Error when creating system with indexed variables

[mabuni1998]

Describe the bug 🐞

When creating a System for a Dynamic control problem the creation fails if the system variables are indexed.

Expected behavior

The system block to be initialized. For example the below code DOES work, but I would like to use indexed variables for a larger system of equations.

using ModelingToolkit
using ModelingToolkit: t_nounits as t, D_nounits as D
@variables begin
    u1(..),[input = true,bounds = (0.0, 10.0)]    # u1, u2   →  u[1], u[2]
    u2(..),[input = true,bounds = (0.0, 10.0)]    
    x1(..) 
    x2(..)
end
@parameters tf
eqs = [D(x1(t)) ~ u1(t) + x2(t),
       D(x2(t)) ~ u2(t) - x1(t)]
constr = vcat([x1(tf) ~ 0.0, x2(tf) ~ 0.0])
cost = [tf]
@named block = System(eqs, t; costs = cost, constraints = constr)

Minimal Reproducible Example 👇

This code does not work because x(..)[1] is indexed. Is there another way it should be declared?

using ModelingToolkit
using ModelingToolkit: t_nounits as t, D_nounits as D
@variables begin
    u(..)[1:2],[input = true,bounds = (0.0, 10.0)]   
    x(..)[1:2] 
end
@parameters tf
eqs = [D(x(t)[1]) ~ u(t)[1] + x(t)[2],
       D(x(t)[2]) ~ u(t)[2] - x(t)[1]]
constr = vcat([x(tf)[1] ~ 0.0, x(tf)[2] ~ 0.0])
cost = [tf]
@named block = System(eqs, t; costs = cost, constraints = constr)

Error & Stacktrace ⚠️

ERROR: ArgumentError: Too many arguments for variable (x(tf))[1].
Stacktrace:
 [1] validate_vars_and_find_ps!(auxvars::OrderedCollections.OrderedSet{…}, auxps::OrderedCollections.OrderedSet{…}, sysvars::OrderedCollections.OrderedSet{…}, iv::Num)
   @ ModelingToolkit C:\Users\mabun\.julia\packages\ModelingToolkit\Ma5jP\src\systems\system.jl:649
 [2] process_constraint_system(constraints::Vector{…}, sts::OrderedCollections.OrderedSet{…}, ps::Set{…}, iv::Num; validate::Bool)
   @ ModelingToolkit C:\Users\mabun\.julia\packages\ModelingToolkit\Ma5jP\src\systems\system.jl:612
 [3] process_constraint_system
   @ C:\Users\mabun\.julia\packages\ModelingToolkit\Ma5jP\src\systems\system.jl:599 [inlined]
 [4] System(eqs::Vector{Equation}, iv::Num; kwargs::@Kwargs{name::Symbol, costs::Vector{Num}, constraints::Vector{Equation}})
   @ ModelingToolkit C:\Users\mabun\.julia\packages\ModelingToolkit\Ma5jP\src\systems\system.jl:491
 [5] top-level scope
   @ C:\Users\mabun\.julia\packages\ModelingToolkit\Ma5jP\src\systems\abstractsystem.jl:2123
Some type information was truncated. Use `show(err)` to see complete types.

Environment (please complete the following information):

• Output of using Pkg; Pkg.status()

(scripts) pkg> status
Status `C:\Users\mabun\OneDrive - Danmarks Tekniske Universitet\Projects\QuantumOptimalControl\scripts\project.toml`
  [6e4b80f9] BenchmarkTools v1.6.0
  [f3b72e0c] DiffEqDevTools v2.48.0
  [20393b10] InfiniteOpt v0.5.9
  [b6b21f68] Ipopt v1.10.6
  [961ee093] ModelingToolkit v10.13.0
  [c4671d76] Piccolo v0.8.0
  [d330b81b] PyPlot v2.11.6
  [4f57444f] QuantumOpticsBase v0.5.8
  [0bca4576] SciMLBase v2.104.0
  [0c5d862f] Symbolics v6.45.0

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

julia> using Pkg; Pkg.status(; mode = PKGMODE_MANIFEST)
Status `C:\Users\mabun\OneDrive - Danmarks Tekniske Universitet\Projects\QuantumOptimalControl\scripts\Manifest.toml`
  [47edcb42] ADTypes v1.15.0
  [c29ec348] AbstractDifferentiation v0.6.2
  [621f4979] AbstractFFTs v1.5.0
  [1520ce14] AbstractTrees v0.4.5
  [7d9f7c33] Accessors v0.1.42
  [79e6a3ab] Adapt v4.3.0
  [66dad0bd] AliasTables v1.1.3
  [ec485272] ArnoldiMethod v0.4.0
  [4fba245c] ArrayInterface v7.19.0
  [4c555306] ArrayLayouts v1.11.2
  [6e4b80f9] BenchmarkTools v1.6.0
  [e2ed5e7c] Bijections v0.2.2
  [62783981] BitTwiddlingConvenienceFunctions v0.1.6
  [8e7c35d0] BlockArrays v1.7.0
  [70df07ce] BracketingNonlinearSolve v1.3.0
  [2a0fbf3d] CPUSummary v0.2.6
  [d360d2e6] ChainRulesCore v1.25.2
  [fb6a15b2] CloseOpenIntervals v0.1.13
  [523fee87] CodecBzip2 v0.8.5
  [944b1d66] CodecZlib v0.7.8
  [3da002f7] ColorTypes v0.12.1
  [5ae59095] Colors v0.13.1
  [861a8166] Combinatorics v1.0.3
  [a80b9123] CommonMark v0.9.1
  [38540f10] CommonSolve v0.2.4
  [bbf7d656] CommonSubexpressions v0.3.1
  [f70d9fcc] CommonWorldInvalidations v1.0.0
  [34da2185] Compat v4.17.0
  [b152e2b5] CompositeTypes v0.1.4
  [a33af91c] CompositionsBase v0.1.2
  [2569d6c7] ConcreteStructs v0.2.3
  [8f4d0f93] Conda v1.10.2
  [187b0558] ConstructionBase v1.6.0
  [adafc99b] CpuId v0.3.1
  [a8cc5b0e] Crayons v4.1.1
  [9a962f9c] DataAPI v1.16.0
  [864edb3b] DataStructures v0.18.22
  [e2d170a0] DataValueInterfaces v1.0.0
  [2b5f629d] DiffEqBase v6.178.0
  [459566f4] DiffEqCallbacks v4.8.0
  [f3b72e0c] DiffEqDevTools v2.48.0
  [77a26b50] DiffEqNoiseProcess v5.24.1
  [163ba53b] DiffResults v1.1.0
  [b552c78f] DiffRules v1.15.1
  [a0c0ee7d] DifferentiationInterface v0.7.3
  [c823fa1f] DirectTrajOpt v0.4.0
  [8d63f2c5] DispatchDoctor v0.4.26
  [b4f34e82] Distances v0.10.12
  [31c24e10] Distributions v0.25.120
  [ffbed154] DocStringExtensions v0.9.5
  [5b8099bc] DomainSets v0.7.15
  [7c1d4256] DynamicPolynomials v0.6.2
  [06fc5a27] DynamicQuantities v1.8.0
  [4e289a0a] EnumX v1.0.5
  [f151be2c] EnzymeCore v0.8.12
  [e24c0720] ExponentialAction v0.2.10
  [d4d017d3] ExponentialUtilities v1.27.0
  [e2ba6199] ExprTools v0.1.10
  [55351af7] ExproniconLite v0.10.14
  [411431e0] Extents v0.1.6
  [7a1cc6ca] FFTW v1.9.0
  [7034ab61] FastBroadcast v0.3.5
  [9aa1b823] FastClosures v0.3.2
  [7868e603] FastExpm v1.1.0
  [442a2c76] FastGaussQuadrature v1.0.2
  [a4df4552] FastPower v1.1.3
  [5789e2e9] FileIO v1.17.0
  [1a297f60] FillArrays v1.13.0
  [64ca27bc] FindFirstFunctions v1.4.1
  [6a86dc24] FiniteDiff v2.27.0
  [53c48c17] FixedPointNumbers v0.8.5
  [1fa38f19] Format v1.3.7
⌃ [f6369f11] ForwardDiff v0.10.38
  [069b7b12] FunctionWrappers v1.1.3
  [77dc65aa] FunctionWrappersWrappers v0.1.3
  [d9f16b24] Functors v0.5.2
  [46192b85] GPUArraysCore v0.2.0
  [c145ed77] GenericSchur v0.5.5
  [5c1252a2] GeometryBasics v0.5.10
  [c27321d9] Glob v1.3.1
  [86223c79] Graphs v1.13.0
  [076d061b] HashArrayMappedTries v0.2.0
  [34004b35] HypergeometricFunctions v0.3.28
  [615f187c] IfElse v0.1.1
  [3263718b] ImplicitDiscreteSolve v0.1.3
  [20393b10] InfiniteOpt v0.5.9
  [d25df0c9] Inflate v0.1.5
  [18e54dd8] IntegerMathUtils v0.1.3
  [8197267c] IntervalSets v0.7.11
  [3587e190] InverseFunctions v0.1.17
  [b6b21f68] Ipopt v1.10.6
  [92d709cd] IrrationalConstants v0.2.4
  [c8e1da08] IterTools v1.10.0
  [82899510] IteratorInterfaceExtensions v1.0.0
  [033835bb] JLD2 v0.5.15
  [692b3bcd] JLLWrappers v1.7.1
  [682c06a0] JSON v0.21.4
  [0f8b85d8] JSON3 v1.14.3
  [ae98c720] Jieko v0.2.1
  [4076af6c] JuMP v1.27.0
  [98e50ef6] JuliaFormatter v2.1.2
⌅ [70703baa] JuliaSyntax v0.4.10
  [ccbc3e58] JumpProcesses v9.16.1
  [ba0b0d4f] Krylov v0.10.1
  [8ac3fa9e] LRUCache v1.6.2
  [b964fa9f] LaTeXStrings v1.4.0
  [23fbe1c1] Latexify v0.16.8
  [10f19ff3] LayoutPointers v0.1.17
  [5078a376] LazyArrays v2.6.2
  [1d6d02ad] LeftChildRightSiblingTrees v0.2.1
  [87fe0de2] LineSearch v0.1.4
  [d3d80556] LineSearches v7.4.0
  [7ed4a6bd] LinearSolve v3.23.0
  [2ab3a3ac] LogExpFunctions v0.3.29
  [d8e11817] MLStyle v0.4.17
  [1914dd2f] MacroTools v0.5.16
  [20f20a25] MakieCore v0.10.0
  [d125e4d3] ManualMemory v0.1.8
  [b8f27783] MathOptInterface v1.42.0
  [bb5d69b7] MaybeInplace v0.1.4
  [e1d29d7a] Missings v1.2.0
  [961ee093] ModelingToolkit v10.13.0
  [2e0e35c7] Moshi v0.3.7
  [46d2c3a1] MuladdMacro v0.2.4
  [102ac46a] MultivariatePolynomials v0.5.9
  [d8a4904e] MutableArithmetics v1.6.4
  [d41bc354] NLSolversBase v7.10.0
  [2774e3e8] NLsolve v4.5.1
  [77ba4419] NaNMath v1.1.3
  [538bc3a1] NamedTrajectories v0.5.0
  [8913a72c] NonlinearSolve v4.10.0
  [be0214bd] NonlinearSolveBase v1.13.0
  [5959db7a] NonlinearSolveFirstOrder v1.6.0
  [9a2c21bd] NonlinearSolveQuasiNewton v1.7.0
  [26075421] NonlinearSolveSpectralMethods v1.2.0
  [510215fc] Observables v0.5.5
  [6fe1bfb0] OffsetArrays v1.17.0
  [429524aa] Optim v1.13.2
  [bac558e1] OrderedCollections v1.8.1
  [1dea7af3] OrdinaryDiffEq v6.101.0
  [89bda076] OrdinaryDiffEqAdamsBashforthMoulton v1.2.0
  [6ad6398a] OrdinaryDiffEqBDF v1.7.0
  [bbf590c4] OrdinaryDiffEqCore v1.26.2
  [50262376] OrdinaryDiffEqDefault v1.5.0
  [4302a76b] OrdinaryDiffEqDifferentiation v1.10.1
  [9286f039] OrdinaryDiffEqExplicitRK v1.1.0
  [e0540318] OrdinaryDiffEqExponentialRK v1.5.0
  [becaefa8] OrdinaryDiffEqExtrapolation v1.5.0
  [5960d6e9] OrdinaryDiffEqFIRK v1.13.0
  [101fe9f7] OrdinaryDiffEqFeagin v1.1.0
  [d3585ca7] OrdinaryDiffEqFunctionMap v1.2.0
  [d28bc4f8] OrdinaryDiffEqHighOrderRK v1.2.0
  [9f002381] OrdinaryDiffEqIMEXMultistep v1.4.0
  [521117fe] OrdinaryDiffEqLinear v1.3.0
  [1344f307] OrdinaryDiffEqLowOrderRK v1.3.0
  [b0944070] OrdinaryDiffEqLowStorageRK v1.3.0
  [127b3ac7] OrdinaryDiffEqNonlinearSolve v1.11.0
  [c9986a66] OrdinaryDiffEqNordsieck v1.1.0
  [5dd0a6cf] OrdinaryDiffEqPDIRK v1.3.1
  [5b33eab2] OrdinaryDiffEqPRK v1.1.0
  [04162be5] OrdinaryDiffEqQPRK v1.1.0
  [af6ede74] OrdinaryDiffEqRKN v1.2.0
  [43230ef6] OrdinaryDiffEqRosenbrock v1.12.0
  [2d112036] OrdinaryDiffEqSDIRK v1.4.0
  [669c94d9] OrdinaryDiffEqSSPRK v1.3.0
  [e3e12d00] OrdinaryDiffEqStabilizedIRK v1.3.0
  [358294b1] OrdinaryDiffEqStabilizedRK v1.2.0
  [fa646aed] OrdinaryDiffEqSymplecticRK v1.4.0
  [b1df2697] OrdinaryDiffEqTsit5 v1.2.0
  [79d7bb75] OrdinaryDiffEqVerner v1.3.0
  [90014a1f] PDMats v0.11.35
  [65ce6f38] PackageExtensionCompat v1.0.2
  [d96e819e] Parameters v0.12.3
  [69de0a69] Parsers v2.8.3
  [c4671d76] Piccolo v0.8.0
  [f42a522c] PiccoloPlots v0.2.1
  [5a402ddf] PiccoloQuantumObjects v0.6.1
  [e409e4f3] PoissonRandom v0.4.5
  [f517fe37] Polyester v0.7.18
  [1d0040c9] PolyesterWeave v0.2.2
  [85a6dd25] PositiveFactorizations v0.2.4
  [d236fae5] PreallocationTools v0.4.29
⌅ [aea7be01] PrecompileTools v1.2.1
  [21216c6a] Preferences v1.4.3
  [08abe8d2] PrettyTables v2.4.0
  [27ebfcd6] Primes v0.5.7
  [92933f4c] ProgressMeter v1.10.4
  [43287f4e] PtrArrays v1.3.0
  [438e738f] PyCall v1.96.4
  [d330b81b] PyPlot v2.11.6
  [1fd47b50] QuadGK v2.11.2
  [0dc23a59] QuantumCollocation v0.8.1
  [5717a53b] QuantumInterface v0.4.1
  [4f57444f] QuantumOpticsBase v0.5.8
  [74087812] Random123 v1.7.1
  [e6cf234a] RandomNumbers v1.6.0
  [3cdcf5f2] RecipesBase v1.3.4
  [731186ca] RecursiveArrayTools v3.35.0
  [189a3867] Reexport v1.2.2
  [ae029012] Requires v1.3.1
  [ae5879a3] ResettableStacks v1.1.1
  [79098fc4] Rmath v0.8.0
  [47965b36] RootedTrees v2.23.1
  [7e49a35a] RuntimeGeneratedFunctions v0.5.15
  [9dfe8606] SCCNonlinearSolve v1.4.0
  [94e857df] SIMDTypes v0.1.0
  [0bca4576] SciMLBase v2.104.0
  [19f34311] SciMLJacobianOperators v0.1.8
  [c0aeaf25] SciMLOperators v1.4.0
  [431bcebd] SciMLPublic v1.0.0
  [53ae85a6] SciMLStructures v1.7.0
  [7e506255] ScopedValues v1.4.0
  [efcf1570] Setfield v1.1.2
  [727e6d20] SimpleNonlinearSolve v2.7.0
  [699a6c99] SimpleTraits v0.9.4
  [ce78b400] SimpleUnPack v1.1.0
  [a2af1166] SortingAlgorithms v1.2.1
  [0a514795] SparseMatrixColorings v0.4.21
  [276daf66] SpecialFunctions v2.5.1
  [aedffcd0] Static v1.2.0
  [0d7ed370] StaticArrayInterface v1.8.0
  [90137ffa] StaticArrays v1.9.14
  [1e83bf80] StaticArraysCore v1.4.3
  [10745b16] Statistics v1.11.1
  [82ae8749] StatsAPI v1.7.1
  [2913bbd2] StatsBase v0.34.5
  [4c63d2b9] StatsFuns v1.5.0
  [7792a7ef] StrideArraysCore v0.5.7
  [5e0ebb24] Strided v2.3.2
  [4db3bf67] StridedViews v0.4.1
  [892a3eda] StringManipulation v0.4.1
  [09ab397b] StructArrays v0.7.1
  [856f2bd8] StructTypes v1.11.0
  [2efcf032] SymbolicIndexingInterface v0.3.42
  [19f23fe9] SymbolicLimits v0.2.2
  [d1185830] SymbolicUtils v3.29.0
  [0c5d862f] Symbolics v6.45.0
  [3783bdb8] TableTraits v1.0.1
  [bd369af6] Tables v1.12.1
  [ed4db957] TaskLocalValues v0.1.3
  [8ea1fca8] TermInterface v2.0.0
  [f8b46487] TestItemRunner v1.1.0
  [1c621080] TestItems v1.0.0
  [8290d209] ThreadingUtilities v0.5.5
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  [6dad8b7f] TrajectoryIndexingUtils v0.1.0
  [3bb67fe8] TranscodingStreams v0.11.3
  [410a4b4d] Tricks v0.1.10
  [781d530d] TruncatedStacktraces v1.4.0
  [9d95972d] TupleTools v1.6.0
  [5c2747f8] URIs v1.6.1
  [3a884ed6] UnPack v1.0.2
  [1986cc42] Unitful v1.23.1
  [a7c27f48] Unityper v0.1.6
  [c4a57d5a] UnsafeArrays v1.0.8
  [81def892] VersionParsing v1.3.0
  [897b6980] WeakValueDicts v0.1.0
  [ae81ac8f] ASL_jll v0.1.3+0
  [6e34b625] Bzip2_jll v1.0.9+0
  [5ae413db] EarCut_jll v2.2.4+0
  [f5851436] FFTW_jll v3.3.11+0
  [e33a78d0] Hwloc_jll v2.12.1+0
  [1d5cc7b8] IntelOpenMP_jll v2025.2.0+0
  [9cc047cb] Ipopt_jll v300.1400.1701+0
  [d00139f3] METIS_jll v5.1.3+0
  [856f044c] MKL_jll v2025.2.0+0
  [d7ed1dd3] MUMPS_seq_jll v500.800.0+0
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  [4af54fe1] LazyArtifacts v1.11.0
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  [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
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  [44cfe95a] Pkg v1.11.0
  [de0858da] Printf v1.11.0
  [9abbd945] Profile v1.11.0
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  [ea8e919c] SHA v0.7.0
  [9e88b42a] Serialization v1.11.0
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  [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
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  [4536629a] OpenBLAS_jll v0.3.27+1
  [05823500] OpenLibm_jll v0.8.1+4
  [bea87d4a] SuiteSparse_jll v7.7.0+0
  [83775a58] Zlib_jll v1.2.13+1
  [8e850b90] libblastrampoline_jll v5.11.0+0
  [8e850ede] nghttp2_jll v1.59.0+0
  [3f19e933] p7zip_jll v17.4.0+2
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> versioninfo()
Julia Version 1.11.5
Commit 760b2e5b73 (2025-04-14 06:53 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Windows (x86_64-w64-mingw32)
  CPU: 12 × AMD Ryzen 5 3600 6-Core Processor
  WORD_SIZE: 64
  LLVM: libLLVM-16.0.6 (ORCJIT, znver2)
Threads: 1 default, 0 interactive, 1 GC (on 12 virtual cores)
Environment:
  JULIA_EDITOR = code
  JULIA_VSCODE_REPL = 1

Additional context

Add any other context about the problem here.

[mabuni1998]

Similarly, the following also does not work:

using ModelingToolkit
using ModelingToolkit: t_nounits as t, D_nounits as D
@variables begin
    x(..)[1:2] 
end
@parameters u[1:2]
eqs = [D(x(t)[1]) ~ u[1] + x(t)[2],
       D(x(t)[2]) ~ u[2] - x(t)[1]]
@named ode = System(eqs, t)
ode = mtkcompile(ode)
u0map = [x(t)[1] => 1.0, x(t)[2] => 0.0]
tspan = (0.0, 10)
parammap = vcat([u[i] => 0.0 for i in 1:length(u)])
prob = ODEProblem(ode, [u0map; parammap], tspan)

Producing:

ERROR: UndefVarError: `x` not defined in `ModelingToolkit`
Suggestion: check for spelling errors or missing imports.
Stacktrace:
  [1] macro expansion
    @ C:\Users\mabun\.julia\packages\SymbolicUtils\aooYZ\src\code.jl:411 [inlined]
  [2] macro expansion
    @ C:\Users\mabun\.julia\packages\Symbolics\BefTf\src\build_function.jl:366 [inlined]
  [3] macro expansion
    @ C:\Users\mabun\.julia\packages\RuntimeGeneratedFunctions\2SjTC\src\RuntimeGeneratedFunctions.jl:161 [inlined]
  [4] macro expansion
    @ .\none:0 [inlined]
  [5] generated_callfunc
    @ .\none:0 [inlined]
  [6] (::RuntimeGeneratedFunctions.RuntimeGeneratedFunction{…})(::Nothing, ::MTKParameters{…})
    @ RuntimeGeneratedFunctions C:\Users\mabun\.julia\packages\RuntimeGeneratedFunctions\2SjTC\src\RuntimeGeneratedFunctions.jl:148
  [7] macro expansion
    @ C:\Users\mabun\.julia\packages\ModelingToolkit\Ma5jP\src\systems\codegen_utils.jl:0 [inlined]
  [8] _generated_call
    @ C:\Users\mabun\.julia\packages\ModelingToolkit\Ma5jP\src\systems\codegen_utils.jl:353 [inlined]
  [9] GeneratedFunctionWrapper
    @ C:\Users\mabun\.julia\packages\ModelingToolkit\Ma5jP\src\systems\codegen_utils.jl:350 [inlined]
 [10] TimeIndependentObservedFunction
    @ C:\Users\mabun\.julia\packages\SymbolicIndexingInterface\qqDIL\src\state_indexing.jl:142 [inlined]
 [11] AbstractStateGetIndexer
    @ C:\Users\mabun\.julia\packages\SymbolicIndexingInterface\qqDIL\src\value_provider_interface.jl:166 [inlined]
 [12] call_composed
    @ .\operators.jl:1054 [inlined]
 [13] call_composed (repeats 2 times)
    @ .\operators.jl:1053 [inlined]
 [14] (::ComposedFunction{…})(x::NonlinearProblem{…}; kw::@Kwargs{})
    @ Base .\operators.jl:1050
 [15] ComposedFunction
    @ .\operators.jl:1050 [inlined]
 [16] #get_initial_values#9
    @ C:\Users\mabun\.julia\packages\SciMLBase\u2Ue2\src\initialization.jl:301 [inlined]
 [17] get_initial_values
    @ C:\Users\mabun\.julia\packages\SciMLBase\u2Ue2\src\initialization.jl:245 [inlined]
 [18] maybe_eager_initialize_problem(prob::ODEProblem{…}, initialization_data::SciMLBase.OverrideInitData{…}, lazy_initialization::Nothing)
    @ SciMLBase C:\Users\mabun\.julia\packages\SciMLBase\u2Ue2\src\remake.jl:1257
 [19] remake(prob::ODEProblem{…}; f::Missing, u0::Missing, tspan::Missing, p::Missing, kwargs::Missing, interpret_symbolicmap::Bool, build_initializeprob::Type, use_defaults::Bool, lazy_initialization::Nothing, _kwargs::@Kwargs{})
    @ SciMLBase C:\Users\mabun\.julia\packages\SciMLBase\u2Ue2\src\remake.jl:266
 [20] remake(prob::ODEProblem{…})
    @ SciMLBase C:\Users\mabun\.julia\packages\SciMLBase\u2Ue2\src\remake.jl:214
 [21] maybe_codegen_scimlproblem(::Type{…}, T::Type, args::@NamedTuple{…}; kwargs::@Kwargs{})
    @ ModelingToolkit C:\Users\mabun\.julia\packages\ModelingToolkit\Ma5jP\src\systems\problem_utils.jl:1766
 [22] maybe_codegen_scimlproblem(::Type{…}, T::Type, args::@NamedTuple{…})
    @ ModelingToolkit C:\Users\mabun\.julia\packages\ModelingToolkit\Ma5jP\src\systems\problem_utils.jl:1764
 [23] (ODEProblem{…})(sys::System, op::Vector{…}, tspan::Tuple{…}; callback::Nothing, check_length::Bool, eval_expression::Bool, expression::Type, eval_module::Module, check_compatibility::Bool, kwargs::@Kwargs{})
    @ ModelingToolkit C:\Users\mabun\.julia\packages\ModelingToolkit\Ma5jP\src\problems\odeproblem.jl:90
 [24] ODEProblem
    @ C:\Users\mabun\.julia\packages\ModelingToolkit\Ma5jP\src\problems\odeproblem.jl:72 [inlined]
 [25] ODEProblem
    @ .\none:0 [inlined]
 [26] ODEProblem(sys::System, op::Vector{Pair{Num, Float64}}, tspan::Tuple{Float64, Int64})
    @ ModelingToolkit .\none:0
 [27] top-level scope
    @ c:\Users\mabun\OneDrive - Danmarks Tekniske Universitet\Projects\QuantumOptimalControl\scripts\src\mtk_conversion.jl:237
Some type information was truncated. Use `show(err)` to see complete types.

[DhairyaLGandhi]

Is it necessary to declare the variables with x(..)[1:2] and not x(t)[1:2]? Then the equations can be simply

eqs = [D(x[1]) ~ u[1] + x[2],
       D(x[2]) ~ u[2] - x[1]]
u0map = [x[1] => 1.0, x[2] => 0.0]

And then it works

[ChrisRackauckas]

I think it was left open ended to deal with delay differential equations. The thing to use though is the newer EvalAt. Can you check if using EvalAt is sufficient in this case? If so, case closed.

[ChrisRackauckas]

Just make up a tau and show it in use

[DhairyaLGandhi]

tau = 1e-2

eqs = [EvalAt(tau)(D(x))[1] ~ u[1] + EvalAt(tau)(x)[2],
       EvalAt(tau)(D(x))[2] ~ u[2] - EvalAt(tau)(x)[1]]

Not sure if this is the correct way to define the equations in here. But if so, it gives

ERROR: Sym doesn't have a operation or arguments!
Stacktrace:
 [1] error(s::String)
   @ Base ./error.jl:35
 [2] error_sym()
   @ SymbolicUtils ~/.julia/packages/SymbolicUtils/aooYZ/src/types.jl:95
 [3] operation
   @ ~/.julia/packages/SymbolicUtils/aooYZ/src/types.jl:145 [inlined]
 [4] operation(x::Symbolics.CallWithMetadata{SymbolicUtils.FnType{Tuple, Vector{Real}}, Base.ImmutableDict{DataType, Any}})
   @ Symbolics ~/.julia/packages/Symbolics/egyPz/src/variable.jl:299
 [5] diff2term(O::SymbolicUtils.BasicSymbolic{SymbolicUtils.FnType{Tuple, Vector{Real}}}, O_metadata::Nothing)
   @ Symbolics ~/.julia/packages/Symbolics/egyPz/src/utils.jl:138
 [6] diff2term(O::SymbolicUtils.BasicSymbolic{SymbolicUtils.FnType{Tuple, Vector{Real}}})
   @ Symbolics ~/.julia/packages/Symbolics/egyPz/src/utils.jl:111
 [7] default_toterm(x::SymbolicUtils.BasicSymbolic{SymbolicUtils.FnType{Tuple, Vector{Real}}})
   @ ModelingToolkit ~/Downloads/arpa/jsmo/temp/ModelingToolkit.jl/src/variables.jl:223
 [8] (::EvalAt)(x::SymbolicUtils.BasicSymbolic{SymbolicUtils.FnType{Tuple, Vector{Real}}})
   @ ModelingToolkit ~/Downloads/arpa/jsmo/temp/ModelingToolkit.jl/src/variables.jl:651
 [9] top-level scope
   @ ~/Downloads/arpa/jsmo/temp/ModelingToolkit.jl/test/indexing_var_mwe.jl:14

I also tried a version which should be able to solve but gives weird results

@variables begin
    x(..)[1:2] 
end
@parameters u[1:2]

tau = 1e-2

eqs = [EvalAt(t)(D(x(t)))[1] ~ u[1] + EvalAt(tau)(x(t))[2],
       EvalAt(t)(D(x(t)))[2] ~ u[2] - EvalAt(tau)(x(t))[1]]

@named ode = System(eqs, t)
ode = mtkcompile(ode)
u0map = [x(t)[1] => 1.0, x(t)[2] => 0.0]

tspan = (0.0, 10)
parammap = vcat([u[i] => 0.0 for i in 1:length(u)])

julia> prob = ODEProblem(ode, [u0map; parammap], tspan)
ODEProblem with uType Nothing and tType Float64. In-place: true
Initialization status: FULLY_DETERMINED
Non-trivial mass matrix: false
timespan: (0.0, 10.0)
u0: nothing

julia> sol = solve(prob, Tsit5())
retcode: Success
Interpolation: 1st order linear
t: 2-element Vector{Float64}:
  0.0
 10.0
u: 2-element Vector{Vector{Float64}}:
 []
 []

Trying to use various versions of D(x) or EvalAt(t/tau)(x) ie without x(t) as the symbol failed the solve with various versions of not being able to find the symbol in the system (which makes sense in some cases since the genned symbol is x*

ERROR: UndefVarError: `x` not defined
Stacktrace:
  [1] macro expansion
    @ ~/.julia/packages/SymbolicUtils/aooYZ/src/code.jl:411 [inlined]
  [2] macro expansion
    @ ~/.julia/packages/Symbolics/egyPz/src/build_function.jl:368 [inlined]
  [3] macro expansion
    @ ~/.julia/packages/RuntimeGeneratedFunctions/2SjTC/src/RuntimeGeneratedFunctions.jl:161 [inlined]
  [4] macro expansion
    @ ./none:0 [inlined]
  [5] generated_callfunc
    @ ./none:0 [inlined]
  [6] (::RuntimeGeneratedFunctions.RuntimeGeneratedFunction{…})(::Vector{…}, ::Nothing, ::MTKParameters{…})
    @ RuntimeGeneratedFunctions ~/.julia/packages/RuntimeGeneratedFunctions/2SjTC/src/RuntimeGeneratedFunctions.jl:148
  [7] macro expansion
    @ ~/Downloads/arpa/jsmo/temp/ModelingToolkit.jl/src/systems/codegen_utils.jl:0 [inlined]
  [8] _generated_call
    @ ~/Downloads/arpa/jsmo/temp/ModelingToolkit.jl/src/systems/codegen_utils.jl:353 [inlined]
  [9] GeneratedFunctionWrapper
    @ ~/Downloads/arpa/jsmo/temp/ModelingToolkit.jl/src/systems/codegen_utils.jl:350 [inlined]
 [10] NonlinearFunction
    @ ~/.julia/packages/SciMLBase/dld4W/src/scimlfunctions.jl:2604 [inlined]
 [11] #build_null_solution#42
    @ ~/.julia/packages/DiffEqBase/7xkMr/src/solve.jl:771 [inlined]
 [12] build_null_solution
    @ ~/.julia/packages/DiffEqBase/7xkMr/src/solve.jl:763 [inlined]
 [13] #solve_call#36
    @ ~/.julia/packages/DiffEqBase/7xkMr/src/solve.jl:649 [inlined]
 [14] solve_call
    @ ~/.julia/packages/DiffEqBase/7xkMr/src/solve.jl:614 [inlined]
 [15] solve_up(::NonlinearLeastSquaresProblem{…}, ::Nothing, ::Nothing, ::MTKParameters{…}; originator::SciMLBase.ChainRulesOriginator, kwargs::@Kwargs{})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/7xkMr/src/solve.jl:1195
 [16] solve_up
    @ ~/.julia/packages/DiffEqBase/7xkMr/src/solve.jl:1188 [inlined]
 [17] #solve#43
    @ ~/.julia/packages/DiffEqBase/7xkMr/src/solve.jl:1083 [inlined]
 [18] solve
    @ ~/.julia/packages/DiffEqBase/7xkMr/src/solve.jl:1073 [inlined]
 [19] hack_null_solution_init(prob::ODEProblem{…})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/7xkMr/src/solve.jl:706
 [20] build_null_solution(prob::ODEProblem{…}, args::Tsit5{…}; saveat::Tuple{}, save_everystep::Bool, save_on::Bool, save_start::Bool, save_end::Bool, kwargs::@Kwargs{})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/7xkMr/src/solve.jl:743
 [21] build_null_solution
    @ ~/.julia/packages/DiffEqBase/7xkMr/src/solve.jl:717 [inlined]
 [22] #solve_call#36
    @ ~/.julia/packages/DiffEqBase/7xkMr/src/solve.jl:649 [inlined]
 [23] solve_call
    @ ~/.julia/packages/DiffEqBase/7xkMr/src/solve.jl:614 [inlined]
 [24] solve_up(prob::SciMLBase.AbstractDEProblem, sensealg::Any, u0::Any, p::Any, args::Vararg{…}; originator::Any, kwargs...)
    @ DiffEqBase ~/.julia/packages/DiffEqBase/7xkMr/src/solve.jl:1211 [inlined]
 [25] solve_up
    @ ~/.julia/packages/DiffEqBase/7xkMr/src/solve.jl:1188 [inlined]
 [26] solve(prob::ODEProblem{…}, args::Tsit5{…}; sensealg::Nothing, u0::Nothing, p::Nothing, wrap::Val{…}, kwargs::@Kwargs{})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/7xkMr/src/solve.jl:1083
 [27] solve(prob::ODEProblem{…}, args::Tsit5{…})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/7xkMr/src/solve.jl:1073
 [28] top-level scope
    @ ~/Downloads/arpa/jsmo/temp/ModelingToolkit.jl/test/indexing_var_mwe.jl:30
Some type information was truncated. Use `show(err)` to see complete types.

[ChrisRackauckas]

The normal case would be t-tau.

[DhairyaLGandhi]

The docs said that I can use Symbolics and Floats, but this gives similar results

eqs = [EvalAt(t-tau)(D(x(t)))[1] ~ u[1] + EvalAt(t-tau)(x(t))[2],
       EvalAt(t-tau)(D(x(t)))[2] ~ u[2] - EvalAt(t-tau)(x(t))[1]]

@named ode = System(eqs, t)
ode = mtkcompile(ode)
u0map = [x(t)[1] => 1.0, x(t)[2] => 0.0]
tspan = (0.0, 10)
parammap = vcat([u[i] => 0.0 for i in 1:length(u)])

julia> prob = ODEProblem(ode, [u0map; parammap], tspan)
ODEProblem with uType Nothing and tType Float64. In-place: true
Initialization status: FULLY_DETERMINED
Non-trivial mass matrix: false
timespan: (0.0, 10.0)
u0: nothing

julia> sol = solve(prob, Tsit5())
retcode: Success
Interpolation: 1st order linear
t: 2-element Vector{Float64}:
  0.0
 10.0
u: 2-element Vector{Vector{Float64}}:
 []
 []

[ChrisRackauckas]

I'm not sure as a model it makes much sense though?

@variables x(t)[1:2] 
@parameters u[1:2]

tau = 1e-2
eqs = [D(x[1]) ~ u[1] + EvalAt(t-tau)(x[2]),
           D(x[2]) ~ u[2] - EvalAt(t-tau)(x[1])]

is what I presume the model would be.

[ChrisRackauckas]

Anyways, the issue is that when specifying dynamic optimization, EvalAt is probably a better way to do it, so we should make sure the docs focus on this. Though we could leave this open because the wildcard form is technically correct and should get fixed.

[DhairyaLGandhi]

I tried something similar and that resulted in a "symbol not found" error. Actually, the version you had also gives

eqs = [D(x(t))[1] ~ u[1] + EvalAt(t-tau)(x(t))[2],
       D(x(t))[2] ~ u[2] - EvalAt(t-tau)(x(t))[1]]

@named ode = System(eqs, t)
ode = mtkcompile(ode)
u0map = [x(t)[1] => 1.0, x(t)[2] => 0.0]
tspan = (0.0, 10)
parammap = vcat([u[i] => 0.0 for i in 1:length(u)])

julia> prob = ODEProblem(ode, [u0map; parammap], tspan)
ERROR: UndefVarError: `x` not defined
Stacktrace:
  [1] macro expansion
    @ ~/.julia/packages/SymbolicUtils/aooYZ/src/code.jl:411 [inlined]
  [2] macro expansion
    @ ~/.julia/packages/Symbolics/egyPz/src/build_function.jl:366 [inlined]
  [3] macro expansion
    @ ~/.julia/packages/RuntimeGeneratedFunctions/2SjTC/src/RuntimeGeneratedFunctions.jl:161 [inlined]
  [4] macro expansion
    @ ./none:0 [inlined]
  [5] generated_callfunc
    @ ./none:0 [inlined]
  [6] (::RuntimeGeneratedFunctions.RuntimeGeneratedFunction{…})(::Nothing, ::MTKParameters{…})
    @ RuntimeGeneratedFunctions ~/.julia/packages/RuntimeGeneratedFunctions/2SjTC/src/RuntimeGeneratedFunctions.jl:148
  [7] macro expansion
    @ ~/Downloads/arpa/jsmo/temp/ModelingToolkit.jl/src/systems/codegen_utils.jl:0 [inlined]
  [8] _generated_call
    @ ~/Downloads/arpa/jsmo/temp/ModelingToolkit.jl/src/systems/codegen_utils.jl:353 [inlined]
  [9] GeneratedFunctionWrapper
    @ ~/Downloads/arpa/jsmo/temp/ModelingToolkit.jl/src/systems/codegen_utils.jl:350 [inlined]
 [10] TimeIndependentObservedFunction
    @ ~/.julia/packages/SymbolicIndexingInterface/qqDIL/src/state_indexing.jl:142 [inlined]
 [11] AbstractStateGetIndexer
    @ ~/.julia/packages/SymbolicIndexingInterface/qqDIL/src/value_provider_interface.jl:166 [inlined]
 [12] call_composed
    @ ./operators.jl:1045 [inlined]
 [13] call_composed (repeats 2 times)
    @ ./operators.jl:1044 [inlined]
 [14] (::ComposedFunction{…})(x::NonlinearProblem{…}; kw::@Kwargs{})
    @ Base ./operators.jl:1041
 [15] ComposedFunction
    @ ./operators.jl:1041 [inlined]
 [16] get_initial_values(prob::ODEProblem{…}, valp::ODEProblem{…}, f::Function, alg::SciMLBase.OverrideInit{…}, iip::Val{…}; nlsolve_alg::Nothing, abstol::Nothing, reltol::Nothing, kwargs::@Kwargs{})
    @ SciMLBase ~/.julia/packages/SciMLBase/dld4W/src/initialization.jl:298 [inlined]
 [17] get_initial_values
    @ ~/.julia/packages/SciMLBase/dld4W/src/initialization.jl:245 [inlined]
 [18] maybe_eager_initialize_problem(prob::ODEProblem{…}, initialization_data::SciMLBase.OverrideInitData{…}, lazy_initialization::Nothing)
    @ SciMLBase ~/.julia/packages/SciMLBase/dld4W/src/remake.jl:1257
 [19] remake(prob::ODEProblem{…}; f::Missing, u0::Missing, tspan::Missing, p::Missing, kwargs::Missing, interpret_symbolicmap::Bool, build_initializeprob::Type, use_defaults::Bool, lazy_initialization::Nothing, _kwargs::@Kwargs{})
    @ SciMLBase ~/.julia/packages/SciMLBase/dld4W/src/remake.jl:266
 [20] remake(prob::ODEProblem{…})
    @ SciMLBase ~/.julia/packages/SciMLBase/dld4W/src/remake.jl:214
 [21] maybe_codegen_scimlproblem(::Type{…}, T::Type, args::@NamedTuple{…}; kwargs::@Kwargs{})
    @ ModelingToolkit ~/Downloads/arpa/jsmo/temp/ModelingToolkit.jl/src/systems/problem_utils.jl:1766
 [22] maybe_codegen_scimlproblem(::Type{…}, T::Type, args::@NamedTuple{…})
    @ ModelingToolkit ~/Downloads/arpa/jsmo/temp/ModelingToolkit.jl/src/systems/problem_utils.jl:1764
 [23] (ODEProblem{…})(sys::System, op::Vector{…}, tspan::Tuple{…}; callback::Nothing, check_length::Bool, eval_expression::Bool, expression::Type, eval_module::Module, check_compatibility::Bool, kwargs::@Kwargs{})
    @ ModelingToolkit ~/Downloads/arpa/jsmo/temp/ModelingToolkit.jl/src/problems/odeproblem.jl:90
 [24] ODEProblem
    @ ModelingToolkit ~/Downloads/arpa/jsmo/temp/ModelingToolkit.jl/src/problems/odeproblem.jl:72 [inlined]
 [25] ODEProblem
    @ ModelingToolkit ./none:0 [inlined]
 [26] ODEProblem(sys::System, op::Vector{Pair{Num, Float64}}, tspan::Tuple{Float64, Int64})
    @ ModelingToolkit ./none:0
 [27] top-level scope
    @ ~/Downloads/arpa/jsmo/temp/ModelingToolkit.jl/test/indexing_var_mwe.jl:29
Some type information was truncated. Use `show(err)` to see complete types.

[ChrisRackauckas]

that's using wildcards? I'm not using wildcards on x.

[DhairyaLGandhi]

@variables begin
    x(t)[1:2] 
end
@parameters u[1:2]

tau = 1e-2

eqs = [D(x[1]) ~ u[1] + EvalAt(t-tau)(x[2]),
       D(x[2]) ~ u[2] - EvalAt(t-tau)(x[1])]

julia> @named ode = System(eqs, t)
ERROR: MethodError: no method matching hasmetadata(::Symbolics.Arr{Num, 1}, ::Type{Symbolics.VariableSource})

Closest candidates are:
  hasmetadata(::Num, ::Any)
   @ Symbolics ~/.julia/packages/Symbolics/egyPz/src/Symbolics.jl:194
  hasmetadata(::Complex{Num}, ::Any)
   @ Symbolics ~/.julia/packages/Symbolics/egyPz/src/Symbolics.jl:194
  hasmetadata(::ModelingToolkit.AbstractSystem, ::DataType)
   @ ModelingToolkit ~/Downloads/arpa/jsmo/temp/ModelingToolkit.jl/src/systems/system.jl:814
  ...

Stacktrace:
  [1] isvariable(x::SymbolicUtils.BasicSymbolic{Num})
    @ ModelingToolkit ~/Downloads/arpa/jsmo/temp/ModelingToolkit.jl/src/utils.jl:358
  [2] vars!(vars::Set{Any}, O::SymbolicUtils.BasicSymbolic{Num}; op::Type)
    @ ModelingToolkit ~/Downloads/arpa/jsmo/temp/ModelingToolkit.jl/src/utils.jl:395
  [3] vars!(vars::Set{Any}, O::SymbolicUtils.BasicSymbolic{Num}; op::Type)
    @ ModelingToolkit ~/Downloads/arpa/jsmo/temp/ModelingToolkit.jl/src/utils.jl:433
  [4] vars!
    @ ~/Downloads/arpa/jsmo/temp/ModelingToolkit.jl/src/utils.jl:394 [inlined]
  [5] (::ModelingToolkit.var"#48#49"{Union})(x::Set{Any}, y::Num)
    @ ModelingToolkit ~/Downloads/arpa/jsmo/temp/ModelingToolkit.jl/src/utils.jl:385 [inlined]
  [6] BottomRF
    @ ./reduce.jl:86 [inlined]
  [7] _foldl_impl(op::Base.BottomRF{…}, init::Set{…}, itr::Vector{…})
    @ Base ./reduce.jl:58
  [8] foldl_impl
    @ Base ./reduce.jl:48 [inlined]
  [9] mapfoldl_impl(f::typeof(identity), op::ModelingToolkit.var"#48#49"{…}, nt::Set{…}, itr::Vector{…})
    @ Base ./reduce.jl:44
 [10] mapfoldl(f::Function, op::Function, itr::Vector{SymbolicUtils.BasicSymbolic{Num}}; init::Set{Any})
    @ Base ./reduce.jl:175
 [11] mapfoldl
    @ ./reduce.jl:175 [inlined]
 [12] foldl
    @ ./reduce.jl:198 [inlined]
 [13] #vars#47
    @ ~/Downloads/arpa/jsmo/temp/ModelingToolkit.jl/src/utils.jl:385 [inlined]
 [14] vars
    @ ~/Downloads/arpa/jsmo/temp/ModelingToolkit.jl/src/utils.jl:383 [inlined]
 [15] vars(exprs::SymbolicUtils.BasicSymbolic{Num}; op::Type)
    @ ModelingToolkit ~/Downloads/arpa/jsmo/temp/ModelingToolkit.jl/src/utils.jl:379
 [16] vars
    @ ~/Downloads/arpa/jsmo/temp/ModelingToolkit.jl/src/utils.jl:378 [inlined]
 [17] collect_vars!(unknowns::OrderedCollections.OrderedSet{…}, parameters::Set{…}, expr::SymbolicUtils.BasicSymbolic{…}, iv::Num; depth::Int64, op::Type)
    @ ModelingToolkit ~/Downloads/arpa/jsmo/temp/ModelingToolkit.jl/src/utils.jl:596
 [18] collect_vars!(unknowns::OrderedCollections.OrderedSet{…}, parameters::Set{…}, eq::Equation, iv::Num; depth::Int64, op::Type)
    @ ModelingToolkit ~/Downloads/arpa/jsmo/temp/ModelingToolkit.jl/src/utils.jl:620
 [19] collect_vars!
    @ ModelingToolkit ~/Downloads/arpa/jsmo/temp/ModelingToolkit.jl/src/utils.jl:617 [inlined]
 [20] System(eqs::Vector{Equation}, iv::Num; kwargs::@Kwargs{name::Symbol})
    @ ModelingToolkit ~/Downloads/arpa/jsmo/temp/ModelingToolkit.jl/src/systems/system.jl:454
 [21] top-level scope
    @ ~/Downloads/arpa/jsmo/temp/ModelingToolkit.jl/src/systems/abstractsystem.jl:2123
Some type information was truncated. Use `show(err)` to see complete types.

[ChrisRackauckas]

yeah that's not good.