Docs Reorganization

[Gregliest]

This PR reorganizes the docs as suggested in #247. I've taken a lot of liberties in reorganizing, with the rough outline as follows:

• Getting Started
• Tutorials
  • Linear Systems
  • Nonlinear Systems
  • Real World Examples
• Unifying SINDy and DMD
• Problems
• Basis
• Solvers
  • Koopman
  • Sparse Optimizers
  • Symbolic Regression
• Solutions

To me, this outline made the most sense because the general workflow is:

1. Define a problem
2. Choose a basis (optional)
3. Solve

However, let me know if you'd like something different.

This PR still has some outstanding issues and questions:

1. The "Basic Usage" example in "Getting Started" does not work. I think I need some help understanding why. I'd like the minimal example here for clarity. [Needs a code change]
2. I was confused by the basis generators. I'd expect something named monomial_basis to return a basis, not a vector of equations. I'll call that out in the docs, but it might be clearer to name them something like monomial_basis_eqs or something like that. [Addressed below]
3. It looks like the OccamNet stuff is in an "optional" function in the module builder, and isn't getting called when I build docs. I assume that gets built properly in CI? [Addressed]
4. Along the same line, none of the examples run locally due to an environment issue, which means that none of the png's are getting generated. [Addressed]

[AlCap23]

You have choosen a case I didn't include right now. 😅

Right now, SINDy-like methods have been dispatched on continuous, but this should be an easy fix in here, where DX has to be changed to get_target(prob).

I will commit during the day and add more test cases for Discrete and Direct Problems.

[Gregliest]

Haha cool, glad I wasn't missing something obvious. Maybe there should be a fallback method for combinations that aren't implemented that throws an error? If you point me in the right direction, I can take a stab at this.

[AlCap23]

True, but this should also be optional ( note for me ).

[AlCap23]

I agree to put a spotlight on SINDy + DMD, but maybe this should be moved into a Math Section and here we highlight Common Solver Interface ? What's your opinion on this?

[Gregliest]

What do you think people are going to be searching for in the docs? I'm not an expert in this field, but my impression is that most people think in terms of SINDy and DMD, and would search based on those terms. If that's the case, I think it's good to have those terms in the headers and side bar. However, if there's a more common search term, we should highlight that instead. I think we can highlight the common solver interface elsewhere, maybe in the getting started page. I don't think it's as important, because it's more of an engineering detail than a use case.

This is just my two cents though: you're the expert, and I'm happy to do whatever you feel is appropriate.

[AlCap23]

Hey Greg!

Very nice work so far! Thank you!

I added some minor discussion points / proposals for changes and reminder for myself 😅 .

For your list above:

1. As stated above, this is my fault. Right now, Sparse Regression is only tuned to continuous dynamical systems, but not for discrete or direct. Should be fixable.
2. Good point. Maybe we should point this out in the docs. The reason for this is due to the general common term basis for e.g. a Fourier basis vs. Our Basis, which is the more carved out representation for use withinin our algorithms. Hence the confusion. I tend to generalize a little to much, hence I wanted to return a Vector of Equations rather than a basis to be able to add my own stuff on top.
3. Yes. I normally activate the docs environment and use LiveServer.jl for the preview.
4. As above.

I am fully back and just adjusting to be fully back right now, so feel free to DM on Slack or keep this conversation going.

[AlCap23]

Ah, and I compiled an initial list of references here.

Once you feel that this PR is mature enough, I can jump in and add it and DocumenterCitations.jl .

[Gregliest]

Ok, I think this PR is in a decent place. I'd still like to check it using your LiveServer.jl workflow, so I can make sure the png's and optional module elements are working properly. But, I think most things are in and working, and stuff is reasonably proofread at this point.