Constant changes when optimising ODE parameters

General Usage
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1

Hi! I’m trying to use Julia for optimizing parameters for an ODE system, but I’m running into the issue that the value C1 that should be constant is changed during the optimization. I currently have the following code (for a toy problem):

using Zygote, DifferentialEquations, SciMLSensitivity

N=10

# included state variables (dummy)
const C1 = vec(float.(rand(N,1).>0.2))

# activation function
act(x) = x./(1 .+ x)

# ODE definition
function ode_fun(du,u,p,t)
    K = zeros(N,N)
    K[1:end] .= p
    
    du.= C1.*act(K*u)-u
end

# loss function
function loss(x)
    prob = ODEProblem(ode_fun,x0,(0.0f0,1.0f0),abs.(x))
    sol = solve(prob)
    u = reduce(hcat,sol.u)
    return sum(abs2,u[:,end]-y) + sum(abs.(x))
end

# number of iterations for optimisation
iters = 100

# set initial condition, initial guess and desired output after simulation
global x0 = rand(10)
global x = rand(100)
y = rand(N,1)

loss_vec =[]

# gradient descent
for _ in 1:iters
    grd = Zygote.withgradient(x) do x
        loss(x)
    end
    push!(loss_vec,grd.val)
    global x = x - 0.01*grd.grad[1]
end

When running the code and printing C1 in ode_fun, I find that C1 is changed to a new value after the first call of ode_fun. Does anybody know why this is happening? I just cannot seem to find how C1 is changed at all in the code.

2

I’m running your code and C1 looks constant. Can you remove the randomness and show a case with constant values where this occurs?

3

Thanks for taking the time to run my code.

Upon rerunning the code, it seems that C1 now stays constant, both when removing randomness and with randomness, each in a clean workspace. I am very confused, I tested the code on two machines before posting and the behavior persisted. It’s good that the code now runs as intended, but I could not say what changed between yesterday and today.

I did find another workaround by passing C1 as an argument to the loss function.