Add self-supervised 3D-Var-based AI data assimilation

[SOHAMPAL23]

Pull Request

• Add self-supervised AI-based data assimilation using 3D-Var loss

Description

• This PR introduces a self-supervised AI-based data assimilation prototype

• The implementation replaces supervised learning with a physics-based 3D-Var cost function, allowing the model to learn directly from:

• Sparse/noisy observations

How Has This Been Tested?

Please describe the tests that you ran to verify your changes. Provide instructions so we can reproduce.
Please also list any relevant details for your test configuration

• Yes

If your changes affect data processing, have you plotted any changes? i.e. have you done a quick sanity check?

• Yes

Checklist:

• My code follows OCF's coding style guidelines
• I have performed a self-review of my own code
• I have made corresponding changes to the documentation
• I have added tests that prove my fix is effective or that my feature works
• I have checked my code and corrected any misspellings
  [Paper] AI-based Data Assimilation #173

[SOHAMPAL23]

Hey @jacobbieker Can you check this pr

[jacobbieker]

Thanks for some simplication. Please look at the comments made on the previous PR, they aren't all addressed in this one.

[jacobbieker]

Thanks for addressing some of the comments, but you haven't addressed them all or fixed the changes I've asked for. Please do that before requesting my review again.

[SOHAMPAL23]

Hey @jacobbieker Can You now give review on this

[Sidharth1743]

@SOHAMPAL23 use the review button. don't tag him. it will be notified in that way itself. thanks:)

[SOHAMPAL23]

@Sidharth1743 Thanks for letting me know that.

So Till he reviews it, I can work on other issues

[jacobbieker]

Could you make sure your newly added code passes the linting? It will need more docstrings at least that I can see. I know running the pre-commit throws a lot of errors, but I just care about this newly added code passing those linting steps as well.