# AD through DataInterpolations, ODE : Gradient calculation, parameter -\> time series -\> DataInterpolation

**URL:** <https://discourse.julialang.org/t/ad-through-datainterpolations-ode-gradient-calculation-parameter-time-series-datainterpolation/126758>\
**Category:** General Usage\
**Tags:** zygote, sciml, differentialequation, datainterpolations\
**Created:** [March 10, 2025, 1:15pm UTC](https://discourse.julialang.org/t/ad-through-datainterpolations-ode-gradient-calculation-parameter-time-series-datainterpolation/126758 "2025-03-10T13:15:09Z")\
**Posts on this page:** 3\
**Page:** 1

<div class="post-metadata">

**Author:** ![Rohan\_Rajagopal](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/rohan_rajagopal/32/34183_2.png) [@Rohan\_Rajagopal](https://discourse.julialang.org/u/Rohan_Rajagopal)\
**Post date:** [March 10, 2025, 1:15pm UTC](https://discourse.julialang.org/t/ad-through-datainterpolations-ode-gradient-calculation-parameter-time-series-datainterpolation/126758/1 "2025-03-10T13:15:09Z")

</div>

Greetings!

The question is regarding AD through DataInterpolations, ODE. The function is described as follows,

```julia
using DataInterpolations, OrdinaryDiffEq, SciMLSensitivity, Zygote

time = 0.:0.1:20
function temp(ps)
    x = sin.(ps .* time)
    x_interp = CubicSpline(x, time)
    x_t = t -> x_interp(t)
    function system_augment!(du, u, ps, t)
        du[1, :] .= u[2, :]'  
        du[2, :] .= (-1 .+ 1 .* ps(t))'
    end
    system!(du, u, ps, t) = system_augment!(du, u, ps, t)
    prob = ODEProblem{true, SciMLBase.FullSpecialize}(system!, rand(2, 1), (0, 2), x_t)  
    sol = solve(prob, saveat = 0.1, )
    out = sum(Array(sol))
    return out  
end
temp(0.1)

```

Now calculating the error,

```julia
gradient(temp, 0.1) # Fails, the error is given by

ERROR: `p` is not a SciMLStructure. This is required for adjoint sensitivity analysis. For more information,
see the documentation on SciMLStructures.jl for the definition of the SciMLStructures interface.
In particular, adjoint sensitivities only applies to `Tunable`.

Stacktrace:
  [1] automatic_sensealg_choice(prob::ODEProblem{…}, u0::Matrix{…}, p::@NamedTuple{…}, verbose::Bool, repack::Functors.var"#3#6"{…})
    @ SciMLSensitivity ~/.julia/packages/SciMLSensitivity/7UEpc/src/concrete_solve.jl:87
  [2] _concrete_solve_adjoint(::ODEProblem{…}, ::Nothing, ::Nothing, ::Matrix{…}, ::Function, ::SciMLBase.ChainRulesOriginator; verbose::Bool, kwargs::@Kwargs{…})
    @ SciMLSensitivity ~/.julia/packages/SciMLSensitivity/7UEpc/src/concrete_solve.jl:274
  [3] _concrete_solve_adjoint
    @ ~/.julia/packages/SciMLSensitivity/7UEpc/src/concrete_solve.jl:245 [inlined]
  [4] #_solve_adjoint#66
    @ ~/.julia/packages/DiffEqBase/PbBEl/src/solve.jl:1584 [inlined]
  [5] _solve_adjoint
    @ ~/.julia/packages/DiffEqBase/PbBEl/src/solve.jl:1557 [inlined]
  [6] #rrule#4
    @ ~/.julia/packages/DiffEqBase/PbBEl/ext/DiffEqBaseChainRulesCoreExt.jl:26 [inlined]
  [7] rrule
    @ ~/.julia/packages/DiffEqBase/PbBEl/ext/DiffEqBaseChainRulesCoreExt.jl:22 [inlined]
  [8] rrule
    @ ~/.julia/packages/ChainRulesCore/U6wNx/src/rules.jl:144 [inlined]
  [9] chain_rrule_kw
    @ ~/.julia/packages/Zygote/TWpme/src/compiler/chainrules.jl:236 [inlined]
 [10] macro expansion
    @ ~/.julia/packages/Zygote/TWpme/src/compiler/interface2.jl:0 [inlined]
 [11] _pullback
    @ ~/.julia/packages/Zygote/TWpme/src/compiler/interface2.jl:91 [inlined]
 [12] _apply
    @ ./boot.jl:946 [inlined]
 [13] adjoint
    @ ~/.julia/packages/Zygote/TWpme/src/lib/lib.jl:202 [inlined]
 [14] _pullback
    @ ~/.julia/packages/ZygoteRules/CkVIK/src/adjoint.jl:67 [inlined]
 [15] #solve#42
    @ ~/.julia/packages/DiffEqBase/PbBEl/src/solve.jl:1043 [inlined]
 [16] _pullback(::Zygote.Context{…}, ::DiffEqBase.var"##solve#42", ::Nothing, ::Nothing, ::Nothing, ::Val{…}, ::@Kwargs{…}, ::typeof(solve), ::ODEProblem{…})
    @ Zygote ~/.julia/packages/Zygote/TWpme/src/compiler/interface2.jl:0
 [17] _apply
    @ ./boot.jl:946 [inlined]
 [18] adjoint
    @ ~/.julia/packages/Zygote/TWpme/src/lib/lib.jl:202 [inlined]
 [19] _pullback
    @ ~/.julia/packages/ZygoteRules/CkVIK/src/adjoint.jl:67 [inlined]
 [20] solve
    @ ~/.julia/packages/DiffEqBase/PbBEl/src/solve.jl:1033 [inlined]
 [21] _pullback(::Zygote.Context{…}, ::typeof(Core.kwcall), ::@NamedTuple{…}, ::typeof(solve), ::ODEProblem{…})
    @ Zygote ~/.julia/packages/Zygote/TWpme/src/compiler/interface2.jl:0
 [22] temp
    @ ~/Documents/Julia/Custom_Lux_DONN/Neural_Feedback_VDP_Network.jl:447 [inlined]
 [23] _pullback(ctx::Zygote.Context{false}, f::typeof(temp), args::Float64)
    @ Zygote ~/.julia/packages/Zygote/TWpme/src/compiler/interface2.jl:0
 [24] pullback(f::Function, cx::Zygote.Context{false}, args::Float64)
    @ Zygote ~/.julia/packages/Zygote/TWpme/src/compiler/interface.jl:90
 [25] pullback
    @ ~/.julia/packages/Zygote/TWpme/src/compiler/interface.jl:88 [inlined]
 [26] gradient(f::Function, args::Float64)
    @ Zygote ~/.julia/packages/Zygote/TWpme/src/compiler/interface.jl:147
 [27] top-level scope
    @ ~/Documents/Julia/Custom_Lux_DONN/Neural_Feedback_VDP_Network.jl:453

```

But this works,

```julia
time = 0.:0.1:20
function temp(ps)
    x = sin.(ps .* time)
    function system_augment!(du, u, ps, t)
        du[1, :] = u[2, :]'  
        du[2, :] = (-1 .+ 1 .* ps[[trunc(Int64, 1 + t/0.1)]])'
    end
    system!(du, u, ps, t) = system_augment!(du, u, ps, t)
    prob = ODEProblem{true, SciMLBase.FullSpecialize}(system!, rand(2, 1), (0,1), x)  
    sol = solve(prob, saveat = 0.1, )
    out = sum(Array(sol))
    return out  
end
temp(0.1)

gradient(temp, 0.1) # (5188.061373048052,)

```

I thought it was interesting. The DataInterpolations usage seemed natural, the latter just seems weird, is there any reason for the DataInterpolations version to work?

Thanks very much

---

<div class="post-metadata">

**Author:** ![BdeKoning](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/bdekoning/32/214557_2.png) [@BdeKoning](https://discourse.julialang.org/u/BdeKoning)\
**Post date:** [March 11, 2025, 7:32pm UTC](https://discourse.julialang.org/t/ad-through-datainterpolations-ode-gradient-calculation-parameter-time-series-datainterpolation/126758/2 "2025-03-11T19:32:12Z")

</div>

In your first example the line `x_t = t -> x_interp(t)` seems redundant; `x_t` is a trivial wrapper of `x_interp`.

The problem could be with `Zygote` support of `DataInterpolations.jl`, that has never been brought to a solid level iirc.

---

<div class="post-metadata">

**Author:** ![Rohan\_Rajagopal](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/rohan_rajagopal/32/34183_2.png) [@Rohan\_Rajagopal](https://discourse.julialang.org/u/Rohan_Rajagopal)\
**Post date:** [March 12, 2025, 5:46am UTC](https://discourse.julialang.org/t/ad-through-datainterpolations-ode-gradient-calculation-parameter-time-series-datainterpolation/126758/3 "2025-03-12T05:46:38Z")

</div>

Ohhh, thanks very much for clarification. I think I read somewhere the focus is on developing Enzyme for most purposes. I will see what Enzyme does.

> In your first example the line `x_t = t -> x_interp(t)` seems redundant; `x_t` is a trivial wrapper of `x_interp` .

Ohh, yes, thank you for this.