Fourier Neural Operator for Parametric Partial Differential Equations · HackerPapers discussions

Fourier Neural Operator for Parametric Partial Differential Equations — mentioned by bjenik

Wed, 26 Feb 2025 15:53:12 GMT

Working in the Fourier domain has been a staple of scientific and engineering applications. Learning those interactions rather than just hardcoding them has been fairly widely explored as well - the term to look for is Fourier Neural Operators [1][2]. It turns out you can prove universality even if the nonlinearity remains in the real domain [3]. The concept is fairly mainstream nowadays, to the degree that Jensen talked about it in his GTC keynote in 2021 [4] and there’s even a mainstage TED talk about its applications [5]. A nice property of doing things this way is that your model ends up…

Paper and discussion history. A mention is not an endorsement.

Fourier Neural Operator for Parametric Partial Differential Equations — mentioned by babel_

Thu, 28 Mar 2024 13:59:52 GMT

So, from the perspective I have within the subfield I work in, explainable AI (XAI), we're seeing a bunch of fascinating developments. First, as you mentioned, Rudin continues to prove that the reason for using AI/ML is that we don't understand the problem well enough; otherwise we wouldn't even think to use it! So, pushing our focus to better understand the problem, and then levy ML concepts and techniques (including "classical AI" and statistical learning), we're able to make something that not only outperforms some state-of-the-art in most metrics, but often even is much less resource…

Paper and discussion history. A mention is not an endorsement.

Fourier Neural Operator for Parametric Partial Differential Equations — mentioned by aqme28

Mon, 02 Nov 2020 17:03:34 GMT

This is a busy week for neural differential equation solvers. Here's another interesting one using a neural network to solve complicated PDEs like Navier-Stokes: https://arxiv.org/abs/2010.08895

Paper and discussion history. A mention is not an endorsement.

Fourier Neural Operator for Parametric Partial Differential Equations — HN submission

Fri, 30 Oct 2020 22:41:52 GMT

Fourier Neural Operator for Parametric Partial Differential Equations

2 points; 0 discussion replies on HN. Paper and source history. A submission is not an endorsement.

Fourier Neural Operator for Parametric Partial Differential Equations — HN submission

Fri, 30 Oct 2020 18:48:36 GMT

Fourier Neural Operator for Parametric Partial Differential Equations

4 points; 0 discussion replies on HN. Paper and source history. A submission is not an endorsement.