# Gradient of ODESystem containing a loop

**URL:** <https://discourse.julialang.org/t/gradient-of-odesystem-containing-a-loop/110103>\
**Category:** Numerics\
**Created:** [February 12, 2024, 2:19pm UTC](https://discourse.julialang.org/t/gradient-of-odesystem-containing-a-loop/110103 "2024-02-12T14:19:22Z")\
**Posts on this page:** 3\
**Page:** 1

<div class="post-metadata">

**Author:** ![Kieran\_Marray](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/kieran_marray/32/35686_2.png) [@Kieran\_Marray](https://discourse.julialang.org/u/Kieran_Marray)\
**Post date:** [February 12, 2024, 2:19pm UTC](https://discourse.julialang.org/t/gradient-of-odesystem-containing-a-loop/110103/1 "2024-02-12T14:19:22Z")

</div>

Hi! I am trying to take the gradient of an ODESystem containing a loop using either Zygote or ForwardDiff. Both seem to fail when I do so. Here is a minimal working example (taken from a previous JuliaForum post)

```julia

using Zygote, SciMLSensitivity, ForwardDiff, DifferentialEquations

# succeeds

function fiip(du,u,p,t)
    du[1] = dx = p[1]*u[1] - p[2]*u[1]*u[2]
    du[2] = dy = -p[3]*u[2] + p[4]*u[1]*u[2]
  end
  
  p = [1.5,1.0,3.0,1.0]; u0 = [1.0;1.0]
  prob = ODEProblem(fiip,u0,(0.0,10.0),p)
  sol = solve(prob,Tsit5())
  
  plot(sol)
  
  function sum_of_solution(x)
      _prob = remake(prob,p=x)
      sum(solve(_prob,Tsit5(),saveat=0.1))
  end
  
  ForwardDiff.gradient(sum_of_solution,p)

# fails with both Zygote and ForwardDiff

function fiip(du,u,p,t,N)
    sv = zeros(Int64(2))
    for i in 1:N
        sv[i] = u[i]
    end
    du[1] = dx = p[1]*sv[1] - p[2]*u[1]*u[2]
    du[2] = dy = -p[3]*sv[2] + p[4]*u[1]*u[2]
  end

  p = [1.5,1.0,3.0,1.0]; u0 = [1.0;1.0]

  fiip2(du,u0,p,t) = fiip(du,u0,p,t, 2)
  prob = ODEProblem(fiip2,u0,(0.0,10.0),p)
  
  sol = solve(prob,Tsit5())
  
  plot(sol)
  
  function sum_of_solution(x)
      _prob = remake(prob,p=x)
      sum(solve(_prob,Tsit5(),saveat=0.1))
  end
  
  ForwardDiff.gradient(sum_of_solution,p)

```

The loop really is necessary in my minimum working example, as using a state variable that is a sum of lots of the us… Any idea how to get this working?

---

<div class="post-metadata">

**Author:** ![baggepinnen](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/baggepinnen/32/693_2.png) [@baggepinnen](https://discourse.julialang.org/u/baggepinnen)\
**Post date:** [February 12, 2024, 2:27pm UTC](https://discourse.julialang.org/t/gradient-of-odesystem-containing-a-loop/110103/2 "2024-02-12T14:27:20Z")

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> [@Kieran\_Marray](#):
>
> `sv = zeros(Int64(2))`

With ForwardDiff, this is likely part of the problem, you are creating an array of `Float64` values. Create this as

```julia
zeros(eltype(u), 2)

```

and then make sure that `u0` has the same element type as `p`, i.e.,

```julia
_prob = remake(prob,p=x, u0 = eltype(p).(u0))

```

or something like that.

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<div class="post-metadata">

**Author:** ![Kieran\_Marray](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/kieran_marray/32/35686_2.png) [@Kieran\_Marray](https://discourse.julialang.org/u/Kieran_Marray)\
**Post date:** [February 12, 2024, 2:38pm UTC](https://discourse.julialang.org/t/gradient-of-odesystem-containing-a-loop/110103/3 "2024-02-12T14:38:32Z")

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Thanks so much! This works perfectly