How to apply the FNO to NS equation

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Mike 2024-4-17

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https://ww2.mathworks.cn/matlabcentral/answers/2108366-how-to-apply-the-fno-to-ns-equation

回答： CSCh 2024-4-25

Hi, can anyone explain me how to adopt this code to solve Navierstokes equation?

fourier-neural-operator - File Exchange - MATLAB Central (mathworks.com)

Many thanks, Mike.

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Answer 1

CSCh 2024-4-25

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Hi Mike,

if I understand correctly, the FNO only learns from data and does not need the NS-PDE equation. So you need a set of data, in the case of 2D NS, x, y as input variables for the network, and U and V representing the solutions at a given time. The FNO now learns the NS from these data that are subject to these laws. If I see this correctly, you only have to embed the additional variables y (additionally as the input variable for the network) and V into the ‘helper function’. Maybe Conor Daly, the author can made some additional comments on that?

BR, Chris