`no method matching hasmetadata` in tearing

[cstjean]

Describe the bug 🐞

I get an obscure error from a seemingly well-constructed system. Perhaps it's just that I would need to specify the derivative of f?

Expected behavior

Better error message?

Minimal Reproducible Example 👇

using ModelingToolkit, DifferentialEquations
using ModelingToolkit: t_nounits as t, D_nounits as D

f(c, T) = (1 - 3 * c ^ 2)
@register_symbolic f(c, T)

@mtkmodel Tank begin
    @variables begin
        M1(t)
        M2(t)
        c(t)
        b(t)
    end
    @equations begin
        D(M1) ~ b + c
        D(M2) ~ (1 - b) + (1 - c)
        c ~ M1 / (M1 + M2)
        (M1 + M2) * f(c, 80) ~ 10
    end
end

@mtkbuild tank = Tank();

u0 = [tank.c => 0.6]

prob = ODEProblem(tank, u0, (0, 10.0), [],
                  guesses=[tank.M1 => 5,
                           tank.M2 => 5])

This is heavily reduced of course.

Error & Stacktrace ⚠️

ERROR: LoadError: MethodError: no method matching hasmetadata(::Nothing, ::Type{ModelingToolkit.VariableUnit})

Closest candidates are:
  hasmetadata(::Num, ::Any)
   @ Symbolics C:\Users\\.julia\packages\Symbolics\Xv70J\src\Symbolics.jl:194
  hasmetadata(::Complex{Num}, ::Any)
   @ Symbolics C:\Users\\.julia\packages\Symbolics\Xv70J\src\Symbolics.jl:194
  hasmetadata(::SymbolicUtils.Symbolic, ::Any)
   @ SymbolicUtils C:\Users\\.julia\packages\SymbolicUtils\6fncq\src\types.jl:859

Stacktrace:
  [1] _with_unit(::Function, ::SymbolicUtils.BasicSymbolic{Real}, ::Nothing, ::Nothing, ::Vararg{Any})
    @ ModelingToolkit C:\Users\\.julia\packages\ModelingToolkit\K8zNC\src\utils.jl:1014
  [2] lower_varname_with_unit
    @ C:\Users\\.julia\packages\ModelingToolkit\K8zNC\src\utils.jl:1023 [inlined]
  [3] lower_varname_withshift(var::SymbolicUtils.BasicSymbolic{Real}, iv::Nothing, order::Int64)
    @ ModelingToolkit.StructuralTransformations C:\Users\\.julia\packages\ModelingToolkit\K8zNC\src\structural_transformation\utils.jl:458
  [4] tearing_reassemble(state::TearingState{…}, var_eq_matching::ModelingToolkit.BipartiteGraphs.Matching{…}, full_var_eq_matching::ModelingToolkit.BipartiteGraphs.Matching{…}; simplify::Bool, mm::ModelingToolkit.SparseMatrixCLIL{…}, cse_hack::Bool, array_hack::Bool)
    @ ModelingToolkit.StructuralTransformations C:\Users\\.julia\packages\ModelingToolkit\K8zNC\src\structural_transformation\symbolics_tearing.jl:413
  [5] tearing_reassemble
    @ C:\Users\\.julia\packages\ModelingToolkit\K8zNC\src\structural_transformation\symbolics_tearing.jl:240 [inlined]
  [6] tearing(sys::NonlinearSystem, state::TearingState{…}; mm::ModelingToolkit.SparseMatrixCLIL{…}, simplify::Bool, cse_hack::Bool, array_hack::Bool, kwargs::@Kwargs{…})
    @ ModelingToolkit.StructuralTransformations C:\Users\\.julia\packages\ModelingToolkit\K8zNC\src\structural_transformation\symbolics_tearing.jl:802
  [7] _structural_simplify!(state::TearingState{…}, io::Nothing; simplify::Bool, check_consistency::Bool, fully_determined::Nothing, warn_initialize_determined::Bool, dummy_derivative::Bool, kwargs::@Kwargs{…})
    @ ModelingToolkit C:\Users\\.julia\packages\ModelingToolkit\K8zNC\src\systems\systemstructure.jl:711
  [8] _structural_simplify!
    @ C:\Users\\.julia\packages\ModelingToolkit\K8zNC\src\systems\systemstructure.jl:676 [inlined]
  [9] #structural_simplify!#1509
    @ C:\Users\\.julia\packages\ModelingToolkit\K8zNC\src\systems\systemstructure.jl:669 [inlined]
 [10] __structural_simplify(sys::NonlinearSystem, io::Nothing; simplify::Bool, kwargs::@Kwargs{…})
    @ ModelingToolkit C:\Users\\.julia\packages\ModelingToolkit\K8zNC\src\systems\systems.jl:102
 [11] __structural_simplify
    @ C:\Users\\.julia\packages\ModelingToolkit\K8zNC\src\systems\systems.jl:83 [inlined]
 [12] structural_simplify(sys::NonlinearSystem, io::Nothing; additional_passes::Vector{…}, simplify::Bool, split::Bool, allow_symbolic::Bool, allow_parameter::Bool, conservative::Bool, fully_determined::Nothing, kwargs::@Kwargs{})
    @ ModelingToolkit C:\Users\\.julia\packages\ModelingToolkit\K8zNC\src\systems\systems.jl:33
 [13] structural_simplify (repeats 2 times)
    @ C:\Users\\.julia\packages\ModelingToolkit\K8zNC\src\systems\systems.jl:28 [inlined]
 [14] ModelingToolkit.InitializationProblem{…}(sys::ODESystem, t::Int64, 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, allow_incomplete::Bool, kwargs::@Kwargs{…})
    @ ModelingToolkit C:\Users\\.julia\packages\ModelingToolkit\K8zNC\src\systems\diffeqs\abstractodesystem.jl:1310
 [15] (ModelingToolkit.InitializationProblem{…})(::ODESystem, ::Int64, ::Vararg{…}; kwargs::@Kwargs{…})
    @ ModelingToolkit C:\Users\\.julia\packages\ModelingToolkit\K8zNC\src\systems\diffeqs\abstractodesystem.jl:1265
 [16] ModelingToolkit.InitializationProblem(::ODESystem, ::Int64, ::Vararg{…}; kwargs::@Kwargs{…})
    @ ModelingToolkit C:\Users\\.julia\packages\ModelingToolkit\K8zNC\src\systems\diffeqs\abstractodesystem.jl:1253
 [17] maybe_build_initialization_problem(sys::ODESystem, op::Dict{…}, u0map::Dict{…}, pmap::Dict{…}, t::Int64, defs::Dict{…}, guesses::Vector{…}, missing_unknowns::Set{…}; implicit_dae::Bool, kwargs::@Kwargs{…})
    @ ModelingToolkit C:\Users\\.julia\packages\ModelingToolkit\K8zNC\src\systems\problem_utils.jl:559
 [18] process_SciMLProblem(constructor::Type, sys::ODESystem, u0map::Vector{…}, pmap::Vector{…}; build_initializeprob::Bool, implicit_dae::Bool, t::Int64, guesses::Vector{…}, warn_initialize_determined::Bool, initialization_eqs::Vector{…}, eval_expression::Bool, eval_module::Module, fully_determined::Nothing, check_initialization_units::Bool, tofloat::Bool, use_union::Bool, u0_constructor::typeof(identity), du0map::Nothing, check_length::Bool, symbolic_u0::Bool, warn_cyclic_dependency::Bool, circular_dependency_max_cycle_length::Int64, circular_dependency_max_cycles::Int64, substitution_limit::Int64, use_scc::Bool, kwargs::@Kwargs{})
    @ ModelingToolkit C:\Users\\.julia\packages\ModelingToolkit\K8zNC\src\systems\problem_utils.jl:705
 [19] (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\\.julia\packages\ModelingToolkit\K8zNC\src\systems\diffeqs\abstractodesystem.jl:832
 [20] (ODEProblem{true})(::ODESystem, ::Vector{Pair{Num, Float64}}, ::Vararg{Any}; kwargs::@Kwargs{guesses::Vector{Pair{…}}})
    @ ModelingToolkit C:\Users\\.julia\packages\ModelingToolkit\K8zNC\src\systems\diffeqs\abstractodesystem.jl:813
 [21] ODEProblem(::ODESystem, ::Vector{Pair{Num, Float64}}, ::Vararg{Any}; kwargs::@Kwargs{guesses::Vector{Pair{Num, Int64}}})
    @ ModelingToolkit C:\Users\\.julia\packages\ModelingToolkit\K8zNC\src\systems\diffeqs\abstractodesystem.jl:802

Environment (please complete the following information):

• Output of using Pkg; Pkg.status()

Julia 1.10.5

MTK v9.62.0

[AayushSabharwal]

The problem here seems to be that the initialization system thinks f(c, 80) is a variable because (somehow) there's a Differential(t)(f(c, 80)) in the system.

[AayushSabharwal]

Okay, so the problem is that dummy derivatives tries to differentiate the last equation (the one involving f(c, 80)), resulting in the Differential(t)(f(c, 80)).

[AayushSabharwal]

This can be solved by providing symbolic derivatives for the registered function as in this section of Symbolics docs. We should surface this in MTK somewhere.

julia> df1(c, T) = -6c
julia> @register_symbolic df1(c, T)
julia> Symbolics.derivative(::typeof(f), args::NTuple{2, Any}, ::Val{1}) = df1(args...)
julia> Symbolics.derivative(::typeof(f), args::NTuple{2, Any}, ::Val{2}) = 0.0
julia> @mtkbuild tank = Tank();
julia> prob = ODEProblem(tank, u0, (0, 10.0), [],
                         guesses=[tank.M1 => 5,
                                  tank.M2 => 5, tank.c => 1.0, tank.b => 1.0])
julia> solve(prob, Rodas5P())
retcode: Success
# ...

[ChrisRackauckas]

Yeah... that needs a better error message 😅 . All it needs is to basically say that a derivative isn't defined and I think that's a solid solution.