# Discrepancy in DiffEqParamEstim
**URL:** https://discourse.julialang.org/t/discrepancy-in-diffeqparamestim/86300
**Category:** Optimization (Mathematical)
**Created:** [August 25, 2022, 3:17am UTC](https://discourse.julialang.org/t/discrepancy-in-diffeqparamestim/86300 "2022-08-25T03:17:45Z")
**Posts on this page:** 2
**Page:** 1
### Author:  [@affans](https://discourse.julialang.org/u/affans)
#### Post date: [August 25, 2022, 3:17am UTC](https://discourse.julialang.org/t/discrepancy-in-diffeqparamestim/86300/1 "2022-08-25T03:17:45Z")
Before I open a bug report on the official repo, just want to make sure I am on the right path. Consider a simple 2 parameter estimation of an ODE.
```julia
using DifferentialEquations
using DiffEqParamEstim
using Optim
# some data for reproducibility
data = [3140, 3232, 3488, 3415, 3192, 3265, 2961, 3548, 4269, 4681, 4415, 4883, 4150, 4394, 5856, 7126, 9130, 9367, 10631, 10737, 11688, 14993, 20665, 23957, 23621, 21338, 22034, 33781, 32013, 39840, 45961, 45359, 46126, 38077, 37410, 39431]
# growth model
function f(C,params,t)
r, p = params[1], params[2]
return r*C^p
end
c0 = 3140n. # initial condition
tspan = (0,length(data)-1) # time span
init_params = [0.5, 0.8] # initial parameters
prob = ODEProblem(f, c0, tspan, init_params) #sets up the problem
sol = solve(prob, Tsit5(), reltol=1e-8, abstol=1e-8, saveat=1) # get the solution to plot, etc
# lets try to optimize the parameters r and p
cost_function = build_loss_objective(prob, Tsit5(), L2Loss(tspan, data), maxiters=10000,verbose=false)
cost_function([0.5, 0.2]) # evaluate the cost of these two specific parameter values
```
The return of `build_loss_objective` is a function (i.e., `cost_function`) can be evaluated for different values of parameters `r` and `p`, i.e., `cost_function([r, p])` which gives you a numeric value. This makes sense.
Now lets use `LeastSquaresOptim.jl` to solve the optimization using least squares. We will build our `cost_function` using the provided `build_lsoptim_objective(prob, t, data, alg)` which is slightly different than `build_loss_objective`. We have:
```julia
cost_function = build_lsoptim_objective(prob, 1, data, Tsit5())
lsp = LeastSquaresProblem(x = [0.5, 0.5], f! = cost_function, output_length = 36)
res = optimize!(lsp, LeastSquaresOptim.Dogleg())
```
and here is where I found the inconsistency. I had to read the [source code](https://github.com/SciML/DiffEqParamEstim.jl/blob/master/src/build_lsoptim_objective.jl) in order to figure out the inconsistency. Let me explain:
- The `t` argument in the `build_lsoptim_objective` function sounds like it accepts `tspan`, i.e., the time span for the ODE problem. This is not the case. [Line 10 of the source code](https://github.com/SciML/DiffEqParamEstim.jl/blob/master/src/build_lsoptim_objective.jl#L10) suggests the `t` argument is used only for the `saveat` parameter in the solver. This is why my cost function has that integer `1`.
- `build_lsoptim_objective` returns a function, just like `build_loss_objective` above. Except, it has the signature
```julia
function (out, p)
...
end
```
where `out` is a pre-allocated vector to **store** the results of the ODE in for a given parameter `p`. This is where the inconsistency is. However, like in the above example, you would expect that `cost_function` would accept an array of parameters and simply evaluate the cost. That is, `cost_function([r, p]` should produce a value for for any two parameters `r` and `p`… but instead the correct call is `cost_function(zeros(length_data), [r, p]`).
- The annoying part here then becomes the argument `output_length` in the `LeastSquaresProblem` constructor. For a few hours, I thought the `output_length` referred to the number of parameters that one is trying to optimize, but infact this is the number of data points in the solution of the ODE.
I hope all that made sense… Kind of seems long. Maybe there is a better way to explain.
---
### Author:  [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)
#### Post date: [December 24, 2022, 6:34am UTC](https://discourse.julialang.org/t/discrepancy-in-diffeqparamestim/86300/2 "2022-12-24T06:34:23Z")
DiffEqParamEstim was overhauled to be built around Optimization.jl. See the new documentation.
[https://docs.sciml.ai/DiffEqParamEstim/stable/getting\_started/](https://docs.sciml.ai/DiffEqParamEstim/stable/getting_started/)