Srk table

[andyElking]

Hi Patrick,
this is a lightweight PR, adding some more SRK documentation. The first commit just adds the table of all SDE solvers into docs/api/solvers/sde_solver.md. The second commit adds a Jupyter notebook to examples/, wherein I gave a walkthrough of the basics SDE simulation in Diffrax. Feel free to get rid of the second commit if you do not find it necessary :)

[patrick-kidger]

So I'm feeling this table is maybe better-suited to the devdocs. It's a useful reference but this is large enough that I don't think I can commit to ensuring its accuracy + that it remains up-to-date. (We can add a reference to it from the main SDE docs, whilst mentioning the above caveats.)

As for the example -- note that WeaklyDiagonalControlTerm is now deprecated in favour of a ControlTerm returning a lx.DiagonalLinearOperator, so we should avoid recommending it. My main comment here is that I think you need to kill some darlings -- I try to keep the examples fairly short to ensure readability.

[andyElking]

I removed some things from sde_example.ipynb and moved it to devdocs. I removed the table from sde_solvers.md, but I added a link pointing to the table at the bottom of sde_example.ipynb.

I feel like it is important to at least somewhere in the docs show users the canonical way of batch-solving SDEs, because Monte Carlo is the primary use case of SDE simulation. This is why I think we should really keep that part of the notebook.

[lockwo]

Should ralston and EulerHeun also be in the table?

[andyElking]

Should ralston and EulerHeun also be in the table?

Good point, I'll add them.

[andyElking]

I added Ralston and EulerHeun to the table.

[patrick-kidger]

Okay, I like this!
I should have clearer in my past message by the way, I think only the table of SDE information needs to be in the devdocs (and it should be included in mkdocs.yml). I think the notebook you have here is really useful, so I'd actually like to include that in the main example docs!

I don't think GitHub lets me comment on notebook files so I'll leave review feedback here instead:

• can you tidy up the Diffrax imports, so that it doesn't appear twice?
• Can you standardise the notation to the same used throughout the rest of the Diffrax documentation, e.g. see here: https://docs.kidger.site/diffrax/usage/how-to-choose-a-solver/#stochastic-differential-equations (Note how I use y instead of Y, w instead of W etc -- the style and characters I use are chosen to allow using equivalent notation for ODEs/SDEs/CDEs interchangably.)
• I'd like to title this 'Advanced SDE example' since it includes topics like Levy area, Monte Carlo etc.
• Let's have just print(f"Minimal levy area for SPaRK: {solver.minimal_levy_area}.") (no __name__) -- I prefer simplicity of code over simplicity of printout in these examples.
• It is very important to have h > bm_tol -- can you briefly add a sentence explaining why?
• I'd really prefer for examples to not rely on private functionality, or functions defined in tests. Let's rewrite the 'optimizing wrt SDE parameters' section to be a bit simpler, focusing on just the optimization?
• For the ito-vs-stratonovich, different noise types, etc., then I'd like to avoid duplicating the information already in https://docs.kidger.site/diffrax/usage/how-to-choose-a-solver/#stochastic-differential-equations -- can you just link to that instead? (And add any extra information there if you think something is missing.)

WDYT? :)

[andyElking]

Hi Patrick!

I agree with all of your comments and I made the appropriate modifications. Two notes however:

• In the definition of commutative noise you originally used \mu and \sigma. Because I instead use f and g everywhere else, including in AbstractSRK documentation, I opted to just convert everything to f and g. I assume you don't mind the change too much as long as the notation is consistent everywhere. LMK
• I agree I shouldn't use a private method such as _batch_sde_solve in the example, so I just wrote an equivalent in the notebook. However, several people (including two of James's new students and another person at the Edinburgh conference) were asking me about canonical ways to do Monte Carlo with Diffrax, so we could consider writing an equivalent of _batch_sde_solve in Diffrax proper and making it public. I don't feel very strongly about this though.

Please let me know if I missed anything or if you notice anything else I should change.