---
title: 'Fourier Neural Operator for Parametric Partial Differential Equations'
license: CC-BY-4.0
license_url: https://creativecommons.org/licenses/by/4.0/
license_note: 'paper is arXiv non-exclusive distribution license (verified on arXiv abs page 2026-11-11); this pointer note is our own words and is CC BY 4.0; we link to the paper rather than reproduce it'
source: https://iinventedlight.com/library/notes/2010-08895-fourier-neural-operator.md
source_license: 'arXiv non-exclusive distribution license'
attribution: '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.'
author: 'iinventedlight (AI-assisted)'
date: 2026-11-11
status: published
approved_by: "Cole Withington, 2026-11-11 20:58 PT, Grok Bot chat widget t1717s7407: \"Publish all 100 including the LLMs Encode Clinical Knowledge note\""
checked_on: 2026-11-11
as_of: 2026-11-11
confidence: medium
untested: 'Pointer note only. Paper not reproduced. Abs page and license checked 2026-11-11.'
category: arxiv
topic_area: 'ai-research: AI-for-science'
tags: arxiv, neural-operators, pdes, ai-for-science
arxiv_id: 2010.08895
alias: 2010.08895-fourier-neural-operator
type: pointer
format: pointer
sources:
  - id: S1
    title: 'Fourier Neural Operator for Parametric Partial Differential Equations'
    publisher: arXiv
    authors: 'Zongyi Li, Nikola Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew Stuart, Anima Anandkumar'
    url: https://arxiv.org/abs/2010.08895
    version_read: 'v3 (17 May 2021)'
    accessed: 2026-11-11
    license: 'arXiv non-exclusive distribution license'
---
# Fourier Neural Operator for Parametric Partial Differential Equations

## Summary
[Fourier Neural Operator for Parametric Partial Differential Equations](https://arxiv.org/abs/2010.08895) (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.

---

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