test: test remaking of initialization problem

test/initializationsystem.jl

@@ -544,3 +544,32 @@ end
     prob = ODEProblem(sys, [], (0.0, 1.0), [spring.s_rel0 => missing])
     test_parameter(prob, spring.s_rel0, -3.905)
 end
+
+@testset "Re-creating initialization problem on remake" begin
+    @variables x(t) y(t)
+    @parameters p
+    @mtkbuild sys = ODESystem(
+        [D(x) ~ x, p ~ x + y], t; defaults = [p => missing], guesses = [x => 0.0, p => 0.0])
+    prob = ODEProblem(sys, [x => 1.0, y => 1.0], (0.0, 1.0))
+    @test init(prob, Tsit5()).ps[p] ≈ 2.0
+    # nonsensical value for y just to test that equations work
+    prob2 = remake(prob; u0 = [x => 1.0, y => 2x + exp(t)])
+    @test init(prob2, Tsit5()).ps[p] ≈ 4.0
+    # solve for `x` given `p` and `y`
+    prob3 = remake(prob; u0 = [y => 1.0], p = [p => 2x + exp(t)])
+    @test init(prob3, Tsit5())[x] ≈ 0.0
+    @test_logs (:warn, r"overdetermined") remake(
+        prob; u0 = [x => 1.0, y => 2.0], p = [p => 4.0])
+    prob4 = remake(prob; u0 = [x => 1.0, y => 2.0], p = [p => 4.0])
+    @test solve(prob4, Tsit5()).retcode == ReturnCode.InitialFailure
+    prob5 = remake(prob)
+    @test init(prob, Tsit5()).ps[p] ≈ 2.0
+
+    @mtkbuild sys = ODESystem([D(x) ~ x, p ~ x + y], t; guesses = [p => 0.0])
+    prob = ODEProblem(sys, [x => 1.0, y => 1.0], (0.0, 1.0), [p => 2.0])
+    # No value for `p`, not `missing`
+    @test_throws ModelingToolkit.MissingParametersError remake(
+        prob; u0 = [x => 1.0, y => 3x])
+    prob2 = remake(prob; u0 = [x => 1.0, y => 2x + exp(t)], p = [p => missing])
+    @test init(prob2, Tsit5()).ps[p] ≈ 4.0
+end