Fix dual type promotion in remake with dummy derivatives

src/systems/diffeqs/abstractodesystem.jl

@@ -1366,6 +1366,21 @@ function InitializationProblem{iip, specialize}(sys::AbstractSystem,
     end
 
     u0map = merge(ModelingToolkit.guesses(sys), todict(guesses), todict(u0map))
+
+    # Replace dummy derivatives in u0map: D(x) -> x_t etc.
+    if has_schedule(sys)
+        schedule = get_schedule(sys)
+        if !isnothing(schedule)
+            for (var, val) in u0map
+                dvar = get(schedule.dummy_sub, var, var) # with dummy derivatives
+                if dvar !== var # then replace it
+                    delete!(u0map, var)
+                    push!(u0map, dvar => val)
+                end
+            end
+        end
+    end
+
     fullmap = merge(u0map, parammap)
     u0T = Union{}
     for sym in unknowns(isys)

test/extensions/ad.jl

@@ -4,6 +4,7 @@ using Zygote
 using SymbolicIndexingInterface
 using SciMLStructures
 using OrdinaryDiffEq
+using NonlinearSolve
 using SciMLSensitivity
 using ForwardDiff
 using ChainRulesCore
@@ -103,3 +104,23 @@ vals = (1.0f0, 3ones(Float32, 3))
 tangent = rand_tangent(ps)
 fwd, back = ChainRulesCore.rrule(remake_buffer, sys, ps, idxs, vals)
 @inferred back(tangent)
+
+@testset "Dual type promotion in remake with dummy derivatives" begin # https://github.com/SciML/ModelingToolkit.jl/issues/3336
+    # Throw ball straight up into the air
+    @variables y(t)
+    eqs = [D(D(y)) ~ -9.81]
+    initialization_eqs = [y^2 ~ 0] # initialize y = 0 in a way that builds an initialization problem
+    @named sys = ODESystem(eqs, t; initialization_eqs)
+    sys = structural_simplify(sys)
+
+    # Find initial throw velocity that reaches exactly 10 m after 1 s
+    dprob0 = ODEProblem(sys, [D(y) => NaN], (0.0, 1.0), []; guesses = [y => 0.0])
+    function f(ics, _)
+        dprob = remake(dprob0, u0 = Dict(D(y) => ics[1]))
+        dsol = solve(dprob, Tsit5())
+        return [dsol[y][end] - 10.0]
+    end
+    nprob = NonlinearProblem(f, [1.0])
+    nsol = solve(nprob, NewtonRaphson())
+    @test nsol[1] ≈ 10.0 / 1.0 + 9.81 * 1.0 / 2 # anal free fall solution is y = v0*t - g*t^2/2 -> v0 = y/t + g*t/2
+end