fixup! test: add extensive modelingtoolkitize tests

Author: AayushSabharwal

test/modelingtoolkitize.jl

@@ -436,7 +436,8 @@ sys = modelingtoolkitize(prob)
         end
         @testset "Nonlinear" begin
             @variables x=1.0 y=2.0
-            @mtkbuild nlsys = NonlinearSystem([0 ~ p * y^2 + x, 0 ~ y + x * q])
+            @parameters p=3.0 q=4.0
+            @mtkbuild nlsys = NonlinearSystem([0 ~ p * y^2 + x, 0 ~ x + exp(x) * q])
             prob1 = NonlinearProblem(nlsys, [])
             newsys = complete(modelingtoolkitize(prob1))
             @test is_variable(newsys, newsys.x)
@@ -450,17 +451,23 @@ sys = modelingtoolkitize(prob)
             @test sol1 ≈ sol2
         end
         @testset "Optimization" begin
-            @mtkbuild optsys = OptimizationSystem((x - p)^3 + y^2 - q)
-            prob1 = OptimizationProblem(optsys, [])
+            @variables begin
+                x = 1.0, [bounds = (-2.0, 10.0)]
+                y = 2.0, [bounds = (-1.0, 10.0)]
+            end
+            @parameters p=3.0 q=4.0
+            loss = (p - x)^2 + q * (y - x^2)^2
+            @mtkbuild optsys = OptimizationSystem(loss, [x, y], [p, q])
+            prob1 = OptimizationProblem(optsys, [], grad=true, hess=true)
             newsys = complete(modelingtoolkitize(prob1))
             @test is_variable(newsys, newsys.x)
             @test is_variable(newsys, newsys.y)
             @test is_parameter(newsys, newsys.p)
             @test is_parameter(newsys, newsys.q)
-            prob2 = OptimizationProblem(newsys, [])
+            prob2 = OptimizationProblem(newsys, [], grad=true, hess=true)
 
-            sol1 = solve(prob1, LBFGS())
-            sol2 = solve(prob2, LBFGS())
+            sol1 = solve(prob1, GradientDescent())
+            sol2 = solve(prob2, GradientDescent())
 
             @test sol1 ≈ sol2
         end