Standardize fields in AbstractDiffEqInterpolation

[bertini97]

Is your feature request related to a problem? Please describe.

I have a function which needs an AbstractDiffEqInterpolation. The interp field of ODEsolution is a InterpolationData <: AbstractDiffEqInterpolation. However, the interpolations provided in SciMLBase have u and t as fields, while InterpolationData has timeseries and ts.

Describe the solution you’d like

I would like for every AbstractDiffEqInterpolation to have the same field names for the timeseries and the times, as I think should be expected.

Additional context

I wanted to start working on a PR, but I noticed timeseries and ts are terms that appear also in the construction of the solution. Maybe it was done for consistency. If so, I would like to keep this consistency, maybe changing them to u, t even there, considering they already are of uType and tType.

[ChrisRackauckas]

We could make them all an RecursiveArrayTools.AbstractDiffEqArray which would mean it would then have a well defined interface. is that sufficient?

[bertini97]

If you intend AbstractDiffEqInterpolation <: AbstractDiffEqArray, then yes 👌

[bertini97]

@ChrisRackauckas I gave it some more thought.

Following SciML/RecursiveArrayTools.jl#415, I wanted to have AbstractTimeseries <: AbstractVectorOfArray and wanted to give it the standard fields u, t, interp. The idea is that every VectorOfArray which has time stamps can be interpolated. Default should be LinearInterpolation. Then one can do AbstractTimeseriesSolution <: AbstractTimeseries and so on, and include the fields like prob only when needed, maybe introducing DiffEqArray as it exists now. Following this, I don't know if it makes sense for an interp to be itself a Timeseries (what would its interp be?).

I want to get through with a PR that defines this interface once and for all so I can move on with this issue. I need some guidance on this given the size of SciML. What is the best place to sketch ideas? Slack?