# How to define parameters of a model built by Lux.jl in ModelingToolkit.jl and perform optimization or computation?

**URL:** <https://discourse.julialang.org/t/how-to-define-parameters-of-a-model-built-by-lux-jl-in-modelingtoolkit-jl-and-perform-optimization-or-computation/112631>\
**Category:** New to Julia\
**Tags:** package, modelingtoolkit, lux\
**Created:** [April 7, 2024, 6:46am UTC](https://discourse.julialang.org/t/how-to-define-parameters-of-a-model-built-by-lux-jl-in-modelingtoolkit-jl-and-perform-optimization-or-computation/112631 "2024-04-07T06:46:07Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![chooron](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chooron/32/208300_2.png) [@chooron](https://discourse.julialang.org/u/chooron)\
**Post date:** [April 7, 2024, 6:46am UTC](https://discourse.julialang.org/t/how-to-define-parameters-of-a-model-built-by-lux-jl-in-modelingtoolkit-jl-and-perform-optimization-or-computation/112631/1 "2024-04-07T06:46:07Z")

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I’ve just started using ModelingToolkit.jl recently, but I would like to describe and compute an ODE problem with a neural network model using ModelingToolkit.jl.

I would like to start by testing the feasibility of this with a simple demo. Here is my code:

```julia
using ModelingToolkit
using ModelingToolkit: t_nounits as t, D_nounits as D
using Optimization, OptimizationOptimisers
using Lux
using OrdinaryDiffEq
using Random

model = Lux.Chain(Lux.Dense(3, 16, tanh), Lux.Dense(16, 1, leakyrelu), name=:model)
rng = MersenneTwister()
Random.seed!(rng, 42)
ps, st = Lux.setup(rng, model)
p, re = destructure(ps)
Lux.apply(model,[1,1,1],re(p),st)
@variables x(t)
@parameters pvec[1:Lux.parameterlength(model)]
temp_func(t) = (model([sin(t), cos(t), tan(t)], re(pvec), st)[1])[1]
eqs = [D(x) ~ temp_func(t) * (x)]
u0 = [x => 1.0]
pset = [
pvec => p,
]
sys = ODESystem(eqs, t, name=:sys)
simple_sys = structural_simplify(sys)
prob = ODEProblem(simple_sys, u0, (0.0, 10.0), pset)
sol = solve(prob, Tsit5())

```

However, I encountered an error when executing `structural_simplify(sys)`

```julia
ERROR: MethodError: no method matching concrete_symtype(::Symbolics.ArrayOp{Vector{Real}})

Closest candidates are:
  concrete_symtype(::Type{Integer})
   @ ModelingToolkit D:\Julia\Julia-1.10.0\packages\packages\ModelingToolkit\hPXD5\src\systems\index_cache.jl:300
  concrete_symtype(::Type{Real})
   @ ModelingToolkit D:\Julia\Julia-1.10.0\packages\packages\ModelingToolkit\hPXD5\src\systems\index_cache.jl:299
  concrete_symtype(::Type{A}) where {T, N, A<:Array{T, N}}
   @ ModelingToolkit D:\Julia\Julia-1.10.0\packages\packages\ModelingToolkit\hPXD5\src\systems\index_cache.jl:301
  ...

```

In addition, I also constructed the ode problem through another method, as shown below:

```julia
model = Lux.Chain(Lux.Dense(3, 16, tanh), Lux.Dense(16, 1, leakyrelu), name=:model)
rng = MersenneTwister()
Random.seed!(rng, 42)
ps, st = Lux.setup(rng, model)

@variables x(t)
@parameters layer1_w[1:16, 1:3], layer1_b[1:16, 1:1]
@parameters layer2_w[1:16, 1:16], layer2_b[1:16, 1:1]

temp_func(t) = (model([sin(t), cos(t), tan(t)], (layer_1=(weight=layer1_w, bias=layer1_b), layer_2=(weight=layer2_w, bias=layer2_b)), st)[1])[1]

eqs = [D(x) ~ temp_func(t)]
u0 = [x => 1.0]
pset = [
    layer1_w => ps[:layer_1][:weight],
    layer1_b => ps[:layer_1][:bias],
    layer2_w => ps[:layer_2][:weight],
    layer2_b => ps[:layer_2][:bias],
]
sys = ODESystem(eqs, t, name=:sys)
simple_sys = structural_simplify(sys)
prob = ODEProblem(simple_sys, u0, (0.0, 10.0), pset)
sol = solve(prob, Tsit5())

```

But this will lead to the following problem:

```julia
ERROR: MethodError: no method matching *(::Int64, ::SymbolicUtils.BasicSymbolic{Matrix{Real}})

Closest candidates are:
  *(::Any, ::Any, ::Any, ::Any...)
   @ Base operators.jl:587
  *(::Integer, ::ForwardDiff.Dual{Ty}) where Ty
   @ ForwardDiff D:\Julia\Julia-1.10.0\packages\packages\ForwardDiff\PcZ48\src\dual.jl:145
  *(::Integer, ::ReverseDiff.TrackedReal)
   @ ReverseDiff D:\Julia\Julia-1.10.0\packages\packages\ReverseDiff\UJhiD\src\derivatives\scalars.jl:18

```

I hope someone can help me solve my problem.

---

<div class="post-metadata">

**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [April 7, 2024, 12:09pm UTC](https://discourse.julialang.org/t/how-to-define-parameters-of-a-model-built-by-lux-jl-in-modelingtoolkit-jl-and-perform-optimization-or-computation/112631/2 "2024-04-07T12:09:55Z")

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Just hold your horses. We only shared the library for putting neural network components into MTK yesterday

> **[GitHub - SciML/UDEComponents.jl: Easily embed neural networks in MTK models](https://github.com/SciML/UDEComponents.jl)**
>
> Easily embed neural networks in MTK models. Contribute to SciML/UDEComponents.jl development by creating an account on GitHub.

We’re still working out the last details.

---

<div class="post-metadata">

**Author:** ![chooron](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chooron/32/208300_2.png) [@chooron](https://discourse.julialang.org/u/chooron)\
**Post date:** [April 7, 2024, 12:40pm UTC](https://discourse.julialang.org/t/how-to-define-parameters-of-a-model-built-by-lux-jl-in-modelingtoolkit-jl-and-perform-optimization-or-computation/112631/3 "2024-04-07T12:40:11Z")

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Thank you very much. Looking forward to the library.