# ODE parameter estimation on a subset of the parameters

**URL:** <https://discourse.julialang.org/t/ode-parameter-estimation-on-a-subset-of-the-parameters/28013>\
**Category:** General Usage\
**Tags:** question, diffeq\
**Created:** [August 26, 2019, 9:51pm UTC](https://discourse.julialang.org/t/ode-parameter-estimation-on-a-subset-of-the-parameters/28013 "2019-08-26T21:51:03Z")\
**Posts on this page:** 3\
**Page:** 1

<div class="post-metadata">

**Author:** ![biona001](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/biona001/32/16497_2.png) [@biona001](https://discourse.julialang.org/u/biona001)\
**Post date:** [August 26, 2019, 9:51pm UTC](https://discourse.julialang.org/t/ode-parameter-estimation-on-a-subset-of-the-parameters/28013/1 "2019-08-26T21:51:03Z")

</div>

Hello, I’m a differential equation newbie.

I have an ODE model with 50 parameters and 10 compartments. I have data measured in only 3 compartments and I wish to fit 6 parameters. The 3 compartment problem is discussed [here](https://discourse.julialang.org/t/differential-equation-parameter-estimation-using-only-a-subset-of-variables/23423), but how do I fit my 6 parameters while holding the other 40 fixed?

For example, I modified the Lotka-Volterra model ([docs](https://docs.juliadiffeq.org/latest/analysis/parameter_estimation.html#Optimization-Based-ODE-Inference-Examples-1)) so the `-3` becomes the second parameter of `p`:

```julia
function f(du,u,p,t)
  du[1] = dx = p[1]*u[1] - u[1]*u[2]
  du[2] = dy = p[2]*u[2] + u[1]*u[2]
end

#problem & initial condition
u0 = [1.0, 1.0]
tspan = (0.0, 10.0)
p = [1.5, -3]
prob = ODEProblem(f,u0,tspan,p)

#simulate data
t = collect(range(0,stop=10,length=200))
using RecursiveArrayTools # for VectorOfArray
randomized = VectorOfArray([(sol(t[i]) + .01randn(2)) for i in 1:length(t)])
data = convert(Array,randomized)

#define cost function to calculate error in both compartments
cost_function = build_loss_objective(prob,Tsit5(),L2Loss(t, data),
                                     maxiters=10000,verbose=false, save_idxs=[1, 2])

function closure()
	# what goes here?
end

```

**Question: How would I just fit the 1st parameter `p[1]` and hold `p[2]` constant at `-3`?**

Possible method 1:  
Following some recommendation on Slack, I am using `save_idxs` in `build_loss_objective`, and I’m trying to build a [closure](http://julianlsolvers.github.io/Optim.jl/latest/#user/tipsandtricks/#_top) to only optimize the parameters I want. However, I can’t figure out what this closure is supposed to look like. Should I redefine a new ODE based on the subset of parameters I care about in this closure? (probably not).

Possible method 2:  
The other way that will work is to redefine a new ODE model where only the parameters I want to estimate are parameters, and those that should be fixed are hard-coded into the equations. However, I have more than 50 parameters and I may wish to estimate different subsets of them in the future, so this method is probably not a good way either.

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<div class="post-metadata">

**Author:** ![biona001](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/biona001/32/16497_2.png) [@biona001](https://discourse.julialang.org/u/biona001)\
**Post date:** [August 26, 2019, 9:58pm UTC](https://discourse.julialang.org/t/ode-parameter-estimation-on-a-subset-of-the-parameters/28013/2 "2019-08-26T21:58:06Z")

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well, I have the following solution for a closure:

```julia
function closure(p)
	p[2] = -1.5
	err = cost_function(p)
	return err
end

result = optimize(cost_function, [1.0, -3.0])

julia> result.minimizer
2-element Array{Float64,1}:
  1.5000022369113704
 -2.9999430279237727

```

I suppose this works?

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<div class="post-metadata">

**Author:** ![alewolf](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/alewolf/32/9000_2.png) [@alewolf](https://discourse.julialang.org/u/alewolf)\
**Post date:** [August 26, 2019, 10:45pm UTC](https://discourse.julialang.org/t/ode-parameter-estimation-on-a-subset-of-the-parameters/28013/3 "2019-08-26T22:45:43Z")

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The easiest solution is just leave p2 as a number and not a parameter.  
Otherwise I have an example at blackboxoptim where I deal exactly with this.

[https://github.com/robertfeldt/BlackBoxOptim.jl/blob/master/examples/ODEwithFixParams.jl](https://github.com/robertfeldt/BlackBoxOptim.jl/blob/master/examples/ODEwithFixParams.jl)

I’m out of the country without computer so I’m not much help, but this example I think address your issue-

I used Julia 1.04 to run the code.

Take care-

A