# Parameters in DiffEqFlux

**URL:** <https://discourse.julialang.org/t/parameters-in-diffeqflux/44959>\
**Category:** New to Julia\
**Tags:** flux\
**Created:** [August 14, 2020, 9:05pm UTC](https://discourse.julialang.org/t/parameters-in-diffeqflux/44959 "2020-08-14T21:05:02Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![colinclout12](https://avatars.discourse-cdn.com/v4/letter/c/dfb087/32.png) [@colinclout12](https://discourse.julialang.org/u/colinclout12)\
**Post date:** [August 14, 2020, 9:05pm UTC](https://discourse.julialang.org/t/parameters-in-diffeqflux/44959/1 "2020-08-14T21:05:02Z")

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I’m having trouble understanding how to enter the trainable parameters into DiffEqFlux.

In order to understand how DiffEqFlux works, I set myself the following exercise: Replace `p = [1.5, 1.0, 3.0, 1.0]` in the [example](https://diffeqflux.sciml.ai/dev/examples/optimization_ode/) of optimizing an ODE, with a neural network that learns the parameters as a function of an input vector (say, `u0`, but it could be anything).

(This is, of course, an impractical complication, the goal is that it prove an instructive exercise.)

The problem I’m running into is that I can’t figure out how to enter the resulting parameters into `DiffEqFlux.sciml_train`.

My code is as follows:

```julia
#Copied from the manual
using DifferentialEquations, Flux, Optim, DiffEqFlux, DiffEqSensitivity, Plots

function lotka_volterra!(du, u, p, t)
  x, y = u
  α, β, δ, γ = p
  du[1] = dx = α*x - β*x*y
  du[2] = dy = -δ*y + γ*x*y
end

#My neural net (by hand for the sake of the exercise):
W1 = rand(5,2)
b1 = rand(5)
W2 = rand(4,5)
b2 = rand(4)
model(x) = relu.(W2*relu.(W1*x + b1) + b2)

#Copied from the manual
tspan = (0.0, 10.0)
tsteps = 0.0:0.1:10.0

#Copied from the manual, but with p replaced by model(u0)).
prob = ODEProblem(lotka_volterra!, u0, tspan, model(u0))
sol = solve(prob, Tsit5())

using Plots
plot(sol) #Generates a plot using the model.

function loss()
  sol = solve(prob, Tsit5(), p=#=Can't see what goes here=#, saveat = tsteps)
  loss = sum(abs2, sol.-1)
  return loss, sol
end

callback = function (p, l, pred)
  display(l)
  plt = plot(pred, ylim = (0, 6))
  display(plt)
  return false
end

result_ode = DiffEqFlux.sciml_train(loss,
                                     #=params(W1,W2,b1,b2) returns error=#,
                                    ADAM(0.1),
                                    cb = callback,
                                    maxiters = 100)

```

Anyway, I’m kinda at a loss here for how to handle the parameters. I can’t put `params(W1,W2,b1,2)` into the `sciml_train` function, since it returns an error:

```julia
ERROR: MethodError: no method matching copy(::Zygote.Params)
Closest candidates are:
  copy(::Expr) at expr.jl:36
  copy(::Core.CodeInfo) at expr.jl:64
  copy(::BitSet) at bitset.jl:46
  ...
Stacktrace:
 [1] sciml_train(::Function, ::Zygote.Params, ::ADAM, ::Base.Iterators.Cycle{Tuple{DiffEqFlux.NullData}}; cb::Function, maxiters::Int64, progress::Bool, save_best::Bool) at C:\Users\MattProgramming\.juliapro\JuliaPro_v1.4.2-1\packages\DiffEqFlux\FZMwP\src\train.jl:77
 [2] top-level scope at none:0

```

And if I put in the parameters explicitly (e.g., using W1 for the parameter), nothing trains.

(I think I may be able to solve this problem as a neural differential equation, by chaining `lotka_volterra` into the neural differential equation, but this problem doesn’t seem, in principle, any more complicated than the manual example. Except I can’t figure out how to tell it which parameters to use.)

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<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:** [August 15, 2020, 3:00pm UTC](https://discourse.julialang.org/t/parameters-in-diffeqflux/44959/2 "2020-08-15T15:00:27Z")

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> [@colinclout12](#):
>
> Anyway, I’m kinda at a loss here for how to handle the parameters. I can’t put `params(W1,W2,b1,2)` into the `sciml_train` function, since it returns an error:

The parameters need to be an array. If you want to use an array that has a bit more structure, I’d suggest using ComponentArrays.jl, which has an example on this:

[https://jonniedie.github.io/ComponentArrays.jl/dev/examples/DiffEqFlux/](https://jonniedie.github.io/ComponentArrays.jl/dev/examples/DiffEqFlux/)

Or if you want to have multiple different arrays for the parameters, you can use the Flux style for the optimization demonstrated at:

[https://diffeqflux.sciml.ai/dev/examples/neural\_ode\_flux/](https://diffeqflux.sciml.ai/dev/examples/neural_ode_flux/)

(However, note that the Flux style does limit the available optimizers)

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**Author:** ![colinclout12](https://avatars.discourse-cdn.com/v4/letter/c/dfb087/32.png) [@colinclout12](https://discourse.julialang.org/u/colinclout12)\
**Post date:** [August 15, 2020, 7:59pm UTC](https://discourse.julialang.org/t/parameters-in-diffeqflux/44959/3 "2020-08-15T19:59:19Z")

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Thank you! This is very helpful.