Linearization fails without input/ouput

[BambOoxX]

Describe the bug 🐞

Linearization of an MTK system fails due to an Invalid Tag object when no input or outputs are provided.
This used to work on MTK v10, but I have no specific versions to report.

Expected behavior

A linearization call such as linearize(model,[],[]) should not fail, and return state-space matrices.
Of course, since no input/output is provided, only the state matrix A should be non-empty.

Minimal Reproducible Example 👇

using ModelingToolkit, ModelingToolkitStandardLibrary
import ModelingToolkit: connect, t_nounits as t, D_nounits as D
import ModelingToolkitStandardLibrary.Mechanical.TranslationalPosition: Mass, Damper, Spring, Fixed
import ModelingToolkitStandardLibrary.Blocks: Sine

# Build model
@named ds = Sine(amplitude=-1, frequency=10)
@named mass = Mass(m=1)
@named spring = Spring(k=4, l=0.)
@named damper = Damper(d=1)
@named fix = Fixed()

eqs = Equation[
    connect(fix.flange, spring.flange_a, damper.flange_a)
    connect(mass.flange, spring.flange_b, damper.flange_b)
]

@named model = ODESystem(eqs, t; systems=[mass, spring, damper, fix])
linearize(model,[],[])

Error & Stacktrace ⚠️

ERROR: Invalid Tag object:
  Expected ForwardDiff.Tag{ModelingToolkit.PFFun{ODEFunction{true, SciMLBase.AutoSpecialize, FunctionWrappersWrappers.FunctionWrappersWrapper{Tuple{FunctionWrappers.FunctionWrapper{Nothing, Tuple{Vector{Float64}, Vector{Float64}, MTKParameters{Vector{Float64}, Vector{Float64}, Tuple{}, Tuple{}, Tuple{}, Tuple{}}, Float64}}, FunctionWrappers.FunctionWrapper{Nothing, Tuple{Vector{ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}, Float64, 1}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}, Float64, 1}}, MTKParameters{Vector{Float64}, Vector{Float64}, Tuple{}, Tuple{}, Tuple{}, Tuple{}}, Float64}}, FunctionWrappers.FunctionWrapper{Nothing, Tuple{Vector{ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}, Float64, 1}}, Vector{Float64}, MTKParameters{Vector{Float64}, Vector{Float64}, Tuple{}, Tuple{}, Tuple{}, Tuple{}}, ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}, Float64, 1}}}, FunctionWrappers.FunctionWrapper{Nothing, Tuple{Vector{ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}, Float64, 1}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}, Float64, 1}}, MTKParameters{Vector{Float64}, Vector{Float64}, Tuple{}, Tuple{}, Tuple{}, Tuple{}}, ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}, Float64, 1}}}}, FunctionWrappersWrappers.AllowNonIsBits, FunctionWrappersWrappers.SingleCacheStorage}, LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, ModelingToolkitBase.ObservedFunctionCache{System, Nothing}, Nothing, System, Union{Nothing, SciMLBase.OverrideInitData}, Union{Nothing, SciMLBase.ODENLStepData}}, SymbolicIndexingInterface.OOPSetter{false, System, Vector{Any}}}, SymbolicUtils.BasicSymbolicImpl.var"typeof(BasicSymbolicImpl)"{SymReal}},
  Observed ForwardDiff.Tag{ModelingToolkit.PFFun{ODEFunction{true, SciMLBase.AutoSpecialize, FunctionWrappersWrappers.FunctionWrappersWrapper{Tuple{FunctionWrappers.FunctionWrapper{Nothing, Tuple{Vector{Float64}, Vector{Float64}, MTKParameters{Vector{Float64}, Vector{Float64}, Tuple{}, Tuple{}, Tuple{}, Tuple{}}, Float64}}, FunctionWrappers.FunctionWrapper{Nothing, Tuple{Vector{ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}, Float64, 1}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}, Float64, 1}}, MTKParameters{Vector{Float64}, Vector{Float64}, Tuple{}, Tuple{}, Tuple{}, Tuple{}}, Float64}}, FunctionWrappers.FunctionWrapper{Nothing, Tuple{Vector{ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}, Float64, 1}}, Vector{Float64}, MTKParameters{Vector{Float64}, Vector{Float64}, Tuple{}, Tuple{}, Tuple{}, Tuple{}}, ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}, Float64, 1}}}, FunctionWrappers.FunctionWrapper{Nothing, Tuple{Vector{ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}, Float64, 1}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}, Float64, 1}}, MTKParameters{Vector{Float64}, Vector{Float64}, Tuple{}, Tuple{}, Tuple{}, Tuple{}}, ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}, Float64, 1}}}}, FunctionWrappersWrappers.AllowNonIsBits, FunctionWrappersWrappers.SingleCacheStorage}, LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, ModelingToolkitBase.ObservedFunctionCache{System, Nothing}, Nothing, System, Union{Nothing, SciMLBase.OverrideInitData}, Union{Nothing, SciMLBase.ODENLStepData}}, SymbolicIndexingInterface.OOPSetter{false, System, Vector{Any}}}, Any}.
Stacktrace:
  [1] checktag(::Type{ForwardDiff.Tag{…}}, f::ModelingToolkit.PFFun{ODEFunction{…}, SymbolicIndexingInterface.OOPSetter{…}}, x::Vector{SymbolicUtils.BasicSymbolicImpl.var"typeof(BasicSymbolicImpl)"{…}})
    @ ForwardDiff D:\bamboo\.julia\packages\ForwardDiff\IleGP\src\config.jl:34
  [2] checktag(::ForwardDiff.JacobianConfig{…}, f::ModelingToolkit.PFFun{…}, x::Vector{…})
    @ ForwardDiff D:\bamboo\.julia\packages\ForwardDiff\IleGP\src\config.jl:191
  [3] jacobian(::ModelingToolkit.PFFun{…}, ::Vector{…}, ::DifferentiationInterfaceForwardDiffExt.ForwardDiffTwoArgJacobianPrep{…}, ::AutoForwardDiff{…}, ::Vector{…}, ::DifferentiationInterface.Constant{…}, ::DifferentiationInterface.Constant{…}, ::DifferentiationInterface.Constant{…})
    @ DifferentiationInterfaceForwardDiffExt D:\bamboo\.julia\packages\DifferentiationInterface\qwb0w\ext\DifferentiationInterfaceForwardDiffExt\twoarg.jl:469
  [4] (::ModelingToolkit.PreparedJacobian{…})(::Vector{…}, ::Vararg{…})
    @ ModelingToolkit D:\bamboo\.julia\packages\ModelingToolkit\GtdTx\src\linearization.jl:370
  [5] (::ModelingToolkit.LinearizationFunction{…})(u::Vector{…}, p::MTKParameters{…}, t::Float64)
    @ ModelingToolkit D:\bamboo\.julia\packages\ModelingToolkit\GtdTx\src\linearization.jl:520
  [6] solve(prob::LinearizationProblem{ModelingToolkit.LinearizationFunction{…}, Float64}; allow_input_derivatives::Bool)
    @ ModelingToolkit D:\bamboo\.julia\packages\ModelingToolkit\GtdTx\src\linearization.jl:664
  [7] linearize(sys::System, lin_fun::ModelingToolkit.LinearizationFunction{…}; t::Float64, op::Dict{…}, allow_input_derivatives::Bool, p::SciMLBase.NullParameters)
    @ ModelingToolkit D:\bamboo\.julia\packages\ModelingToolkit\GtdTx\src\linearization.jl:991
  [8] linearize(sys::System, inputs::Vector{Any}, outputs::Vector{Any}; op::Dict{Any, Any}, t::Float64, allow_input_derivatives::Bool, zero_dummy_der::Bool, kwargs::@Kwargs{})
    @ ModelingToolkit D:\bamboo\.julia\packages\ModelingToolkit\GtdTx\src\linearization.jl:1107
  [9] linearize(sys::System, inputs::Vector{Any}, outputs::Vector{Any})
    @ ModelingToolkit D:\bamboo\.julia\packages\ModelingToolkit\GtdTx\src\linearization.jl:1071
 [10] top-level scope
    @ REPL[104]:1
Some type information was truncated. Use `show(err)` to see complete types.

Environment (please complete the following information):

• Output of using Pkg; Pkg.status()

  [961ee093] ModelingToolkit v11.38.0
  [16a59e39] ModelingToolkitStandardLibrary v2.29.6

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

  [47edcb42] ADTypes v1.22.4
  [14f7f29c] AMD v0.5.3
  [6e696c72] AbstractPlutoDingetjes v1.4.0
  [1520ce14] AbstractTrees v0.4.5
  [7d9f7c33] Accessors v0.1.45
  [79e6a3ab] Adapt v4.7.0
  [ec485272] ArnoldiMethod v0.4.0
  [4fba245c] ArrayInterface v7.28.1
  [4c555306] ArrayLayouts v1.12.2
  [aae01518] BandedMatrices v1.11.0
  [e2ed5e7c] Bijections v0.2.2
  [b2a6c25c] BinaryHeaps v1.0.4
  [caf10ac8] BipartiteGraphs v0.1.11
  [8e7c35d0] BlockArrays v1.10.0
  [70df07ce] BracketingNonlinearSolve v1.12.4
  [d360d2e6] ChainRulesCore v1.26.1
⌅ [861a8166] Combinatorics v1.0.2
  [38540f10] CommonSolve v0.2.13
  [bbf7d656] CommonSubexpressions v0.3.1
  [f70d9fcc] CommonWorldInvalidations v1.1.2
  [34da2185] Compat v4.18.1
  [b152e2b5] CompositeTypes v0.1.4
  [a33af91c] CompositionsBase v0.1.2
  [2569d6c7] ConcreteStructs v0.2.7
  [187b0558] ConstructionBase v1.6.0
  [a8cc5b0e] Crayons v4.2.0
  [9a962f9c] DataAPI v1.16.0
  [864edb3b] DataStructures v0.19.6
  [e2d170a0] DataValueInterfaces v1.0.0
  [2b5f629d] DiffEqBase v7.11.0
  [459566f4] DiffEqCallbacks v4.19.1
  [163ba53b] DiffResults v1.1.0
  [b552c78f] DiffRules v1.16.0
  [a0c0ee7d] DifferentiationInterface v0.7.20
  [ffbed154] DocStringExtensions v0.9.5
  [5b8099bc] DomainSets v0.8.1
  [7c1d4256] DynamicPolynomials v0.6.6
  [4e289a0a] EnumX v1.0.7
  [f151be2c] EnzymeCore v0.8.21
  [e2ba6199] ExprTools v0.1.11
  [55351af7] ExproniconLite v0.10.14
  [7034ab61] FastBroadcast v1.3.6
  [9aa1b823] FastClosures v0.3.2
  [a4df4552] FastPower v1.4.1
  [1a297f60] FillArrays v1.17.0
  [64ca27bc] FindFirstFunctions v3.2.1
  [6a86dc24] FiniteDiff v2.32.1
  [f6369f11] ForwardDiff v1.4.4
  [a85aefff] FunctionMaps v0.1.2
  [069b7b12] FunctionWrappers v1.1.3
  [77dc65aa] FunctionWrappersWrappers v1.12.1
  [46192b85] GPUArraysCore v0.2.0
  [86223c79] Graphs v1.14.0
  [3263718b] ImplicitDiscreteSolve v2.1.5
  [d25df0c9] Inflate v0.1.5
  [18e54dd8] IntegerMathUtils v0.1.4
  [8197267c] IntervalSets v0.7.14
  [3587e190] InverseFunctions v0.1.17
  [92d709cd] IrrationalConstants v0.2.6
  [82899510] IteratorInterfaceExtensions v1.0.0
  [692b3bcd] JLLWrappers v1.8.0
  [ae98c720] Jieko v0.2.1
  [ccbc3e58] JumpProcesses v9.29.2
  [ba0b0d4f] Krylov v0.10.9
  [b964fa9f] LaTeXStrings v1.4.0
  [87fe0de2] LineSearch v0.1.13
  [7ed4a6bd] LinearSolve v5.4.1
  [2ab3a3ac] LogExpFunctions v1.0.1
  [e6f89c97] LoggingExtras v1.2.0
  [1914dd2f] MacroTools v0.5.16
  [bb5d69b7] MaybeInplace v0.1.7
  [961ee093] ModelingToolkit v11.38.0
  [7771a370] ModelingToolkitBase v1.60.0
  [16a59e39] ModelingToolkitStandardLibrary v2.29.6
  [6bb917b9] ModelingToolkitTearing v1.20.5
  [2e0e35c7] Moshi v0.3.12
  [46d2c3a1] MuladdMacro v0.2.7
  [102ac46a] MultivariatePolynomials v0.5.19
  [d8a4904e] MutableArithmetics v1.8.0
  [77ba4419] NaNMath v1.1.4
  [be0214bd] NonlinearSolveBase v2.40.0
  [5959db7a] NonlinearSolveFirstOrder v2.2.4
  [6fe1bfb0] OffsetArrays v1.17.0
⌅ [bac558e1] OrderedCollections v1.8.2
  [bbf590c4] OrdinaryDiffEqCore v4.13.0
  [e409e4f3] PoissonRandom v0.4.13
  [d236fae5] PreallocationTools v1.4.0
  [aea7be01] PrecompileTools v1.3.4
  [21216c6a] Preferences v1.5.2
  [08abe8d2] PrettyTables v3.4.4
  [27ebfcd6] Primes v0.5.7
  [0c0d3e7f] PureKLU v1.3.0
  [988b38a3] ReadOnlyArrays v0.2.0
  [795d4caa] ReadOnlyDicts v1.0.1
  [3cdcf5f2] RecipesBase v1.3.4
  [731186ca] RecursiveArrayTools v4.3.6
  [189a3867] Reexport v1.2.2
  [9fe22ead] RespecializeParams v1.2.0
  [7e49a35a] RuntimeGeneratedFunctions v0.5.24
  [9dfe8606] SCCNonlinearSolve v1.14.1
  [0bca4576] SciMLBase v3.42.0
  [19f34311] SciMLJacobianOperators v0.1.16
  [a6db7da4] SciMLLogging v2.0.4
  [c0aeaf25] SciMLOperators v1.26.0
  [431bcebd] SciMLPublic v1.2.4
  [53ae85a6] SciMLStructures v1.10.4
  [efcf1570] Setfield v1.1.2
  [727e6d20] SimpleNonlinearSolve v2.13.1
  [699a6c99] SimpleTraits v0.9.6
  [a57abbd0] SparseColumnPivotedQR v2.1.5
  [276daf66] SpecialFunctions v2.8.2
  [0c0c59c1] StarAlgebras v0.3.0
  [64909d44] StateSelection v1.11.0
  [90137ffa] StaticArrays v1.9.18
  [1e83bf80] StaticArraysCore v1.4.4
  [10745b16] Statistics v1.11.1
  [892a3eda] StringManipulation v0.4.7
  [2efcf032] SymbolicIndexingInterface v0.3.52
  [19f23fe9] SymbolicLimits v1.1.4
  [d1185830] SymbolicUtils v4.44.1
  [0c5d862f] Symbolics v7.35.0
  [3783bdb8] TableTraits v1.0.1
  [bd369af6] Tables v1.13.0
  [ed4db957] TaskLocalValues v0.1.3
  [8ea1fca8] TermInterface v2.0.0
  [a759f4b9] TimerOutputs v1.1.0
  [781d530d] TruncatedStacktraces v1.4.0
  [3a884ed6] UnPack v1.0.2
  [d30d5f5c] WeakCacheSets v0.1.0
  [1d5cc7b8] IntelOpenMP_jll v2025.2.0+0
  [856f044c] MKL_jll v2025.2.0+0
  [efe28fd5] OpenSpecFun_jll v0.5.6+0
  [1317d2d5] oneTBB_jll v2022.3.0+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
  [f43a241f] Downloads v1.7.0
  [7b1f6079] FileWatching v1.11.0
  [9fa8497b] Future v1.11.0
  [b77e0a4c] InteractiveUtils v1.11.0
  [ac6e5ff7] JuliaSyntaxHighlighting v1.12.0
  [4af54fe1] LazyArtifacts v1.11.0
  [b27032c2] LibCURL v0.6.4
  [76f85450] LibGit2 v1.11.0
  [8f399da3] Libdl v1.11.0
  [37e2e46d] LinearAlgebra v1.12.0
  [56ddb016] Logging v1.11.0
  [d6f4376e] Markdown v1.11.0
  [ca575930] NetworkOptions v1.3.0
  [44cfe95a] Pkg v1.12.1
  [de0858da] Printf v1.11.0
  [3fa0cd96] REPL v1.11.0
  [9a3f8284] Random v1.11.0
  [ea8e919c] SHA v0.7.0
  [9e88b42a] Serialization v1.11.0
  [6462fe0b] Sockets v1.11.0
  [2f01184e] SparseArrays v1.12.0
  [f489334b] StyledStrings v1.11.0
  [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 v1.3.0+1
  [deac9b47] LibCURL_jll v8.15.0+0
  [e37daf67] LibGit2_jll v1.9.0+0
  [29816b5a] LibSSH2_jll v1.11.3+1
  [14a3606d] MozillaCACerts_jll v2025.11.4
  [4536629a] OpenBLAS_jll v0.3.29+0
  [05823500] OpenLibm_jll v0.8.7+0
  [458c3c95] OpenSSL_jll v3.5.4+0
  [bea87d4a] SuiteSparse_jll v7.8.3+2
  [83775a58] Zlib_jll v1.3.1+2
  [8e850b90] libblastrampoline_jll v5.15.0+0
  [8e850ede] nghttp2_jll v1.64.0+1
  [3f19e933] p7zip_jll v17.7.0+0

• Output of versioninfo()

Julia Version 1.12.6
Commit 15346901f0 (2026-04-09 19:20 UTC)
Build Info:
  Official https://julialang.org release
Platform Info:
  OS: Windows (x86_64-w64-mingw32)
  CPU: 8 × 11th Gen Intel(R) Core(TM) i7-1185G7 @ 3.00GHz
  WORD_SIZE: 64
  LLVM: libLLVM-18.1.7 (ORCJIT, tigerlake)
  GC: Built with stock GC
Threads: 1 default, 1 interactive, 1 GC (on 8 virtual cores)

Additional context

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