New tutorial: Partitioned Burgers eq. 1D

[vidulejs]

New tutorial case: Partitioned Burgers' Equation in 1D solved with SciPy Finite Volume implementation and a Neural Network surrogate model !

• Fix README.md to comply with the standard
• How to run surrogate,
• Improve README.md further
• Clean up the scripts in base directory
• What to do with the initial condition generation? Steps are too complex currently
• How to reproduce the offline model, i.e., training scripts
• Either remove old .solver-nutils-dgalerkin or fix
• Read through again https://precice.org/community-contribute-to-precice.html
• Allow skipping venv setup

Checklist:

• I added a summary of any user-facing changes (compared to the last release) in the changelog-entries/<PRnumber>.md.
• I will remember to squash-and-merge, providing a useful summary of the changes of this PR.

[uekerman]

Thanks for the very nice addition already! I only had brief look in this first iteration and did not yet try to run things. Please see comments below.

Let's indeed remove the Nutils solver. Could always be added later again.

[uekerman]

I was able to run the cases and got meaningful results. We are probably close to merging this. Mainly cosmetics now.

I think a few scripts of utils could go into solver-scipy. Only keep those in utils that are used by neumann-surrogate as well.

[MakisH]

@vidulejs it would be great to be able to include this in the upcoming distribution release. With a quick look, I think that most/all of the open points here are rather easy to resolve.

Let me know if I can help; I could also resolve some of these (but not all) directly.

[MakisH]

@vidulejs I applied as much of the feedback as I could. Only a few comments are still missing:

• A reference to your thesis (ideally with a URL, but let's not wait for it)
• Some documentation on how the surrogate model has been trained
• Some description of the .pth files
• An example or more details on visualizing

It would be great if you could quickly add these comments, so that we can finally get this one merged and published.

[vidulejs]

Hey Makis! Thanks so much for the help and for budging me! Please see my commits, I hope I've addressed the last problems. Regarding the surrogate model training -- I added another paragraph to the existing README to explain what the .pth checkpoints are.

Actually, I can do one better and provide the full training scripts or the Jupyter notebook to reproduce the models. Problem is that those scripts are not up to the quality of the preCICE tutorials repo. I had created a public repo called neural-adapter where I did all of my master's thesis development work. It contains a bunch of slightly disorganized Jupyter notebooks and a few development artifacts. Anyway, today I pulled the repo on my new system and was able to reproduce the model training. I updated the README of that repo to include the model training workflow.

Now the question is whether to point to that repo for the model training or not. Please take a look and let me know if this is acceptable. Otherwise I could try to re-create a standalone training script just for this tutorial.