Benchmarks

[foldfelis]

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[yuehhua]

• [ ] Solve Burgers' equation by finite element method FEniCS.jl
• [ ] Solve Burgers' equation by Neural Fourier Operators

[foldfelis]

For the second task, please refer to the example. The dataset for the example is exactly the same with the one that @zongyi-li used in his repo.

[yuehhua]

Should this be documented? Or just give an example code or benchmark report?

[foldfelis]

Let's see what we get first.

[yuehhua]

FEniCS.jl seems to be not maintained for a long time. I cannot even install the package.

[foldfelis]

Try this instead… https://github.com/quinnj/There.jl

[foldfelis]

Well, I meant this： https://github.com/Ferrite-FEM/Ferrite.jl

[yuehhua]

I built a new environment for FEniCS.jl and it works! Too many deps are not up-to-date.

[yuehhua]

Maybe I need to discuss with you directly.

[yuehhua]

Does solving a finite element method need a analytic solution?

[foldfelis]

That's OK, I'll take care of the whole task.

[yuehhua]

If there is anything I can help, just let me know.

[yuehhua]

I did some search. I found that Burgers' equation need to rewrite into the weak form to code it and you may want to take a look at this. There are three common types of boundary conditions for Burgers' equation: Dirichlet, Neumann and Robin’s. The example that FNO use is Dirichlet.

As for coding the weak form, you can reference the Poisson equation tutorial here.

For installation of FEniCS.jl, I create a conda environment following the scripts here and direct PyCall.jl to the python path of the conda environment by scripts. It also need a new project environment for Julia, otherwise many packages will conflict with FEniCS.jl.

[yuehhua]

Maybe we can reference this.

[yuehhua]

Keep going, we will have better solution.

[dynamic-queries]

I am late to the discussion, but it would be nice to solve the time dependent version of the Burgers equation as well, in addition to the stationary one they solve in the paper. What do you think?