  The classical development of neural networks has primarily focused on
learning mappings between finite-dimensional Euclidean spaces. Recently, this
has been generalized to neural operators that learn mappings between function
spaces. For partial differential equations (PDEs), neural operators directly
learn the mapping from any functional parametric dependence to the solution.
Thus, they learn an entire family of PDEs, in contrast to classical methods
which solve one instance of the equation. 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 Navier-Stokes equation. The
Fourier neural operator is the first ML-based method to successfully model
turbulent flows with zero-shot super-resolution. It is up to three orders of
magnitude faster compared to traditional PDE solvers. Additionally, it achieves
superior accuracy compared to previous learning-based solvers under fixed
resolution.
