Remake does not handle dual type promotion with dummy derivatives

[hersle]

Here is a simple throw-ball-straight-up-into-the-air example (2nd order ODE)

using ModelingToolkit, OrdinaryDiffEq, NonlinearSolve
using ModelingToolkit: t_nounits as t, D_nounits as D

# Throw ball straight up into the air
@variables y(t)
@named sys = ODESystem([
    D(D(y)) ~ -9.81
], t; initialization_eqs = [
    y^2 ~ 0 # initialize y = 0 in a way that builds an initialization problem
])
sys = structural_simplify(sys)

# Find initial throw velocity that reaches exactly 100 m after 1 s
dprob0 = ODEProblem(sys, [D(y) => NaN], (0.0, 1.0), []; guesses = [y => 0.0])
nprob = NonlinearProblem((ics, _) -> begin
    dprob = remake(dprob0, u0 = Dict(D(y) => ics[1]))
    dsol = solve(dprob, Tsit5())
    return [dsol[y][end] - 100.0]
end, [1.0])
nsol = solve(nprob, NewtonRaphson())

This crashes with

ERROR: MethodError: no method matching Float64(::ForwardDiff.Dual{ForwardDiff.Tag{DifferentiationInterface.FixTail{…}, Float64}, Float64, 1})       
The type `Float64` exists, but no method is defined for this combination of argument types when trying to construct it.

Closest candidates are:
  (::Type{T})(::Real, ::RoundingMode) where T<:AbstractFloat
   @ Base rounding.jl:265
  (::Type{T})(::T) where T<:Number
   @ Core boot.jl:900
  Float64(::Float16)
   @ Base float.jl:342
  ...

Stacktrace:
  [1] #1117
    @ C:\Users\herma\.julia\dev\ModelingToolkit\src\systems\diffeqs\abstractodesystem.jl:1386 [inlined]
  [2] (::ModelingToolkit.var"#1117#1120")(::Pair{Any, Any})
    @ ModelingToolkit .\none:0
  [3] iterate
    @ .\generator.jl:48 [inlined]
  [4] grow_to!(dest::Dict{Any, Any}, itr::Base.Generator{Dict{Any, Any}, ModelingToolkit.var"#1117#1120"})
    @ Base .\abstractdict.jl:587
  [5] dict_with_eltype
    @ .\abstractdict.jl:641 [inlined]
  [6] Dict
    @ .\dict.jl:117 [inlined]
  [7] ModelingToolkit.InitializationProblem{…}(sys::ODESystem, t::Float64, u0map::Dict{…}, parammap::Dict{…}; guesses::Dict{…}, check_length::Bool, warn_initialize_determined::Bool, initialization_eqs::Vector{…}, fully_determined::Nothing, check_units::Bool, use_scc::Bool, kwargs::@Kwargs{})    
    @ ModelingToolkit C:\Users\herma\.julia\dev\ModelingToolkit\src\systems\diffeqs\abstractodesystem.jl:1385
  [8] InitializationProblem
    @ C:\Users\herma\.julia\dev\ModelingToolkit\src\systems\diffeqs\abstractodesystem.jl:1287 [inlined]
  [9] #_#1112
    @ C:\Users\herma\.julia\dev\ModelingToolkit\src\systems\diffeqs\abstractodesystem.jl:1265 [inlined]
 [10] InitializationProblem
    @ C:\Users\herma\.julia\dev\ModelingToolkit\src\systems\diffeqs\abstractodesystem.jl:1264 [inlined]
 [11] #InitializationProblem#1110
    @ C:\Users\herma\.julia\dev\ModelingToolkit\src\systems\diffeqs\abstractodesystem.jl:1253 [inlined]
 [12] InitializationProblem
    @ C:\Users\herma\.julia\dev\ModelingToolkit\src\systems\diffeqs\abstractodesystem.jl:1252 [inlined]
 [13] maybe_build_initialization_problem(sys::ODESystem, op::Dict{…}, u0map::Dict{…}, pmap::Dict{…}, t::Float64, defs::Dict{…}, guesses::Dict{…}, missing_unknowns::Set{…}; implicit_dae::Bool, kwargs::@Kwargs{…})
    @ ModelingToolkit C:\Users\herma\.julia\dev\ModelingToolkit\src\systems\problem_utils.jl:546
 [14] remake_initialization_data(sys::ODESystem, odefn::Function, u0::Dict{…}, t0::Float64, p::Missing, newu0::Vector{…}, newp::MTKParameters{…})   
    @ ModelingToolkit C:\Users\herma\.julia\dev\ModelingToolkit\src\systems\nonlinear\initializesystem.jl:343
 [15] remake(prob::ODEProblem{…}; f::Missing, u0::Dict{…}, tspan::Missing, p::Missing, kwargs::Missing, interpret_symbolicmap::Bool, build_initializeprob::Bool, use_defaults::Bool, lazy_initialization::Nothing, _kwargs::@Kwargs{})
    @ SciMLBase C:\Users\herma\.julia\packages\SciMLBase\XzPx0\src\remake.jl:230
  ...

[hersle]

I think the issue is here:

• fullmap contains Differential(t)(y(t)) (without dummy derivative)
• unknowns(isys) and/or observed(isys) contains y_t(t) (with dummy derivative)
• These two are not found to match, so u0T does not promote to the type of D(y)

[hersle]

The above PR seems to fix this particular example.

I will open another issue for my other issue, which seems unrelated to dummy derivatives upon further investigation.