacking Layers with Lifting & Projection
11:01 Our Example: Solving the 1d Burgers equation
12:04 Minor technicalities
13:07 Installing and Importing packages
14:02 Obtaining the dataset and reading it in
15:44 Plot and Discussion of the dataset
17:51 Prepare training & test data
22:23 Implementing Spectral Convolution
34:25 Implementing a Fourier Layer/Block
37:48 Implementing the full FNO
43:14 A simple dataloader in JAX
44:18 Loss Function & Training Loop
52:34 Visualize loss history
53:31 Test prediction with trained FNO
57:13 Zero-Shot superresolution
59:59 Compute error as reported in FNO paper
01:03:45 Summary
01:05:46 Outro