[ANN] OperatorLearning.jl: Functional mappings to solve parametric PDEs

Dear Community,

I’d like to share a package with you (my first one actually) that I created recently in order to learn (nonlinear) operators to solve PDEs: OperatorLearning.jl

This is basically a port from Zongyi Li’s Fourier Neural Operator and Lu Lu’s DeepONet that is currently implemented in DeepXDE.

I simply wanted to use these architectures in Julia, with some added flexibility and the nice syntax we all love :blush:

Last time I checked, this implementation of the FNO even does training a little faster than the original version on the Burgers equation example that Li and colleagues provide, thanks to the awesome work of the Flux.jl team :tada:

It’s far from complete and there are still some features that I would like to incorporate, most importantly the use of physics-informed losses to alleviate the amount of data needed for training - following the respective recent works 1 2.

I’m looking forward to your impressions! Of course, if you see something wrong in the code or with the package, feel free to let me know.


Looks like there is an existing implementation of some of these operator-learning methods (https://github.com/foldfelis/NeuralOperators.jl). Did your implementations end up being similar?

Hi, thanks for bringing it up. I sort of realized that afterwards as well. Both packages include the Fourier Neural Operator (the rest going in different directions though), but as far as I can tell the implementations are rather different when comparing the relevant sources of OperatorLearning vs. NeuralOperators side by side.

I’m not really sure about which one would perform better on a given problem, but I guess having choices doesn’t hurt :smile:

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