Incorrect mean in the EnsembleSummary plot?

Specific Domains Numerics
, , ,
1

I have the following snippet:

module mwe

using OrdinaryDiffEq
using Plots
using Distributions
using Statistics

tspan = (0.0, 10.0)
Δt = 0.5
g(u, p, t) = p[1] * t
x0 = 0.0

# base problem
prob_x = ODEProblem(g, x0, tspan, [1])

# ensemble problem
dist_a = Exponential()
function prob_func(prob, i, repeat)
    remake(prob, p=[rand(dist_a)])
end
n_traj = 10^4
ensemble_prob = EnsembleProblem(prob_x, prob_func=prob_func)
sim = solve(ensemble_prob, Euler(), dt=Δt, EnsembleThreads(), trajectories=n_traj)
display(plot(EnsembleSummary(sim)))

println("Mean at the final time")
display(mean([a[end] for a in sim.u]))

end # module mwe

which outputs

Mean at the final time
47.418223069301085

and

ensemble
ensemble1084×728 20.1 KB

Do I understand it correctly that the thick blue line in the plot of the EnsembleSummary is the mean as a function of time? And [a[end] for a in sim.u] gets me the endpoint of every trajectory? If so, why the plot mean at tspan[end] is 30 and the calculated mean is 47? If not, where am I mistaken?

3

It is plotting the median, see here.

The default ci_type=:quantile uses the median.

To plot the mean do:

plot(EnsembleSummary(sim); ci_type=:SEM)
1 Like