Initial conditions set by mapping `unknowns(sys)` do not override defaults

[hersle]

This should work:

using ModelingToolkit
using ModelingToolkit: t_nounits as t, D_nounits as D
@variables x(t) y(t)

# system 1 should solve to x = 1
ics1 = [x => 1]
sys1 = ODESystem([D(x) ~ 0], t; defaults = ics1, name = :sys1) |> structural_simplify

# system 2 should solve to x = y = 2
sys2 = extend(sys1, ODESystem([D(y) ~ 0], t; initialization_eqs = [y ~ 2], name = :sys2)) |> structural_simplify
ics2 = unknowns(sys1) .=> 2 # but "ics2 = [x => 2]" works
prob2 = ODEProblem(sys2, ics2, (0.0, 1.0), []; fully_determined = true)

In sys2, ics2 should override ics1, so x = 2 instead of 1. But the initialization fails with

ERROR: LoadError: ExtraEquationsSystemException: The system is unbalanced. There are 2 highest order derivative variables and 3 equations.
More equations than variables, here are the potential extra equation(s):
 0 ~ 1 - x(t)
Note that the process of determining extra equations is a best-effort heuristic. The true extra equations are dependent on the model and may not be in this list.
Stacktrace:
  [1] error_reporting(state::TearingState{…}, bad_idxs::Vector{…}, n_highest_vars::Int64, iseqs::Bool, orig_inputs::Set{…})
    @ ModelingToolkit.StructuralTransformations C:\Users\herma\.julia\dev\ModelingToolkit\src\structural_transformation\utils.jl:44
  [2] check_consistency(state::TearingState{NonlinearSystem}, orig_inputs::Set{Any})
    @ ModelingToolkit.StructuralTransformations C:\Users\herma\.julia\dev\ModelingToolkit\src\structural_transformation\utils.jl:85
  [3] _structural_simplify!(state::TearingState{…}, io::Nothing; simplify::Bool, check_consistency::Bool, fully_determined::Bool, warn_initialize_determined::Bool, dummy_derivative::Bool, kwargs::@Kwargs{…})
    @ ModelingToolkit C:\Users\herma\.julia\dev\ModelingToolkit\src\systems\systemstructure.jl:692
  [4] _structural_simplify!
    @ C:\Users\herma\.julia\dev\ModelingToolkit\src\systems\systemstructure.jl:675 [inlined]      
  [5] #structural_simplify!#1197
    @ C:\Users\herma\.julia\dev\ModelingToolkit\src\systems\systemstructure.jl:668 [inlined]      
  [6] __structural_simplify(sys::NonlinearSystem, io::Nothing; simplify::Bool, kwargs::@Kwargs{…})
    @ ModelingToolkit C:\Users\herma\.julia\dev\ModelingToolkit\src\systems\systems.jl:85
  [7] __structural_simplify
    @ C:\Users\herma\.julia\dev\ModelingToolkit\src\systems\systems.jl:66 [inlined]
  [8] structural_simplify(sys::NonlinearSystem, io::Nothing; simplify::Bool, split::Bool, allow_symbolic::Bool, allow_parameter::Bool, conservative::Bool, fully_determined::Bool, kwargs::@Kwargs{})
    @ ModelingToolkit C:\Users\herma\.julia\dev\ModelingToolkit\src\systems\systems.jl:24
  [9] structural_simplify (repeats 2 times)
    @ C:\Users\herma\.julia\dev\ModelingToolkit\src\systems\systems.jl:20 [inlined]
 [10] ModelingToolkit.InitializationProblem{…}(sys::ODESystem, t::Float64, u0map::Vector{…}, parammap::SciMLBase.NullParameters; guesses::Dict{…}, check_length::Bool, warn_initialize_determined::Bool, initialization_eqs::Vector{…}, fully_determined::Bool, check_units::Bool, kwargs::@Kwargs{…})
    @ ModelingToolkit C:\Users\herma\.julia\dev\ModelingToolkit\src\systems\diffeqs\abstractodesystem.jl:1445
 [11] (ModelingToolkit.InitializationProblem{…})(::ODESystem, ::Float64, ::Vararg{…}; kwargs::@Kwargs{…})
    @ ModelingToolkit C:\Users\herma\.julia\dev\ModelingToolkit\src\systems\diffeqs\abstractodesystem.jl:1404
 [12] ModelingToolkit.InitializationProblem(::ODESystem, ::Float64, ::Vararg{…}; kwargs::@Kwargs{…})
    @ ModelingToolkit C:\Users\herma\.julia\dev\ModelingToolkit\src\systems\diffeqs\abstractodesystem.jl:1392
 [13] process_DEProblem(constructor::Type, sys::ODESystem, u0map::Vector{…}, parammap::Vector{…}; implicit_dae::Bool, du0map::Nothing, version::Nothing, tgrad::Bool, jac::Bool, checkbounds::Bool, sparse::Bool, simplify::Bool, linenumbers::Bool, parallel::Symbolics.SerialForm, eval_expression::Bool, eval_module::Module, use_union::Bool, tofloat::Bool, symbolic_u0::Bool, u0_constructor::typeof(identity), guesses::Dict{…}, t::Float64, warn_initialize_determined::Bool, build_initializeprob::Bool, initialization_eqs::Vector{…}, fully_determined::Bool, check_units::Bool, kwargs::@Kwargs{…})
    @ ModelingToolkit C:\Users\herma\.julia\dev\ModelingToolkit\src\systems\diffeqs\abstractodesystem.jl:822
 [14] process_DEProblem
    @ C:\Users\herma\.julia\dev\ModelingToolkit\src\systems\diffeqs\abstractodesystem.jl:766 [inlined]
 [15] (ODEProblem{…})(sys::ODESystem, u0map::Vector{…}, tspan::Tuple{…}, parammap::Vector{…}; callback::Nothing, check_length::Bool, warn_initialize_determined::Bool, eval_expression::Bool, eval_module::Module, kwargs::@Kwargs{…})
    @ ModelingToolkit C:\Users\herma\.julia\dev\ModelingToolkit\src\systems\diffeqs\abstractodesystem.jl:992
 [16] (ODEProblem{true})(::ODESystem, ::Vector{Pair{…}}, ::Vararg{Any}; kwargs::@Kwargs{fully_determined::Bool})
    @ ModelingToolkit C:\Users\herma\.julia\dev\ModelingToolkit\src\systems\diffeqs\abstractodesystem.jl:967
 [17] ODEProblem(::ODESystem, ::Vector{Pair{…}}, ::Vararg{Any}; kwargs::@Kwargs{fully_determined::Bool})
    @ ModelingToolkit C:\Users\herma\.julia\dev\ModelingToolkit\src\systems\diffeqs\abstractodesystem.jl:956

[hersle]

The reason is that unknowns(sys) returns unwrapped symbolic variables, which are handled differently than wrapped symbolic variables when setting up the initialization system. This is shown by this simple example:

sys2 = ODESystem([D(x) ~ 0, D(y) ~ 0], t; defaults = [x => 1], initialization_eqs = [y ~ 2], name = :sys2) |> structural_simplify
prob2 = ODEProblem(sys2, [ModelingToolkit.unwrap(x) => 2], (0.0, 1.0), []; fully_determined = true)

It fails with the same error. But it runs if x is not unwrapped.

[ChrisRackauckas]

Interesting. Yeah that's a subtle bug that would need some digging.

[ChrisRackauckas]

Interesting. Yeah that's a subtle bug that would need some digging.