Inplace Problem Specification for Methods with size(residual) != size(u)

[avik-pal]

Currently, for inplace problems the residual vector is determined by the size of the input u. This is not necessarily correct for problems that support overconstrained / underconstrained setups. For example:

NonlinearSolve.jl/src/levenberg.jl

Lines 269 to 270 in 691e10a

	fu = zero(u)
	f(fu, u, p)

Could we potentially add a kwarg like residual_size which could be used to initialize this?

[ChrisRackauckas]

I think it may just be best to just use jac_prototype for this?

[avik-pal]

That seems like the proper solution. I will prototype this in NeuralBVP.jl and then port it over here.