Automatically return extrapolated solution

[valentinsulzer]

Right now, a solution needs to be multiplied by prob.extrapolation to obtain the solution including boundary conditions.
Should this be done automatically instead?
solve receives all the necessary information to do so (contained in the PDEProblem)

[ChrisRackauckas]

Yes, there's a similar issue in NeuralPDE. Different discretizations all end up doing standard numerical problems, but afterwards they want to take the solution have some common way to analyze the result. This'll take some thinking to unify how to do this.

[valentinsulzer]

I don't have the big picture for a unified solution with NeuralPDE, but for the MOL cases at the very least the solution should be returned at the points in prob.space. Since prob stores the discretization this should be possible even allowing for different MOL discretizations (FiniteDifference, FiniteElement, FiniteVolume, etc)

[ChrisRackauckas]

Superseded by https://github.com/SciML/DiffEqOperators.jl/issues/357