Hi,
I am using ModellingToolkit to define a system following the spring-mass example in the documentation. I solve the ODEForwardSensitivityProblem of the system.
The problem is when I try to access the states of the system in the solution using solS[mass.v[1]]. I get the following error:
ERROR: LoadError: Indexing symbol mass₊v[1](t) is unknown.
It seems that ModellingToolkit is not working well with the ODEForwardSensisitivityProblem. Indeed, there is no problem when I solve the usual ODEProblem.
This is the code:
using ModelingToolkit
using DiffEqSensitivity
using Plots, DifferentialEquations, LinearAlgebra
using Symbolics: scalarize
@variables t
D = Differential(t)
function Mass(; name, m = 1.0, xy = [0., 0.], u = [0., 0.])
ps = @parameters m=m
sts = @variables pos[1:2](t)=xy v[1:2](t)=u
eqs = scalarize(D.(pos) .~ v)
ODESystem(eqs, t, [pos..., v...], ps; name)
end
function Spring(; name, k = 1e4, l = 1.)
ps = @parameters k=k l=l
@variables x(t), dir[1:2](t)
ODESystem(Equation[], t, [x, dir...], ps; name)
end
function connect_spring(spring, a, b)
[
spring.x ~ norm(scalarize(a .- b))
scalarize(spring.dir .~ scalarize(a .- b))
]
end
spring_force(spring) = -spring.k .* scalarize(spring.dir) .* (spring.x - spring.l) ./ spring.x
m = 1.0
xy = [1., -1.]
k = 1e4
l = 1.
center = [0., 0.]
g = [0., -9.81]
@named mass = Mass(m=m, xy=xy)
@named spring = Spring(k=k, l=l)
eqs = [
connect_spring(spring, mass.pos, center)
scalarize(D.(mass.v) .~ spring_force(spring) / mass.m .+ g)
]
@named _model = ODESystem(eqs, t)
@named model = compose(_model, mass, spring)
sys = structural_simplify(model)
prob = ODEProblem(sys, ones(length(states(sys))), (0., 3.))
sol = solve(prob, Rosenbrock23())
plot(sol.t,sol[mass.v[1]])
probS = ODELocalSensitivityProblem(sys, ones(length(states(sys))), (0., 3.),[k,l,m])
solS = solve(probS)
plot(solS.t,solS[mass.v[1]])
Thanks! I appreciate any help.