Local sensitivity analysis with SciMLSensitivity

[MichielStock]

The docs and paper mention that SciMLSensitivity can be used for local sensitivity analysis, though the two are not compatible in a neat way.

For example, one would expect the following to work

using Catalyst
using DifferentialEquations
using SciMLSensitivity

brusselator = @reaction_network begin
    A, ∅ → X
    1, 2X + Y → 3X
    B, X → Y
    1, X → ∅
end
p = [:A => 1., :B => 2.]

u0 = [:X => 1.0, :Y => 1.0]
tspan = (0.0, 30.0)

prob = ODEForwardSensitivityProblem(brusselator, u0, tspan, p)

solve(prob)

Yet, it doesn't because ODEForwardSensitivityProblem requires a function, not a system. Is there a correct way of doing this (I would love to add this to the docs) or is there some kind of form you have to give the system.

Relatedly, is there a way to linearized a reaction network using linearization of ModelingToolkit?

[MichielStock]

I found it, based on the explanation in the bifurcation settings. My solution was (for a slightly different system):

prob_sens = ODEForwardSensitivityProblem(oprob.f, [0.0, 0.1], tspan, [1.7, 29, 50, 10, 100])
sol_sens = solve(prob_sens)

u, dp = extract_local_sensitivities(sol_sens)

dC = dp[3]  # C is the third parameter

plot(sol_sens.t, dC', title="Sensitivity on the ingoing concentration", label=["dS/dt" "dX/dt"])

Should this be added to the docs?

[isaacsas]

We should probably get ModelingToolkit to add a dispatch so that the following works:

osys = convert(ODESystem, brusselator)
ODEForwardSensitivityProblem(osys, u0, tspan, p)

Then we can add a dispatch here to make

ODEForwardSensitivityProblem(brusselator, u0, tspan, p)

work.

I believe @TorkelE was planning to add a tutorial on sensitivity analysis via Catalyst. I don't know if he has started on it yet.

[isaacsas]

It would probably make sense to just add a SciMLSensitivity extension to ModelingToolkit to define that dispatch, hopefully it could reuse most of the current ODEFunction and ODEProblem code there to work.

[isaacsas]

It looks like ODEForwardSensitivityFunction is itself missing needed fields for symbolic indexing and such to work too: https://github.com/SciML/SciMLSensitivity.jl/blob/fde15237adef794d3b544fb62d80db3188abbdf6/src/forward_sensitivity.jl#L10-L37

[TorkelE]

Just confirming that a tutorial and some additional helper functions for the context of Catalyst is in the works.