chore: set indexing style

[DhairyaLGandhi]

Checklist

• Appropriate tests were added
• Any code changes were done in a way that does not break public API
• All documentation related to code changes were updated
• The new code follows the
  contributor guidelines, in particular the SciML Style Guide and
  COLPRAC.
• Any new documentation only uses public API

Additional context

ReverseDiff restricts array types to IndexLinear() indexing style as written in their docs: https://juliadiff.org/ReverseDiff.jl/dev/limits/

Not following this causes failures with using ReverseDiff:

@parameters σ ρ β
@variables x(t) y(t) z(t)

eqs = [D(D(x)) ~ σ * (y - x),
    D(y) ~ x * (ρ - z) - y,
    D(z) ~ x * y - β * z,
    w ~ x + y + z + 2 * β,
    ]

@mtkbuild sys = ODESystem(eqs, t)

ModelingToolkit.observed(sys)

u0 = [D(x) => 2.0,
    x => 1.0,
    y => 0.0,
    z => 0.0,]

p = [σ => 28.0,
    ρ => 10.0,
    β => 8 / 3,]

tspan = (0.0, 100.0)
prob = ODEProblem(sys, u0, tspan, p, jac = true)
sol = solve(prob, Tsit5())

mtkp = parameter_values(sol)
gt = rand(873)

gradient(mtkparams) do p
    sol = solve(prob, Rosenbrock23(), p = p, sensealg = SciMLSensitivity.GaussAdjoint(autojacvec = ReverseDiffVJP()))
    mean(abs.(sol[sys.x] .- gt))
end

cc @AayushSabharwal

Add any other context about the problem here.

[ChrisRackauckas]

But its index style is naturally Cartesian?

[DhairyaLGandhi]

Ah, that is right, maybe we can restrict it to the case of Vector of Vector? The reason is that when we call canonicalize we get an ArrayPartition, and that runs into this ReverseDiff limitation as I diagnosed this today with @AayushSabharwal. It runs into this assert https://github.com/JuliaDiff/ReverseDiff.jl/blob/bff801b75ea23ead2ece6f594ce1deee79898ba4/src/tracked.jl#L77

[ChrisRackauckas]

Where does ReverseDiff come into play?

[DhairyaLGandhi]

This is when we pass sensealg = GaussAdjoint(autojacvec = ReverseDiffVJP())

gradient(mtkparams) do p
    sol = solve(prob, Rosenbrock23(), p = p, sensealg = SciMLSensitivity.GaussAdjoint(autojacvec = ReverseDiffVJP()))
    mean(abs.(sol[sys.x] .- gt))
end

[ChrisRackauckas]

With Array or ComponentArray? Is there a case that regresses/breaks or is it that case is not handled for the newer stuff?

[DhairyaLGandhi]

It's not handled when we integrate SciMLStructures and SII with Sensitivity.