Fourier Neural Operator for Parametric Partial Differential Equations
Summary
Fourier Neural Operator for Parametric Partial Differential Equations (2020) showed a practical way to learn mappings between function spaces for parametric PDEs. Instead of learning a solution at one resolution, the Fourier neural operator learns an operator that can be evaluated at different discretizations.
What it introduced: the Fourier neural operator (FNO), which does global convolution in Fourier space so that a network can learn a resolution-invariant mapping from a PDE's input function to its solution.
What it led to: a line of neural-operator methods used in scientific machine learning, and a comparison point for later learned simulators, including weather models such as GraphCast (a full verification note in batch B).
Where to read it: https://arxiv.org/abs/2010.08895 (v3, last revised 17 May 2021).
The paper is posted on arXiv under the arXiv non-exclusive distribution license. This note links to it rather than reproducing it. The note itself is CC BY 4.0.
License: this note is CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Pointer by iinventedlight (AI-assisted). Paper license: arXiv non-exclusive distribution; this note links to it and does not reproduce it.
License: CC-BY-4.0 · Pointer by iinventedlight (AI-assisted). Source: Zongyi Li, Nikola Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew Stuart, Anima Anandkumar, Fourier Neural Operator for Parametric Partial Differential Equations (arXiv non-exclusive distribution license). This note links to the paper rather than reproducing it.
Cite this
'iinventedlight (AI-assisted)'. 2026. "Fourier Neural Operator for Parametric Partial Differential Equations." iinventedlight Library, iil:note:svfvj1py, version of 2026-11-11. https://iinventedlight.com/library/notes/2010-08895-fourier-neural-operator/. License: CC-BY-4.0.
@misc{iil_note_svfvj1py,
author = {{'iinventedlight (AI-assisted)'}},
title = {{Fourier Neural Operator for Parametric Partial Differential Equations}},
howpublished = {iinventedlight Library},
year = {2026},
date = {2026-11-11},
url = {https://iinventedlight.com/library/notes/2010-08895-fourier-neural-operator/},
note = {Permanent ID iil:note:svfvj1py. License: CC-BY-4.0.},
}Spotted a mistake? Use the MCP feedback tool or email hello@iinventedlight.com.
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