Fourier Neural Operator for Parametric Partial Differential Equations - Paper Explained

Explore an in-depth explanation of the Fourier Neural Operator for Parametric Partial Differential Equations in this comprehensive video. Delve into the innovative approach that revolutionizes the solution of PDEs by learning mappings between function spaces. Understand the Navier-Stokes problem statement, formal problem definition, and the concept of neural operators. Discover how the Fourier Neural Operator parameterizes the integral kernel in Fourier space, resulting in an expressive and efficient architecture. Examine experimental examples, including Burgers' equation, Darcy flow, and the Navier-Stokes equation in the turbulent regime. Follow along with a code walkthrough and gain insights into the state-of-the-art performance of this method compared to traditional PDE solvers and existing neural network methodologies.

- Intro & Overview
- Navier Stokes Problem Statement
- Formal Problem Definition
- Neural Operator
- Fourier Neural Operator
- Experimental Examples
- Code Walkthrough
- Summary & Conclusion