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structural_simplify cannot deal with algebraic equations of array variables #3292

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tpdsantos opened this issue Jan 7, 2025 · 9 comments
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@tpdsantos
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I'm trying to implement a model of a Continuously Stirred Tank with multiple components. I first started assuming there was only one component:

@mtkmodel CST begin
    @parameters begin
        Q = 2.0
        V = 1.0
        c_in = 1.0
    end
    @variables begin
        cin(t)
        cout(t) = 0.0
    end
    @equations begin
        D(cout) ~ Q/V * (cin - cout)
        cin ~ c_in
    end
end

This one works perfectly. Afterwards I wanted to add multiple components by using array variables:

@mtkmodel CST begin
    @structural_parameters begin
        NC = 1
    end
    @parameters begin
        Q = 2.0
        V = 1.0
        c_in[1:NC] = [1.0 for i in 1:NC]
    end
    @variables begin
        cin(t)[1:NC]
        cout(t)[1:NC] = 0.0
    end
    @equations begin
        [D(cout)[i] ~ Q/V * (cin[i] - cout[i]) for i in 1:NC]
        cin ~ c_in
    end
end

However, running this example:

    @mtkbuild m = CST()
    prob = ODEProblem(m, [], (0.0, 5.0))

I get the error:

ERROR: MethodError: no method matching -(::ModelingToolkit.NoValue, ::SymbolicUtils.BasicSymbolic{Real})
The function `-` exists, but no method is defined for this combination of argument types.

Closest candidates are:
  -(::MutableArithmetics.Zero, ::Any)
   @ MutableArithmetics ~/.julia/packages/MutableArithmetics/BLlgj/src/rewrite.jl:67
  -(::Any, ::ChainRulesCore.NotImplemented)
   @ ChainRulesCore ~/.julia/packages/ChainRulesCore/U6wNx/src/tangent_arithmetic.jl:50
  -(::ChainRulesCore.NotImplemented, ::Any)
   @ ChainRulesCore ~/.julia/packages/ChainRulesCore/U6wNx/src/tangent_arithmetic.jl:49
  ...

Stacktrace:
  [1] (::ModelingToolkit.var"#744#748")(eq::Equation)
    @ ModelingToolkit ./none:0
  [2] iterate
    @ ./generator.jl:48 [inlined]
  [3] collect_to!(dest::Vector{…}, itr::Base.Generator{…}, offs::Int64, st::Int64)
    @ Base ./array.jl:849
  [4] collect_to_with_first!
    @ ./array.jl:827 [inlined]
  [5] collect(itr::Base.Generator{Vector{Equation}, ModelingToolkit.var"#744#748"})
    @ Base ./array.jl:801
  [6] NonlinearSystem(eqs::Vector{…}, unknowns::Vector{…}, ps::Vector{…}; observed::Vector{…}, name::Symbol, description::String, default_u0::Dict{…}, default_p::Dict{…}, defaults::Dict{…}, systems::Vector{…}, connector_type::Nothing, continuous_events::Nothing, discrete_events::Nothing, checks::Bool, parameter_dependencies::Vector{…}, metadata::ModelingToolkit.InitializationSystemMetadata, gui_metadata::Nothing)
    @ ModelingToolkit ~/.julia/packages/ModelingToolkit/klLLV/src/systems/nonlinear/nonlinearsystem.jl:151
  [7] generate_initializesystem(sys::ODESystem; u0map::Dict{…}, pmap::Dict{…}, initialization_eqs::Vector{…}, guesses::Dict{…}, default_dd_guess::Float64, algebraic_only::Bool, check_units::Bool, check_defguess::Bool, name::Symbol, extra_metadata::@NamedTuple{}, kwargs::@Kwargs{})
    @ ModelingToolkit ~/.julia/packages/ModelingToolkit/klLLV/src/systems/nonlinear/initializesystem.jl:184
  [8] generate_initializesystem
    @ ~/.julia/packages/ModelingToolkit/klLLV/src/systems/nonlinear/initializesystem.jl:6 [inlined]
  [9] 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 ~/.julia/packages/ModelingToolkit/klLLV/src/systems/diffeqs/abstractodesystem.jl:1312
 [10] InitializationProblem
    @ ~/.julia/packages/ModelingToolkit/klLLV/src/systems/diffeqs/abstractodesystem.jl:1295 [inlined]
 [11] #_#1065
    @ ~/.julia/packages/ModelingToolkit/klLLV/src/systems/diffeqs/abstractodesystem.jl:1273 [inlined]
 [12] InitializationProblem
    @ ~/.julia/packages/ModelingToolkit/klLLV/src/systems/diffeqs/abstractodesystem.jl:1272 [inlined]
 [13] #InitializationProblem#1063
    @ ~/.julia/packages/ModelingToolkit/klLLV/src/systems/diffeqs/abstractodesystem.jl:1261 [inlined]
 [14] InitializationProblem
    @ ~/.julia/packages/ModelingToolkit/klLLV/src/systems/diffeqs/abstractodesystem.jl:1260 [inlined]
 [15] 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 ~/.julia/packages/ModelingToolkit/klLLV/src/systems/problem_utils.jl:545
 [16] process_SciMLProblem(constructor::Type, sys::ODESystem, u0map::Vector{…}, pmap::SciMLBase.NullParameters; build_initializeprob::Bool, implicit_dae::Bool, t::Float64, guesses::Dict{…}, 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 ~/.julia/packages/ModelingToolkit/klLLV/src/systems/problem_utils.jl:666
 [17] (ODEProblem{})(sys::ODESystem, u0map::Vector{…}, tspan::Tuple{…}, parammap::SciMLBase.NullParameters; callback::Nothing, check_length::Bool, warn_initialize_determined::Bool, eval_expression::Bool, eval_module::Module,
 kwargs::@Kwargs{})
    @ ModelingToolkit ~/.julia/packages/ModelingToolkit/klLLV/src/systems/diffeqs/abstractodesystem.jl:840
 [18] ODEProblem
    @ ~/.julia/packages/ModelingToolkit/klLLV/src/systems/diffeqs/abstractodesystem.jl:828 [inlined]
 [19] (ODEProblem{true, SciMLBase.AutoSpecialize})(sys::ODESystem, u0map::Vector{Any}, tspan::Tuple{Float64, Float64})
    @ ModelingToolkit ~/.julia/packages/ModelingToolkit/klLLV/src/systems/diffeqs/abstractodesystem.jl:828
 [20] (ODEProblem{true})(::ODESystem, ::Vector{Any}, ::Vararg{Any}; kwargs::@Kwargs{})
    @ ModelingToolkit ~/.julia/packages/ModelingToolkit/klLLV/src/systems/diffeqs/abstractodesystem.jl:821
 [21] (ODEProblem{true})(::ODESystem, ::Vector{Any}, ::Vararg{Any})
    @ ModelingToolkit ~/.julia/packages/ModelingToolkit/klLLV/src/systems/diffeqs/abstractodesystem.jl:820
 [22] ODEProblem(::ODESystem, ::Vector{Any}, ::Vararg{Any}; kwargs::@Kwargs{})
    @ ModelingToolkit ~/.julia/packages/ModelingToolkit/klLLV/src/systems/diffeqs/abstractodesystem.jl:810
 [23] ODEProblem(::ODESystem, ::Vector{Any}, ::Vararg{Any})
    @ ModelingToolkit ~/.julia/packages/ModelingToolkit/klLLV/src/systems/diffeqs/abstractodesystem.jl:809
 [24] run_CST()
    @ Main ~/Repositories/WIP/ModelingToolkit-test/run-MTKModels.jl:29
 [25] top-level scope
    @ REPL[8]:1
Some type information was truncated. Use `show(err)` to see complete types.

I can circumvent it by:

@mtkmodel CST begin
    @structural_parameters begin
        NC = 1
    end
    @parameters begin
        Q = 2.0
        V = 1.0
        c_in[1:NC] = [1.0 for i in 1:NC]
    end
    @variables begin
        cin(t)[1:NC] = c_in
        cout(t)[1:NC] = [0.0 for i in 1:NC]
    end
    @equations begin
        D(cout) ~ Q/V * (cin - cout)
        D(cin) ~ [0.0 for i in 1:NC]
    end
end

However this is not ideal. I want to escale this to second order PDEs where the space discretization is by Orthogonal Collocation, which has algebraic equations in the boundary conditions and in the nodes between the collocation elements, where I can't use this workaround.

To note that by transforming this to a DAE form:

@mtkmodel CST begin
    @structural_parameters begin
        NC = 1
    end
    @parameters begin
        Q = 2.0
        V = 1.0
        c_in[1:NC] = [1.0 for i in 1:NC]
    end
    @variables begin
        cin(t)[1:NC] = 0.0
        cout(t)[1:NC] = 0.0
    end
    @equations begin
        [D(cout)[i] ~ Q/V * (cin[i] - cout[i]) for i in 1:NC]
        [0.0 ~ c_in[i] - cin[i] for i in 1:NC]
    end
end

And then using complete:

@named m = CST()
m = complete(m)
prob = ODEProblem(m, [], (0.0, 5.0))
sol = solve(prob, Rodas5P())

Works fine. However this is not ideal because structural_simplify eliminates a lot of equations from the system and I would prefer to use it. Can it be done using structural_simplify?

  • Output of using Pkg; Pkg.status()
Status `~/.julia/environments/v1.11/Project.toml`
  [6e4b80f9] BenchmarkTools v1.6.0
  [13f3f980] CairoMakie v0.12.18
  [501788e0] CollocationMethods v0.1.0 `../../../Repositories/WIP/Repositories/CollocationMethods`
  [0c46a032] DifferentialEquations v7.15.0
  [e9467ef8] GLMakie v0.10.18
  [65ed5ab3] ModelingBI v0.1.0 `../../../Repositories/WIP/Repositories/ModelingBI`
⌃ [961ee093] ModelingToolkit v9.59.0
  [f5f84d89] NumericalTools v0.1.0 `../../../Repositories/WIP/Repositories/NumericalTools`
  [127b3ac7] OrdinaryDiffEqNonlinearSolve v1.3.0
  [91a5bcdd] Plots v1.40.9
  [295af30f] Revise v3.7.1
  [2efcf032] SymbolicIndexingInterface v0.3.37
Info Packages marked with ⌃ have new versions available and may be upgradable.
  • Output of using Pkg; Pkg.status(; mode = PKGMODE_MANIFEST)
Status `~/.julia/environments/v1.11/Manifest.toml`
  [47edcb42] ADTypes v1.11.0
  [621f4979] AbstractFFTs v1.5.0
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  [e2ed5e7c] Bijections v0.1.9
  [d1d4a3ce] BitFlags v0.1.9
  [62783981] BitTwiddlingConvenienceFunctions v0.1.6
  [8e7c35d0] BlockArrays v1.3.0
  [764a87c0] BoundaryValueDiffEq v5.12.0
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  [ed55bfe0] BoundaryValueDiffEqShooting v1.2.0
  [fa961155] CEnum v0.5.0
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⌅ [5ae59095] Colors v0.12.11
  [861a8166] Combinatorics v1.0.2
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Info Packages marked with ⌃ and ⌅ have new versions available. Those with ⌃ may be upgradable, but those with ⌅ are restricted by compatibility constraints from upgrading. To see why use `status --outdated -m`
  • Output of versioninfo()
Julia Version 1.11.2
Commit 5e9a32e7af2 (2024-12-01 20:02 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 8 × 11th Gen Intel(R) Core(TM) i5-1135G7 @ 2.40GHz
  WORD_SIZE: 64
  LLVM: libLLVM-16.0.6 (ORCJIT, tigerlake)
Threads: 1 default, 0 interactive, 1 GC (on 8 virtual cores)

Additional context

I know sometimes the problem might be in the WSL environment, by I also reproduced the error in Windows 11.

@tpdsantos tpdsantos added the bug Something isn't working label Jan 7, 2025
@AayushSabharwal
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This is not a bug with structural_simplify. Rather, @mtkmodel is giving an incorrect default to cin which causes ODEProblem construction to fail.

@tpdsantos
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I thought about that and tried to add a defaults entry. However, I don't know the syntax for array variables, and I tried in several ways... How do I set defaults for array variables inside @mtkmodel?

@AayushSabharwal
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It works the same way for all array variables: defaults(sys)[var] = val

@AayushSabharwal
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Oops, I misunderstood: you meant setting the default inside @mtkmodel

@mtkmodel Foo begin
    @variables begin
        arr(t)[1:4] = ones(4)
    end
end

You just need to set the value to an array of the appropriate size.

@tpdsantos
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But in that way it won't work, since those values are also considered initial conditions and then the problem will become overdetermined and will error... is there any way to give those value in the @defaults environment?

@AayushSabharwal
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AayushSabharwal commented Jan 8, 2025

Even for @defaults it should work the same: val => var. However, specifying in @defaults won't stop it from being an initial condition. Defaults are always initial conditions. This version of your model should work:

julia> @mtkmodel CST begin
           @structural_parameters begin
               NC = 1
           end
           @parameters begin
               Q = 2.0
               V = 1.0
               c_in[1:NC] = [1.0 for i in 1:NC]
           end
           @variables begin
               cin(t)[1:NC] = nothing
               cout(t)[1:NC] = zeros(NC)
           end
           @equations begin
               [D(cout)[i] ~ Q/V * (cin[i] - cout[i]) for i in 1:NC]
               cin ~ c_in
           end
       end

julia> @mtkbuild m = CST()

julia> prob = ODEProblem(m, [], (0.0, 5.0))
ODEProblem with uType Vector{Float64} and tType Float64. In-place: true
timespan: (0.0, 5.0)
u0: 1-element Vector{Float64}:
 0.0

@tpdsantos
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Perfection, it worked like a charm. Thank you. Is there any plan to change this behaviour or should this approach be standard?

@AayushSabharwal
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The incorrect default is a bug and will be fixed. You shouldn't have to specify a default of nothing in this case.

@tpdsantos
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I see. Interestingly, it only affects array variables, scalar variables have no issue

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