Adding SciMLLogging Integration

[jClugstor]

Creating an issue here to keep track of stuff and as a convenient place to ask questions.

We want to add SciMLLogging integration (https://github.com/SciML/SciMLLogging.jl), at this point it's been added to most of the main numerical solvers in SciML, so it's about time to add it to MTK.

A couple of things that need to be figured out:

• In the numerical solvers, the verbosity object used by SciMLLogging is put in to the solver caches in some way, e.g. in OrdinaryDiffEq the verbosity is in the DEOptions, which is part of the integrator. For LinearSolve it's just in the LinearCache. The reason to have it in these caches is that in order for the SciMLMessage macro to work, it needs access to the verbosity object. It just so happens that in many of the places you would want to emit a log message, the cache is available, so it's a convenient place to store the verbosity. Otherwise we would need to make the verbosity object a global, or else thread it through to every function that needs to emit a log message. I'm not sure if there's an analogous object that is able to hold the verbosity object in MTK that also is able to be accessed at most of the places where we want to emit logs. So it might end up being necessary to thread the verbosity object through many of these functions, or finding some other alternative.

• We might want to do Symbolics / SymbolicUtils verbosity first?

[AayushSabharwal]

Symbolics/SymbolicUtils can happen later. There's a lot of entry points there. Basically every API function that wants to log would require its own verbosity object. The solver libraries benefit from solve/init being basically the only two entry points.

For MTK, I think it makes sense to start from the ground up. Verbosity specifiers for mtkcompile, complete and generate_initializesystem. Then one for process_SciMLProblem. The last one can likely be reused for ODEProblem, though individual problem constructors may want their own.