Create a model with interval parameters

[rasmuskovacs]

Describe the bug 🐞

In a fresh Julia REPL I can setup a model using @mtkmodel and have some of the parameters as intervals (from IntervalArithmetics.jl). However if I then run the code again and change it to a normal (non-interval) parameter i get a TypeError. However, if I start another fresh REPL and run the code witha normal parameter, it works. And by changing it to an interval, it doesn't work. So depending in what order I run it, they both work. In my case it happens for the parameters, R, L, k, J, f but not the other two.

Expected behavior

Since both of them work with a fresh Julia REPL I would expect them to work if I simply change the parameter. The order should not matter.

Minimal Reproducible Example 👇
I tried to create a smaller example but then it worked for some reason. This is an example in the ModelingToolkitStandardLibrary documentation.

using ModelingToolkit
using ModelingToolkit: t_nounits as t
using IntervalArithmetic
using ModelingToolkitStandardLibrary.Electrical
using ModelingToolkitStandardLibrary.Blocks
using ModelingToolkitStandardLibrary.Mechanical.Rotational

@mtkmodel DCMotor begin
    @parameters begin
        R = 0.5# first run this and then add ±0.1 and run again to get the error,(or the other way around) [description = "Armature resistance"] # Ohm
        L = 4.5e-3, [description = "Armature inductance"] # H
        k = 0.5±0.01, [description = "Motor constant"] # N.m/A
        J = 0.02, [description = "Inertia"] # kg.m²
        f = 0.01, [description = "Friction factor"] # N.m.s/rad
        tau_L_step = -0.3, [description = "Amplitude of the load torque step"] # N.m
        u_max=1
    end
    @components begin
        ground = Ground()
        source = Voltage()
        ref = Blocks.Step(height = 1, start_time = 0)
        pi_controller = Blocks.LimPI(k = 1.1, T = 0.035, u_max = u_max, Ta = 0.035)
        feedback = Blocks.Feedback()
        R1 = Resistor(R = R)
        L1 = Inductor(L = L,i=0)
        emf = EMF(k = k)
        fixed = Fixed()
        load = Torque()
        load_step = Blocks.Step(height = tau_L_step, start_time = 3)
        inertia = Inertia(J = J, phi = 0.0, w = 0.0)
        friction = Damper(d = f)
        speed_sensor = SpeedSensor()
    end
    @equations begin
        connect(fixed.flange, emf.support, friction.flange_b)
        connect(emf.flange, friction.flange_a, inertia.flange_a)
        connect(inertia.flange_b, load.flange)
        connect(inertia.flange_b, speed_sensor.flange)
        connect(load_step.output, load.tau)
        connect(ref.output, feedback.input1)
        connect(speed_sensor.w, :y, feedback.input2)
        connect(feedback.output, pi_controller.err_input)
        connect(pi_controller.ctr_output, :u, source.V)
        connect(source.p, R1.p)
        connect(R1.n, L1.p)
        connect(L1.n, emf.p)
        connect(emf.n, source.n, ground.g)
    end
end

@named model = DCMotor()

Error & Stacktrace ⚠️

ERROR: LoadError: TypeError: non-boolean (Interval{Float64}) used in boolean context
Stacktrace:
  [1] signequal(x::Float64, y::Interval{Float64})
    @ Base ./operators.jl:136
  [2] isequal(x::Float64, y::Interval{Float64})
    @ Base ./operators.jl:141
  [3] isequal_with_metadata(a::Float64, b::Interval{Float64})
    @ SymbolicUtils ~/.julia/packages/SymbolicUtils/2cE5G/src/types.jl:365
  [4] isequal_with_metadata(a::Base.ImmutableDict{DataType, Any}, b::Base.ImmutableDict{DataType, Any})
    @ SymbolicUtils ~/.julia/packages/SymbolicUtils/2cE5G/src/types.jl:346
  [5] isequal_with_metadata(a::SymbolicUtils.BasicSymbolic{Real}, b::SymbolicUtils.BasicSymbolic{Real})
    @ SymbolicUtils ~/.julia/packages/SymbolicUtils/2cE5G/src/types.jl:303
  [6] isequal_with_metadata(a::Base.ImmutableDict{DataType, Any}, b::Base.ImmutableDict{DataType, Any})
    @ SymbolicUtils ~/.julia/packages/SymbolicUtils/2cE5G/src/types.jl:346
  [7] isequal_with_metadata(a::SymbolicUtils.BasicSymbolic{Real}, b::SymbolicUtils.BasicSymbolic{Real})
    @ SymbolicUtils ~/.julia/packages/SymbolicUtils/2cE5G/src/types.jl:303
  [8] SymbolicUtils.BasicSymbolic(s::SymbolicUtils.BasicSymbolic{Real})
    @ SymbolicUtils ~/.julia/packages/SymbolicUtils/2cE5G/src/types.jl:516
  [9] #_#15
    @ ~/.julia/packages/SymbolicUtils/2cE5G/src/types.jl:525 [inlined]
 [10] setproperties(obj::SymbolicUtils.BasicSymbolic{Real}, patch::@NamedTuple{metadata::Base.ImmutableDict{DataType, Any}})
    @ SymbolicUtils ~/.julia/packages/SymbolicUtils/2cE5G/src/types.jl:100
 [11] set
    @ ~/.julia/packages/Setfield/PdKfV/src/lens.jl:122 [inlined]
 [12] macro expansion
    @ ~/.julia/packages/Setfield/PdKfV/src/sugar.jl:197 [inlined]
 [13] setmetadata(s::SymbolicUtils.BasicSymbolic{Real}, ctx::DataType, val::SymbolicUtils.BasicSymbolic{Real})
    @ SymbolicUtils ~/.julia/packages/SymbolicUtils/2cE5G/src/types.jl:902
 [14] set_scalar_metadata
    @ ~/.julia/packages/Symbolics/rjrbr/src/variable.jl:43 [inlined]
 [15] setdefaultval(x::SymbolicUtils.BasicSymbolic{Real}, val::SymbolicUtils.BasicSymbolic{Real})
    @ Symbolics ~/.julia/packages/Symbolics/rjrbr/src/variable.jl:45
 [16] setdefault(v::Num, val::Num)
    @ ModelingToolkit ~/.julia/packages/ModelingToolkit/41wGH/src/utils.jl:244
 [17] __Resistor__(; name::Symbol, R::Num)
    @ ModelingToolkitStandardLibrary.Electrical ~/.julia/packages/ModelingToolkit/41wGH/src/systems/model_parsing.jl:914
 [18] __Resistor__
    @ ~/.julia/packages/ModelingToolkit/41wGH/src/systems/model_parsing.jl:138 [inlined]
 [19] #_#449
    @ ~/.julia/packages/ModelingToolkit/41wGH/src/systems/model_parsing.jl:25 [inlined]
 [20] macro expansion
    @ ~/.julia/packages/ModelingToolkit/41wGH/src/systems/abstractsystem.jl:2081 [inlined]
 [21] 
    @ Main ~/.julia/packages/ModelingToolkit/41wGH/src/systems/model_parsing.jl:914
 [22] __DCMotor__
    @ ~/.julia/packages/ModelingToolkit/41wGH/src/systems/model_parsing.jl:138 [inlined]
 [23] #_#449
    @ ~/.julia/packages/ModelingToolkit/41wGH/src/systems/model_parsing.jl:25 [inlined]
 [24] top-level scope
    @ ~/.julia/packages/ModelingToolkit/41wGH/src/systems/abstractsystem.jl:2081
in expression starting at /home/rasmus/Exjobb/julia_testing_environment/mwe.jl:51
Some type information was truncated. Use `show(err)` to see complete types.

Environment (please complete the following information):

• Output of using Pkg; Pkg.status()

Status `/tmp/jl_gcMq8z/Project.toml`
  [d1acc4aa] IntervalArithmetic v0.22.22
  [961ee093] ModelingToolkit v9.62.0
  [16a59e39] ModelingToolkitStandardLibrary v2.19.0

• Output of using Pkg; Pkg.status(; mode = PKGMODE_MANIFEST)

Status `/tmp/jl_gcMq8z/Manifest.toml`
  [47edcb42] ADTypes v1.12.1
  [1520ce14] AbstractTrees v0.4.5
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  [e2ed5e7c] Bijections v0.1.9
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  [70df07ce] BracketingNonlinearSolve v1.1.0
  [2a0fbf3d] CPUSummary v0.2.6
  [00ebfdb7] CSTParser v3.4.3
  [d360d2e6] ChainRulesCore v1.25.1
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  [861a8166] Combinatorics v1.0.2
  [a80b9123] CommonMark v0.8.15
  [38540f10] CommonSolve v0.2.4
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  [f70d9fcc] CommonWorldInvalidations v1.0.0
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⌅ [6b7a57c9] Expronicon v0.8.5
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  [2ab3a3ac] LogExpFunctions v0.3.29
  [bdcacae8] LoopVectorization v0.12.171
  [d8e11817] MLStyle v0.4.17
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  [16a59e39] ModelingToolkitStandardLibrary v2.19.0
  [46d2c3a1] MuladdMacro v0.2.4
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  [be0214bd] NonlinearSolveBase v1.4.0
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  [26075421] NonlinearSolveSpectralMethods v1.1.0
  [6fe1bfb0] OffsetArrays v1.15.0
  [429524aa] Optim v1.11.0
  [bac558e1] OrderedCollections v1.8.0
  [90014a1f] PDMats v0.11.32
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  [f2c3362d] RecursiveFactorization v0.2.23
  [189a3867] Reexport v1.2.2
  [ae029012] Requires v1.3.0
  [ae5879a3] ResettableStacks v1.1.1
  [79098fc4] Rmath v0.8.0
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  [94e857df] SIMDTypes v0.1.0
  [476501e8] SLEEFPirates v0.6.43
  [0bca4576] SciMLBase v2.72.2
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  [727e6d20] SimpleNonlinearSolve v2.1.0
  [699a6c99] SimpleTraits v0.9.4
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  [aedffcd0] Static v1.1.1
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  [7792a7ef] StrideArraysCore v0.5.7
  [2efcf032] SymbolicIndexingInterface v0.3.37
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  [d1185830] SymbolicUtils v3.13.0
  [0c5d862f] Symbolics v6.27.0
  [3783bdb8] TableTraits v1.0.1
  [bd369af6] Tables v1.12.0
  [8ea1fca8] TermInterface v2.0.0
  [1c621080] TestItems v1.0.0
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  [f50d1b31] Rmath_jll v0.5.1+0
  [1317d2d5] oneTBB_jll v2021.12.0+0
  [0dad84c5] ArgTools v1.1.2
  [56f22d72] Artifacts v1.11.0
  [2a0f44e3] Base64 v1.11.0
  [ade2ca70] Dates v1.11.0
  [8ba89e20] Distributed v1.11.0
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  [7b1f6079] FileWatching v1.11.0
  [9fa8497b] Future v1.11.0
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  [4af54fe1] LazyArtifacts v1.11.0
  [b27032c2] LibCURL v0.6.4
  [76f85450] LibGit2 v1.11.0
  [8f399da3] Libdl v1.11.0
  [37e2e46d] LinearAlgebra v1.11.0
  [56ddb016] Logging v1.11.0
  [d6f4376e] Markdown v1.11.0
  [a63ad114] Mmap v1.11.0
  [ca575930] NetworkOptions v1.2.0
  [44cfe95a] Pkg v1.11.0
  [de0858da] Printf v1.11.0
  [9a3f8284] Random v1.11.0
  [ea8e919c] SHA v0.7.0
  [9e88b42a] Serialization v1.11.0
  [1a1011a3] SharedArrays v1.11.0
  [6462fe0b] Sockets v1.11.0
  [2f01184e] SparseArrays v1.11.0
  [4607b0f0] SuiteSparse
  [fa267f1f] TOML v1.0.3
  [a4e569a6] Tar v1.10.0
  [8dfed614] Test v1.11.0
  [cf7118a7] UUIDs v1.11.0
  [4ec0a83e] Unicode v1.11.0
  [e66e0078] CompilerSupportLibraries_jll v1.1.1+0
  [deac9b47] LibCURL_jll v8.6.0+0
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  [bea87d4a] SuiteSparse_jll v7.7.0+0
  [83775a58] Zlib_jll v1.2.13+1
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  [3f19e933] p7zip_jll v17.4.0+2
Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated -m`

• Output of versioninfo()

Julia Version 1.11.3
Commit d63adeda50d (2025-01-21 19:42 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 8 × 11th Gen Intel(R) Core(TM) i7-1165G7 @ 2.80GHz
  WORD_SIZE: 64
  LLVM: libLLVM-16.0.6 (ORCJIT, tigerlake)
Threads: 1 default, 0 interactive, 1 GC (on 8 virtual cores)
Environment:
  JULIA_EDITOR = code
  JULIA_NUM_THREADS = 

Additional context

[AayushSabharwal]

Hi! This issue is partially due to a relatively recent addition to the underlying symbolic manipulation infrastructure. We now have a global cache of expression trees, and when creating a new one we look to see if an identical tree already exists. This checking of "are these trees identical" uses isequal, and IntervalArithmetic does not allow comparing Intervals with anything else via isequal, so the symbolic manipulation library has no way to check "are these two things equal".

Thus, the order of evaluation bug happens because when running the model with k = 0.5±0.01, the cached tree stores 0.5±0.01. When trying to re-create it with k = 0.5 it tries to compare the two and fails when comparing isequal(0.5, 0.5±0.01). If you restart the REPL the cache is cleared. The first expression created works, and the second expression fails due to the equality check failing.

[AayushSabharwal]

If you really need this, it might be worth downgrading to [email protected] and trying again.

[rasmuskovacs]

Okay, got it, thank you for the explanation!