# Optimization of states and parameters with Multibody.jl and ModelingToolkit
**URL:** https://discourse.julialang.org/t/optimization-of-states-and-parameters-with-multibody-jl-and-modelingtoolkit/126156
**Category:** Modelling & Simulations
**Tags:** optimization, modelingtoolkit
**Created:** [February 21, 2025, 3:32pm UTC](https://discourse.julialang.org/t/optimization-of-states-and-parameters-with-multibody-jl-and-modelingtoolkit/126156 "2025-02-21T15:32:09Z")
**Posts on this page:** 2
**Page:** 1
### Author:  [@Odie](https://discourse.julialang.org/u/Odie)
#### Post date: [February 21, 2025, 3:32pm UTC](https://discourse.julialang.org/t/optimization-of-states-and-parameters-with-multibody-jl-and-modelingtoolkit/126156/1 "2025-02-21T15:32:09Z")
Hi all,
I’m working with a large model created with Multibody.jl and would like to use it to run some optimizations. The optimization variables could be model parameters as well as model states (see a simple problem example below).
I am facing a difficulty to use the auto-differentiation in my problem.
Basing my code on the documentation found here : docs.sciml.ai/ModelingToolkit/v9.59/examples/remake/ , I can’t find a way to use an AutoForwardDiff method. Indeed, on one hand, the replace/remake function are not happy with the JuliaSimCompiler system (used for Multibody.jl), and on the other hand, I can’t find a way to replace state values (equivalent to ‘setu’) with these methods. The functions setp/setu don’t allow a type change and I want to use ForwardDiff.Dual because my model is fully differentiable. Is there a way I could use AutoForwardDiff in my use case?
Below is a MWE of my problem type. I built this one because the solution is trivial and I can debug easily my syntax.
```julia
using ModelingToolkit
using Multibody
using OrdinaryDiffEq
using Optimization, OptimizationMOI, Ipopt
using SymbolicIndexingInterface
opt_solver = OptimizationMOI.MOI.OptimizerWithAttributes(Ipopt.Optimizer,
"hessian_approximation" => "limited-memory",
"print_level" => 5,
"max_iter" => 10)
t = Multibody.t
Dt = Differential(t)
@mtkmodel DummyExampleModel begin
@structural_parameters begin
r_trans = [0.0, 0.0, -1.0]
end
@variables begin
w_dot(t)
end
@components begin
world = Multibody.World(n=[0.0, 0.0, -1.0])
motion = Multibody.Revolute(n=[0, 1, 0])
body = Multibody.Body(state_priority=true)
trans = Multibody.FixedTranslation(r=r_trans)
end
@equations begin
w_dot ~ Dt(motion.w)
connect(world.frame_b, motion.frame_a)
connect(motion.frame_b, trans.frame_a)
connect(body.frame_a, trans.frame_b)
end
end
@named mdl = DummyExampleModel()
mdl = complete(mdl)
ssys = structural_simplify(multibody(mdl))
modified_params = [
mdl.motion.phi => deg2rad(90.0)
]
ode_prob = ODEProblem(ssys, modified_params, (0.0, 0.001))
function loss(x, p)
ode_prob_loc = p[1]
setter_states_loc! = p[2]
setter_states_loc!(ode_prob_loc, x)
sol = solve(p[1], Tsit5(), saveat=0.01)
objective = -sol[mdl.w_dot][1]^2
return objective
end
function cons!(r, x, p)
ode_prob_loc = p[1]
setter_states_loc! = p[2]
setter_states_loc!(ode_prob_loc, x)
sol = solve(p[1], Tsit5(), saveat=0.01)
r .= [sol[mdl.motion.w][1]]
end
optim_var = [mdl.motion.phi]
setter_states! = setu(ssys, optim_var) # Limitation : 'setu' is not compatible with ForwardDiff.Dual according to doc
optim_var_x0 = [deg2rad(170.0)]
opt_fun = OptimizationFunction(loss, Optimization.AutoFiniteDiff(); cons=cons!) # I'd like to use Optimization.AutoForwardDiff() but it's not compatible with 'setu'
opt_prob = OptimizationProblem(opt_fun, optim_var_x0, (ode_prob, setter_states!); lb=[deg2rad(0.0)], ub=[deg2rad(180.0)], lcons=[0.0], ucons=[0.0])
sol = solve(opt_prob, opt_solver)
# sol_timeseries = solve(ode_prob, Tsit5(), saveat=0.01)
# import GLMakie
# Multibody.render(mdl, sol_timeseries, display=true, up=[0, 0, 1], x=0, y=5, z=0, lookat=[0, 0, 0], loop=true, cache=false, framerate=10)
```
I am using the current LTS v1.10.8 with :
```julia-repl
[e9467ef8] GLMakie v0.10.18
[b6b21f68] Ipopt v1.7.2
[8391cb6b] JuliaSimCompiler v0.1.26
[961ee093] ModelingToolkit v9.59.0
[e1cad5d1] Multibody v0.3.2
[7f7a1694] Optimization v4.1.1
[fd9f6733] OptimizationMOI v0.5.2
[36348300] OptimizationOptimJL v0.4.1
[1dea7af3] OrdinaryDiffEq v6.91.0
[53ae85a6] SciMLStructures v1.6.1
[2efcf032] SymbolicIndexingInterface v0.3.38
```
---
### Author:  [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)
#### Post date: [March 2, 2025, 10:15pm UTC](https://discourse.julialang.org/t/optimization-of-states-and-parameters-with-multibody-jl-and-modelingtoolkit/126156/2 "2025-03-02T22:15:20Z")
> [@Odie](#):
>
> Indeed, on one hand, the replace/remake function are not happy with the JuliaSimCompiler system (used for [Multibody.jl](https://juliaregistries.github.io/General/packages/redirect_to_repo/Multibody)), and on the other hand, I can’t find a way to replace state values (equivalent to ‘setu’) with these methods. The functions setp/setu don’t allow a type change and I want to use ForwardDiff.Dual because my model is fully differentiable. Is there a way I could use AutoForwardDiff in my use case?
Yes currently that is not compatible with autodiff because it’s using an alternative compiler, but we’re working to remedy that with the next phase of the multibody system.