Incomplete derivative expansion with DataInterpolations

[contradict]

See this discourse discussion for the source of this example, simplified here.

using ModelingToolkit, OrdinaryDiffEq, DataInterpolations

Cp = 0.0244:0.011:0.387
TSR = 2.0:0.25:10.0
cp = CubicSpline(Cp, TSR)

@variables t ω(t)
D = Differential(t)
eqs = [D(ω) ~ cp(8*ω)]
@named sys = ODESystem(eqs, t)
sys = structural_simplify(sys)

u0 = [ω=>0.9]
tspan = (0.0, 1000.0)
prob = ODEProblem(sys, u0, tspan, [], jac = true)

Inspecting prob.f.jac.jac_iip

julia> prob.f.jac.jac_iip
RuntimeGeneratedFunction(#=in ModelingToolkit=#, #=using ModelingToolkit=#, :((ˍ₋out, ˍ₋arg1, ˍ₋arg2, t)->begin
          #= /home/user/.julia/packages/SymbolicUtils/H684H/src/code.jl:350 =#
          #= /home/user/.julia/packages/SymbolicUtils/H684H/src/code.jl:351 =#
          #= /home/user/.julia/packages/SymbolicUtils/H684H/src/code.jl:352 =#
          begin
              begin
                  begin
                      #= /home/user/.julia/packages/Symbolics/3jLt1/src/build_function.jl:520 =#
                      #= /home/user/.julia/packages/SymbolicUtils/H684H/src/code.jl:399 =# @inbounds begin
                              #= /home/user/.julia/packages/SymbolicUtils/H684H/src/code.jl:395 =#
                              ˍ₋out[1] = (*)(8, (Differential(ω(t)))(([0.0244, 0.0354, 0.0464, 0.0574, 0.0684, 0.0794, 0.0904, 0.1014, 0.1124, 0.1234, 0.1344, 0.1454, 0.1564, 0.1674, 0.1784, 0.1894, 0.2004, 0.2114, 0.2224, 0.2334, 0.2444, 0.2554, 0.2664, 0.2774, 0.2884, 0.2994, 0.3104, 0.3214, 0.3324, 0.3434, 0.3544, 0.3654, 0.3764, 2.0, 2.25, 2.5, 2.75, 3.0, 3.25, 3.5, 3.75, 4.0, 4.25, 4.5, 4.75, 5.0, 5.25, 5.5, 5.75, 6.0, 6.25, 6.5, 6.75, 7.0, 7.25, 7.5, 7.75, 8.0, 8.25, 8.5, 8.75, 9.0, 9.25, 9.5, 9.75, 10.0])((*)(8, ˍ₋arg1[1]))))
                              #= /home/user/.julia/packages/SymbolicUtils/H684H/src/code.jl:397 =#
                              nothing
                          end
                  end
              end
          end
      end))

There is still an unexpanded Differential(ω(t)) in there.

[ufechner7]

Thanks for opening this issue!

[ChrisRackauckas]

There is still an unexpanded Differential(ω(t)) in there.

That's because DataInterpolations seems to be missing a derivative definition. It has a registration:

https://github.com/PumasAI/DataInterpolations.jl/blob/master/ext/DataInterpolationsSymbolicsExt.jl#L11

and it has derivatives defined:

https://github.com/PumasAI/DataInterpolations.jl/blob/master/src/derivatives.jl

But someone needs to add the symbolic derivative definition. That's done like:

https://symbolics.juliasymbolics.org/stable/manual/derivatives/#Adding-Analytical-Derivatives

by eye I think it's:

function Symbolics.derivative(::typeof(interp), args::NTuple{1,Any}, ::Val{1}) where {interp<:DataInterpolations.AbstractInterpolation}
   derivative(interp, args[1])
end

Try that. If that works then we just need some tests and can add that to DataInterpolations.

[contradict]

PR here SciML/DataInterpolations.jl#166