Leaner serialization for solution types

[ChrisRackauckas]

The solution types contain functions, and things like JLD2 don't like functions. So it would be nice to have a "strip_solution` function that generates a much leaner form of the solution for simply doing easier serialization. Here's how that should look:

1. we should make a new trait for has_lazy_interpolation in https://github.com/SciML/SciMLBase.jl/blob/master/src/alg_traits.jl which is then set to true on BS5 and VernX solvers. strip_solution should then give an informative error message that these problems are not supported by this function. Just some proper error handling, and with that out of the way the other solvers should be free to go.
2. https://github.com/SciML/SciMLBase.jl/blob/master/src/solutions/ode_solutions.jl#L102-L118 we can strip out any of the function information from this object. I.e. make a new problem where prob and alg are nothing.
3. Downstream, sol.interp holds some extra information as well. So in SciMLBase we need strip_interp(::AbstractInterpolation). The SciMLBase ones are just the identity function, so that's easy https://github.com/SciML/SciMLBase.jl/blob/master/src/interpolation.jl .
4. At this point any non-OrdinaryDiffEq algorithm will strip well. The only downstream interp to handle is the OrdinaryDiffEq one. https://github.com/SciML/OrdinaryDiffEq.jl/blob/master/src/interp_func.jl#L4-L15 . f is only in there for the lazy interpolations, so set it to nothing. You need to keep the caches because that's used for dispatch, but at this point you're done with explicit methods.
5. For implicit methods, you need to strip https://github.com/SciML/OrdinaryDiffEq.jl/blob/master/src/caches/rosenbrock_caches.jl#L30-L33 jac_config and grad_config, as those contain function information. As a simple thing, you can just create a new cache with everything nothing though since this is only used for dispatch (and addsteps!, but since you know these caches are non-lazy the interpolation addsteps! post solution is trivial so it won't use anything in the cache). We need to make good functionality for this anyways for better default solvers (CC @oscardssmith), so it might be a good time to do this now.

With that done strip_solution(sol) should return a lean solution with no function information in it (or rather, any function information in it is in SciMLBase, which also defines the structure so that's a required import) and so it should work just fine with any BSON, JLD2, etc. package.

[jClugstor]

For the first item, should it be has_lazy_interpolation(alg::AbstractDEAlgorithm) = false,? Then e.g. has_lazy_interpolation(alg::Vern6) = true, would that go somewhere in here : https://github.com/SciML/OrdinaryDiffEq.jl/tree/07470f95ab5d76864e2d1565468305459bf39b00/lib/OrdinaryDiffEqVerner/src ?

[ChrisRackauckas]

yes, and traits go in alg_utils.jl, you'll see one in that folder.

[ChrisRackauckas]

It's just Verner and BS5 (low order RK)

[jClugstor]

Where should the strip functions go? SciMLBase utils.jl ?

[ChrisRackauckas]

BTW I created the trait SciML/OrdinaryDiffEq.jl@9734f49 since I ended up needing it. It needs to get raised to the SciMLBase level.

Where should the strip functions go? SciMLBase utils.jl ?

yes that's fine.

[jClugstor]

This adds a has_lazy_interpolation trait to SciMLBase, and sets strip_interpolation for the SciMLBase interpolations to identity, since they don't have functions in them.
#761

This adds strip_interpolation and strip_solution functions for the stuff in OrdinaryDiffEq. They basically copy the objects, just setting the function field to nothing.
SciML/OrdinaryDiffEq.jl#2316

Now I need to make a strip_solution for SciMLSolution, and work on the implicit method stuff.

[jClugstor]

https://github.com/SciML/OrdinaryDiffEq.jl/blob/master/src/caches/rosenbrock_caches.jl doesn't exist it seems
Did you mean the caches here https://github.com/SciML/OrdinaryDiffEq.jl/blob/master/src/caches/basic_caches.jl?

Or these caches for each implicit solver, e.g. https://github.com/SciML/OrdinaryDiffEq.jl/blob/master/lib/OrdinaryDiffEqRosenbrock/src/rosenbrock_caches.jl ?

[ChrisRackauckas]

The latter

[jClugstor]

It looks like SciML/OrdinaryDiffEq.jl#2320 will combine the cache types, so I'll only need to deal with RosenbrockConstantCache and RosenbrockCache, right?

[jClugstor]

Also, is there any way to tell whether an algorithm is implicit/has caches, other than looking at the docs? Would that be worth having as a trait?

[oscardssmith]

It looks like SciML/OrdinaryDiffEq.jl#2320 will combine the cache types, so I'll only need to deal with RosenbrockConstantCache and RosenbrockCache, right?

right

[ChrisRackauckas]

@jClugstor what's the next step here?