test: add a simple test for AD

Author: DhairyaLGandhi

test/extensions/Project.toml

@@ -1,3 +1,8 @@
 [deps]
 BifurcationKit = "0f109fa4-8a5d-4b75-95aa-f515264e7665"
 ModelingToolkit = "961ee093-0014-501f-94e3-6117800e7a78"
+OrdinaryDiffEq = "1dea7af3-3e70-54e6-95c3-0bf5283fa5ed"
+SciMLSensitivity = "1ed8b502-d754-442c-8d5d-10ac956f44a1"
+SciMLStructures = "53ae85a6-f571-4167-b2af-e1d143709226"
+SymbolicIndexingInterface = "2efcf032-c050-4f8e-a9bb-153293bab1f5"
+Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"

test/extensions/ad.jl

@@ -0,0 +1,31 @@
+using ModelingToolkit
+using ModelingToolkit: t_nounits as t, D_nounits as D
+using Zygote
+using SymbolicIndexingInterface
+using SciMLStructures
+using OrdinaryDiffEq
+using SciMLSensitivity
+
+@variables x(t)[1:3] y(t)
+@parameters p[1:3, 1:3] q
+eqs = [
+         D(x) ~ p * x
+         D(y) ~ sum(p) + q * y
+]
+u0 = [x => zeros(3),
+      y => 1.]
+ps = [p => zeros(3, 3),
+    q => 1.]
+tspan = (0., 10.)
+@mtkbuild sys = ODESystem(eqs, t)
+prob = ODEProblem(sys, u0, tspan, ps)
+sol = solve(prob, Tsit5())
+
+mtkparams = parameter_values(prob)
+new_p = rand(10)
+gs = gradient(new_p) do new_p
+    new_params = SciMLStructures.replace(SciMLStructures.Tunable(), mtkparams, new_p)
+    new_prob = remake(prob, p = new_params)
+    new_sol = solve(new_prob, Tsit5())
+    sum(new_sol)
+end

test/runtests.jl

@@ -104,5 +104,6 @@ end
     if GROUP == "All" || GROUP == "Extensions"
         activate_extensions_env()
         @safetestset "BifurcationKit Extension Test" include("extensions/bifurcationkit.jl")
+        @safetestset "Auto Differentiation Test" include("extensions/ad.jl")
     end
 end