test: add test for observable functions

test/downstream/observables_autodiff.jl

@@ -0,0 +1,34 @@
+using ModelingToolkit, OrdinaryDiffEq
+using Zygote
+
+@parameters σ ρ β
+@variables x(t) y(t) z(t) w(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)
+
+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())
+
+@testset "AutoDiff Observable Functions" begin
+    gs, = gradient(sol) do sol
+        sum(sol[sys.w])
+    end
+    du_ = [0., 1., 1., 1.]
+    du = [du_ for _ = sol.u]
+    @test du == gs.u
+end