# Optimization problem inside \`ODESystem\`
**URL:** https://discourse.julialang.org/t/optimization-problem-inside-odesystem/123445
**Category:** Modelling & Simulations
**Created:** [December 4, 2024, 10:21am UTC](https://discourse.julialang.org/t/optimization-problem-inside-odesystem/123445 "2024-12-04T10:21:16Z")
**Posts on this page:** 3
**Page:** 1
### Author:  [@Sushrut\_Deshpande](https://discourse.julialang.org/u/Sushrut_Deshpande)
#### Post date: [December 4, 2024, 10:21am UTC](https://discourse.julialang.org/t/optimization-problem-inside-odesystem/123445/1 "2024-12-04T10:21:16Z")
Hello,
I am trying to solve an optimization problem with the variables of an `ODESystem`. I have a toy code below:
```julia
using ModelingToolkit, DifferentialEquations, Optimization, OptimizationOptimJL,ForwardDiff, Optim
using ModelingToolkit: t_nounits as t, D_nounits as D
function SolveAlpha(x0,p)
f(x,p) = 1
f_opt = OptimizationFunction(f,AutoForwardDiff())
prob = OptimizationProblem(f_opt,x0,p)
sol = solve(prob,Optim.BFGS())
return sol.u
end
@register_symbolic SolveAlpha(x0,p)
@component function system(;name)
vars =@variables begin
x(t),
y(t),
α(t)
end
para = @parameters begin
x0 = [1.0]
end
eqs = [
D(x) ~ -y
D(y) ~ x
α ~ SolveAlpha(x0,[x,y])
]
System(eqs, t, vars, para;name=name)
end
@named mysys = system()
sys = structural_simplify(mysys)
u0 = [sys.x => 1.0, sys.y => 0.0]
tspan = (0,10)
para = []
prob = ODEProblem(sys,u0,tspan,para)
sol = solve(prob)
```
The error i get is the following:
```julia
ERROR: LoadError: MethodError: no method matching fill!(::Num, ::Num)
The function `fill!` exists, but no method is defined for this combination of argument types
```
This is internal to Optimization.jl → NLSolversBase.jl.
So my question would be is it possible to pass the local variables of a `@component` to optimizers? Or is there something wrong with the way iI have used `@register_symbolic` which fails here?
Thank you
---
### Author:  [@Bart\_van\_de\_Lint](https://discourse.julialang.org/u/Bart_van_de_Lint)
#### Post date: [December 4, 2024, 2:33pm UTC](https://discourse.julialang.org/t/optimization-problem-inside-odesystem/123445/2 "2024-12-04T14:33:17Z")
You are getting into problems with packing your variables in vectors. Here is the working solution.
```julia
using ModelingToolkit, DifferentialEquations, Optimization, OptimizationOptimJL,ForwardDiff, Optim
using ModelingToolkit: t_nounits as t, D_nounits as D
function solve_alpha(x0,x,y)
x0 = [x0]
p = [x, y]
f(x,p) = 1
f_opt = OptimizationFunction(f,AutoForwardDiff())
prob = OptimizationProblem(f_opt,x0,p)
sol = solve(prob,Optim.BFGS())
return sol.u
end
@register_symbolic solve_alpha(x0,x,y)
@component function system(;name)
vars =@variables begin
x(t),
y(t),
α(t)
end
para = @parameters begin
x0 = 1.0
end
eqs = [
D(x) ~ -y
D(y) ~ x
α ~ solve_alpha(x0,x,y)
]
System(eqs, t, vars, para;name=name)
end
@named mysys = system()
sys = structural_simplify(mysys)
u0 = [sys.x => 1.0, sys.y => 0.0]
tspan = (0,10)
para = []
prob = ODEProblem(sys,u0,tspan,para)
sol = solve(prob)
```
---
### Author:  [@Sushrut\_Deshpande](https://discourse.julialang.org/u/Sushrut_Deshpande)
#### Post date: [December 4, 2024, 2:58pm UTC](https://discourse.julialang.org/t/optimization-problem-inside-odesystem/123445/3 "2024-12-04T14:58:55Z")
Thanks!!