structural_simplify changes the name of the variables from discretized PDEs in the observed equations ( X[n](t) -> var"X(t)[n]_t" )

[GHE-HS]

Describe the bug 🐞

When structural_simplify ing a system, the names of many observed variables (ie. variable X(t)) become var"Xˍt" in an equation describing an observed state, messing up with everything downstream.

Expected behavior

The variable should not change name after applying structural_simplify.

Minimal Reproducible Example 👇

Unfortunately my code is quite complex, so simplifying it to make a MWE would take me a time I don't have right now, I mostly wanted to report the issue. I will provide one later if time allows.

Environment:

• Output of using Pkg; Pkg.status()

[9901752a] Ai4EComponentLib v0.10.2 `https://github.com/ai4energy/Ai4EComponentLib.jl#main`
  [c9ce4bd3] ArchGDAL v0.10.1
  [6e4b80f9] BenchmarkTools v1.3.2
  [a134a8b2] BlackBoxOptim v0.6.2
⌃ [336ed68f] CSV v0.10.10
⌃ [35d6a980] ColorSchemes v3.21.0
  [5ae59095] Colors v0.12.10
⌃ [3abffc1c] ControlSystemIdentification v2.5.3
⌃ [a6e380b2] ControlSystems v1.7.2
⌃ [aaaaaaaa] ControlSystemsBase v1.4.2
⌃ [687d7614] ControlSystemsMTK v0.1.12
  [e084ae63] CoolProp v0.1.0
⌃ [a93c6f00] DataFrames v1.5.0
⌃ [82cc6244] DataInterpolations v4.0.1
⌃ [0c46a032] DifferentialEquations v7.7.0
⌃ [31c24e10] Distributions v0.25.88
⌅ [5b8099bc] DomainSets v0.6.6
⌃ [634d3b9d] DrWatson v2.12.4
⌃ [b18b359b] FourierTools v0.4.1
⌃ [5c1252a2] GeometryBasics v0.4.7
⌅ [cd3eb016] HTTP v0.9.17
  [615f187c] IfElse v0.1.1
  [a98d9a8b] Interpolations v0.14.7
⌅ [d1acc4aa] IntervalArithmetic v0.20.9
  [d2bf35a9] IntervalRootFinding v0.5.11
  [682c06a0] JSON v0.21.4
⌃ [0f8b85d8] JSON3 v1.12.0
  [b9914132] JSONTables v1.0.3
⌅ [ee78f7c6] Makie v0.19.6
⌃ [94925ecb] MethodOfLines v0.9.2
⌃ [961ee093] ModelingToolkit v8.55.1
⌃ [23d639d0] ModelingToolkitDesigner v0.3.0
⌅ [16a59e39] ModelingToolkitStandardLibrary v1.15.0
⌃ [0987c9cc] MonteCarloMeasurements v1.1.4
⌃ [1dea7af3] OrdinaryDiffEq v6.50.0
  [ccf2f8ad] PlotThemes v3.1.0
  [58dd65bb] Plotly v0.4.1
  [91a5bcdd] Plots v1.39.0
⌅ [f27b6e38] Polynomials v3.2.10
⌃ [1fd47b50] QuadGK v2.8.2
⌃ [f2b01f46] Roots v2.0.13
  [3f865c0f] ScatteredInterpolation v0.3.6
⌃ [276daf66] SpecialFunctions v2.2.0
⌃ [f3b207a7] StatsPlots v0.15.5
  [fd094767] Suppressor v0.2.6
⌃ [0c5d862f] Symbolics v5.3.1
⌃ [1986cc42] Unitful v1.13.1
  [3351c21f] CoolProp_jll v6.5.0+0
  [ade2ca70] Dates
  [8f399da3] Libdl

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

[47edcb42] ADTypes v0.2.4
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  [79e6a3ab] Adapt v3.6.2
  [9901752a] Ai4EComponentLib v0.10.2 `https://github.com/ai4energy/Ai4EComponentLib.jl#main`
  [27a7e980] Animations v0.4.1
  [c9ce4bd3] ArchGDAL v0.10.1
  [dce04be8] ArgCheck v2.3.0
  [ec485272] ArnoldiMethod v0.2.0
  [7d9fca2a] Arpack v0.5.4
  [4fba245c] ArrayInterface v7.4.11
  [30b0a656] ArrayInterfaceCore v0.1.29
⌃ [4c555306] ArrayLayouts v0.8.18
  [bf4720bc] AssetRegistry v0.1.0
⌅ [67c07d97] Automa v0.8.4
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⌅ [aae01518] BandedMatrices v0.17.18
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⌃ [0c46a032] DifferentialEquations v7.7.0
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⌃ [31c24e10] Distributions v0.25.88
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  [d5829a12] TriangularSolve v0.1.19
  [410a4b4d] Tricks v0.1.8
  [981d1d27] TriplotBase v0.1.0
  [781d530d] TruncatedStacktraces v1.4.0
  [9d95972d] TupleTools v1.4.3
  [30578b45] URIParser v0.4.1
  [5c2747f8] URIs v1.5.1
  [3a884ed6] UnPack v1.0.2
  [1cfade01] UnicodeFun v0.4.1
⌃ [1986cc42] Unitful v1.13.1
  [45397f5d] UnitfulLatexify v1.6.3
  [a7c27f48] Unityper v0.1.5
  [41fe7b60] Unzip v0.2.0
  [3d5dd08c] VectorizationBase v0.21.64
  [19fa3120] VertexSafeGraphs v0.2.0
  [ea10d353] WeakRefStrings v1.4.2
  [0f1e0344] WebIO v0.8.21
⌃ [104b5d7c] WebSockets v1.5.9
  [cc8bc4a8] Widgets v0.6.6
  [efce3f68] WoodburyMatrices v0.5.5
  [76eceee3] WorkerUtilities v1.6.1
  [700de1a5] ZygoteRules v0.2.3
⌅ [68821587] Arpack_jll v3.5.1+1
  [8ce61222] Arrow_jll v10.0.0+1
  [6e34b625] Bzip2_jll v1.0.8+0
  [4e9b3aee] CRlibm_jll v1.0.1+0
  [83423d85] Cairo_jll v1.16.1+1
  [3351c21f] CoolProp_jll v6.5.0+0
  [5ae413db] EarCut_jll v2.2.4+0
  [2702e6a9] EpollShim_jll v0.0.20230411+0
  [2e619515] Expat_jll v2.5.0+0
⌃ [b22a6f82] FFMPEG_jll v4.4.2+2
  [f5851436] FFTW_jll v3.3.10+0
  [a3f928ae] Fontconfig_jll v2.13.93+0
  [d7e528f0] FreeType2_jll v2.13.1+0
  [559328eb] FriBidi_jll v1.0.10+0
⌃ [a7073274] GDAL_jll v301.600.200+0
⌅ [d604d12d] GEOS_jll v3.11.2+0
  [0656b61e] GLFW_jll v3.3.8+0
⌅ [d2c73de3] GR_jll v0.72.8+0
  [78b55507] Gettext_jll v0.21.0+0
  [7746bdde] Glib_jll v2.76.5+0
  [3b182d85] Graphite2_jll v1.3.14+0
⌅ [0234f1f7] HDF5_jll v1.12.2+2
  [2e76f6c2] HarfBuzz_jll v2.8.1+1
  [905a6f67] Imath_jll v3.1.7+0
  [1d5cc7b8] IntelOpenMP_jll v2023.2.0+0
  [aacddb02] JpegTurbo_jll v2.1.91+0
  [f7e6163d] Kaleido_jll v0.2.1+0
  [b39eb1a6] Kerberos_krb5_jll v1.19.3+0
  [c1c5ebd0] LAME_jll v3.100.1+0
  [88015f11] LERC_jll v3.0.0+1
⌅ [dad2f222] LLVMExtra_jll v0.0.23+0
  [1d63c593] LLVMOpenMP_jll v15.0.4+0
  [dd4b983a] LZO_jll v2.10.1+0
⌃ [08be9ffa] LibPQ_jll v14.3.0+1
⌅ [e9f186c6] Libffi_jll v3.2.2+1
  [d4300ac3] Libgcrypt_jll v1.8.7+0
  [7e76a0d4] Libglvnd_jll v1.6.0+0
  [7add5ba3] Libgpg_error_jll v1.42.0+0
  [94ce4f54] Libiconv_jll v1.17.0+0
  [4b2f31a3] Libmount_jll v2.35.0+0
⌅ [89763e89] Libtiff_jll v4.4.0+0
  [38a345b3] Libuuid_jll v2.36.0+0
⌃ [d3a379c0] LittleCMS_jll v2.12.0+0
  [5ced341a] Lz4_jll v1.9.4+0
  [856f044c] MKL_jll v2023.2.0+0
⌃ [7243133f] NetCDF_jll v400.902.206+0
  [e7412a2a] Ogg_jll v1.3.5+1
  [18a262bb] OpenEXR_jll v3.1.4+0
⌃ [643b3616] OpenJpeg_jll v2.4.0+0
⌅ [458c3c95] OpenSSL_jll v1.1.23+0
  [efe28fd5] OpenSpecFun_jll v0.5.5+0
  [91d4177d] Opus_jll v1.3.2+0
⌅ [58948b4f] PROJ_jll v900.100.0+0
  [36c8627f] Pango_jll v1.50.14+0
  [30392449] Pixman_jll v0.42.2+0
  [460c41e3] QhullMiniWrapper_jll v1.0.0+1
⌅ [784f63db] Qhull_jll v8.0.1003+0
  [ea2cea3b] Qt5Base_jll v5.15.3+2
  [f50d1b31] Rmath_jll v0.4.0+0
  [76ed43ae] SQLite_jll v3.43.0+0
⌅ [fb77eaff] Sundials_jll v5.2.1+0
⌅ [e0b8ae26] Thrift_jll v0.16.0+0
  [a2964d1f] Wayland_jll v1.21.0+1
  [2381bf8a] Wayland_protocols_jll v1.25.0+0
  [02c8fc9c] XML2_jll v2.11.5+0
  [aed1982a] XSLT_jll v1.1.34+0
  [4f6342f7] Xorg_libX11_jll v1.8.6+0
  [0c0b7dd1] Xorg_libXau_jll v1.0.11+0
  [935fb764] Xorg_libXcursor_jll v1.2.0+4
  [a3789734] Xorg_libXdmcp_jll v1.1.4+0
  [1082639a] Xorg_libXext_jll v1.3.4+4
  [d091e8ba] Xorg_libXfixes_jll v5.0.3+4
  [a51aa0fd] Xorg_libXi_jll v1.7.10+4
  [d1454406] Xorg_libXinerama_jll v1.1.4+4
  [ec84b674] Xorg_libXrandr_jll v1.5.2+4
  [ea2f1a96] Xorg_libXrender_jll v0.9.10+4
  [14d82f49] Xorg_libpthread_stubs_jll v0.1.1+0
  [c7cfdc94] Xorg_libxcb_jll v1.15.0+0
  [cc61e674] Xorg_libxkbfile_jll v1.1.2+0
  [12413925] Xorg_xcb_util_image_jll v0.4.0+1
  [2def613f] Xorg_xcb_util_jll v0.4.0+1
  [975044d2] Xorg_xcb_util_keysyms_jll v0.4.0+1
  [0d47668e] Xorg_xcb_util_renderutil_jll v0.3.9+1
  [c22f9ab0] Xorg_xcb_util_wm_jll v0.4.1+1
  [35661453] Xorg_xkbcomp_jll v1.4.6+0
  [33bec58e] Xorg_xkeyboard_config_jll v2.39.0+0
  [c5fb5394] Xorg_xtrans_jll v1.5.0+0
  [3161d3a3] Zstd_jll v1.5.5+0
⌅ [28df3c45] boost_jll v1.76.0+1
  [214eeab7] fzf_jll v0.35.1+0
  [9a68df92] isoband_jll v0.2.3+0
  [a4ae2306] libaom_jll v3.4.0+0
  [0ac62f75] libass_jll v0.15.1+0
  [f638f0a6] libfdk_aac_jll v2.0.2+0
⌃ [06c338fa] libgeotiff_jll v100.700.100+0
  [b53b4c65] libpng_jll v1.6.38+0
  [075b6546] libsixel_jll v1.10.3+0
  [f27f6e37] libvorbis_jll v1.3.7+1
  [fe1e1685] snappy_jll v1.1.9+1
  [1270edf5] x264_jll v2021.5.5+0
  [dfaa095f] x265_jll v3.5.0+0
  [d8fb68d0] xkbcommon_jll v1.4.1+1
  [0dad84c5] ArgTools v1.1.1
  [56f22d72] Artifacts
  [2a0f44e3] Base64
  [8bf52ea8] CRC32c
  [ade2ca70] Dates
  [8ba89e20] Distributed
  [f43a241f] Downloads v1.6.0
  [7b1f6079] FileWatching
  [9fa8497b] Future
  [b77e0a4c] InteractiveUtils
  [4af54fe1] LazyArtifacts
  [b27032c2] LibCURL v0.6.3
  [76f85450] LibGit2
  [8f399da3] Libdl
  [37e2e46d] LinearAlgebra
  [56ddb016] Logging
  [d6f4376e] Markdown
  [a63ad114] Mmap
  [ca575930] NetworkOptions v1.2.0
  [44cfe95a] Pkg v1.9.0
  [de0858da] Printf
  [9abbd945] Profile
  [3fa0cd96] REPL
  [9a3f8284] Random
  [ea8e919c] SHA v0.7.0
  [9e88b42a] Serialization
  [1a1011a3] SharedArrays
  [6462fe0b] Sockets
  [2f01184e] SparseArrays
  [10745b16] Statistics v1.9.0
  [4607b0f0] SuiteSparse
  [fa267f1f] TOML v1.0.3
  [a4e569a6] Tar v1.10.0
  [8dfed614] Test
  [cf7118a7] UUIDs
  [4ec0a83e] Unicode
  [e66e0078] CompilerSupportLibraries_jll v1.0.2+0
  [deac9b47] LibCURL_jll v7.84.0+0
  [29816b5a] LibSSH2_jll v1.10.2+0
  [c8ffd9c3] MbedTLS_jll v2.28.2+0
  [14a3606d] MozillaCACerts_jll v2022.10.11
  [4536629a] OpenBLAS_jll v0.3.21+4
  [05823500] OpenLibm_jll v0.8.1+0
  [efcefdf7] PCRE2_jll v10.42.0+0
  [bea87d4a] SuiteSparse_jll v5.10.1+6
  [83775a58] Zlib_jll v1.2.13+0
  [8e850b90] libblastrampoline_jll v5.7.0+0
  [8e850ede] nghttp2_jll v1.48.0+0
  [3f19e933] p7zip_jll v17.4.0+0

• Output of versioninfo()

Julia Version 1.9.0
Commit 8e63055292 (2023-05-07 11:25 UTC)
Platform Info:
  OS: Windows (x86_64-w64-mingw32)
  CPU: 8 × Intel(R) Core(TM) i7-8665U CPU @ 1.90GHz
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-14.0.6 (ORCJIT, skylake)
  Threads: 1 on 8 virtual cores
Environment:
  JULIA_EDITOR = code
  JULIA_NUM_THREADS =

Additional context

What I am doing in my code is to symbolically discretize a PDE system with MethodOfLines and then tinkering with the ODESystem that comes out of it then simplyfying and finally solving it with MTK. I believe this problem only happens with the discretized variables (written X(t)[n]).

[GHE-HS]

I think I found the piece of code that is responsible for this transformation but fixing it is beyond what I can do I'm afraid:
In model_parsing.jl, l 73-77:

if ext[] === nothing
    push!(exprs.args, :(var"#___sys___" = $sys))
else
    push!(exprs.args, :(var"#___sys___" = $extend($sys, $(ext[]))))
end

Any advice will be appreciated!

[ChrisRackauckas]

the names of many observed variables (ie. variable X(t)) become var"Xˍt" in an equation describing an observed state

That's not the same variable. The latter is the dummy derivative of the first variable