How to incorporate time dependent interpolation functions while solving ensemble parameter estimation problem?

New to Julia
4

Just put it in the parameters.

function V(du, u, _p, t)
    p, Rate = _p
    du[1] =  Rate(t)
    du[2] = p[1]*u[1] + (Rate(t) / u[1]) *u[2]
end

p0 = [1.]
u0 = [1.0, 0.2]
N = 8
prob = ODEProblem(V, u0, (0., 12.), p0)

function prob_func(prob, i , repeat)
    Rate = ConstantInterpolation(y[i], x[i], extrapolate=true)
    tspan = (tspan_data[i][1], tspan_data[i][2])
    remake(prob; u0 = initial_conditions[i], tspan = (tspan_data[i][1], tspan_data[i][2]), p = (prob.p, Rate))
end

enprob = EnsembleProblem(prob, prob_func = prob_func)

sim = solve(enprob, Tsit5(), trajectories = N)