BoundsError in Discretizing Interface Domains with Different Point Counts

[canbozdogan]

When attempting to discretize two domains in MethodOfLines.jl with different point counts (50 for the first domain and 5 for the second), I encounter a BoundsError. The error occurs specifically when the second domain (substrate domain) has fewer points than the first domain (film domain). This limitation impacts the flexibility of the domain discretization in my model.

Discretizing domains with different point counts is crucial for accurately modeling systems with varying spatial resolution requirements and interfaces.

The issue arises in the following minimal working example:

using DifferentialEquations
using ModelingToolkit, MethodOfLines, DomainSets

@variables Id(..) T(..) T_sub(..) cumuSum(..) 

@parameters t z z_sub
@parameters ϵ ϵ_PIG c_PIG β κ κ_sub rho_cp_M rho_cp_sub I₀ delH

Dt = Differential(t)
Dz = Differential(z)
Dzz = Differential(z)^2
Dz_sub = Differential(z_sub)
Dzz_sub = Differential(z_sub)^2

param_list = [
    I₀   => 6000.0,
    κ                   => 0.292,    
    κ_sub               => 50.0,
    rho_cp_M            => 1.919e6,        
    rho_cp_sub          => 1.9e6,
    delH                => -54800.0,
    β                   => 2,
    c_PIG                => 0.0,         
    ϵ                   => 120.982128,        
    ϵ_PIG               => 1.39579974e7,
]

t_min = z_min = 0.0
z_max = 1.2e-5
t_max = 30.0
z_sub_min = 1.2e-5 
z_sub_max = 1.2e-5  +  0.0002

domains = [z ∈ Interval(z_min, z_max),
z_sub ∈ Interval(z_max, z_sub_max),
t ∈ Interval(t_min, t_max)]

Iz = Integral(z in DomainSets.ClosedInterval(z_min, z))

eq  = [ 

cumuSum(t, z) ~ Iz(Id(t,z)),

Dt(Id(t,z))     ~ 0,

Dt(T(t,z))      ~ ((1/rho_cp_M)*(κ*Dzz(T(t,z)) - delH*β + I₀*exp(- ϵ*cumuSum(t, z) -  ϵ_PIG*c_PIG*z)*(ϵ*Id(t,z) + c_PIG*ϵ_PIG))),

Dt(T_sub(t,z_sub))  ~ (κ_sub/rho_cp_sub)*Dzz_sub(T_sub(t,z_sub)),] 

bcs = [

    Id(0,z) ~ 100,    
    Dz(Id(t,0)) ~ 0.0,      
    Dz(Id(t,z_max)) ~ 0.0, 

    T(0,z) ~ 298.0,          
    T_sub(0,z_sub) ~ 298,

    Dz(T(t,0)) ~ 0.0,      

    T(t,z_max) ~ T_sub(t,z_sub_min),               
    κ*Dz(T(t,z_max)) ~ κ_sub*Dz_sub(T_sub(t,z_sub_min)),    

    T_sub(t,z_sub_max) ~ 298,
]   

@named pdesys = PDESystem(eq,
    bcs,
    domains,
    [z,z_sub,t],
    [Id(t,z),T(t,z),T_sub(t,z_sub),cumuSum(t, z)],param_list
)

discretization = MOLFiniteDifference([z=>50,z_sub=>5],t,approx_order=2);
prob = discretize(pdesys,discretization)

Error & Stacktrace ⚠️

ERROR: BoundsError: attempt to access 5-element Vector{SymbolicUtils.BasicSymbolic{Real}} at index [50]
Stacktrace:
  [1] getindex
    @ .\essentials.jl:13 [inlined]
  [2] getindex(::Vector{SymbolicUtils.BasicSymbolic{Real}}, ::CartesianIndex{1})
    @ Base .\multidimensional.jl:668
  [3] (::MethodOfLines.var"#48#49"{MethodOfLines.DiscreteSpace{2, 4, MethodOfLines.CenterAlignedGrid}, CartesianIndex{1}, Dict{SymbolicUtils.BasicSymbolic{Real}, Int64}})(u::SymbolicUtils.BasicSymbolic{Real})
    @ MethodOfLines .\none:0
  [4] iterate
    @ .\generator.jl:47 [inlined]
  [5] collect_to!(dest::Vector{Pair{SymbolicUtils.BasicSymbolic{Real}, SymbolicUtils.BasicSymbolic{Real}}}, itr::Base.Generator{Vector{SymbolicUtils.BasicSymbolic{Real}}, MethodOfLines.var"#48#49"{MethodOfLines.DiscreteSpace{2, 4, MethodOfLines.CenterAlignedGrid}, CartesianIndex{1}, Dict{SymbolicUtils.BasicSymbolic{Real}, Int64}}}, offs::Int64, st::Int64)
    @ Base .\array.jl:840
  [6] collect_to_with_first!(dest::Vector{Pair{SymbolicUtils.BasicSymbolic{Real}, SymbolicUtils.BasicSymbolic{Real}}}, v1::Pair{SymbolicUtils.BasicSymbolic{Real}, SymbolicUtils.BasicSymbolic{Real}}, itr::Base.Generator{Vector{SymbolicUtils.BasicSymbolic{Real}}, MethodOfLines.var"#48#49"{MethodOfLines.DiscreteSpace{2, 4, MethodOfLines.CenterAlignedGrid}, CartesianIndex{1}, Dict{SymbolicUtils.BasicSymbolic{Real}, Int64}}}, st::Int64)
    @ Base .\array.jl:818
  [7] collect(itr::Base.Generator{Vector{SymbolicUtils.BasicSymbolic{Real}}, MethodOfLines.var"#48#49"{MethodOfLines.DiscreteSpace{2, 4, MethodOfLines.CenterAlignedGrid}, CartesianIndex{1}, Dict{SymbolicUtils.BasicSymbolic{Real}, Int64}}})
    @ Base .\array.jl:792
  [8] varmaps(s::MethodOfLines.DiscreteSpace{2, 4, MethodOfLines.CenterAlignedGrid}, depvars::Vector{SymbolicUtils.BasicSymbolic{Real}}, II::CartesianIndex{1}, indexmap::Dict{SymbolicUtils.BasicSymbolic{Real}, Int64})
    @ MethodOfLines C:\Users\bozdoc\.julia\packages\MethodOfLines\qu7lv\src\discretization\discretize_vars.jl:282
  [9] (::MethodOfLines.var"#509#511"{MethodOfLines.DiscreteSpace{2, 4, MethodOfLines.CenterAlignedGrid}, Vector{Any}, PDEBase.HigherOrderInterfaceBoundary, Dict{SymbolicUtils.BasicSymbolic{Real}, Int64}, Equation})(II::CartesianIndex{1})
    @ MethodOfLines C:\Users\bozdoc\.julia\packages\MethodOfLines\qu7lv\src\discretization\generate_bc_eqs.jl:227
 [10] iterate
    @ .\generator.jl:47 [inlined]
 [11] _collect(c::Vector{CartesianIndex{1}}, itr::Base.Generator{Vector{CartesianIndex{1}}, MethodOfLines.var"#509#511"{MethodOfLines.DiscreteSpace{2, 4, MethodOfLines.CenterAlignedGrid}, Vector{Any}, PDEBase.HigherOrderInterfaceBoundary, Dict{SymbolicUtils.BasicSymbolic{Real}, Int64}, Equation}}, #unused#::Base.EltypeUnknown, isz::Base.HasShape{1})
    @ Base .\array.jl:802
 [12] collect_similar(cont::Vector{CartesianIndex{1}}, itr::Base.Generator{Vector{CartesianIndex{1}}, MethodOfLines.var"#509#511"{MethodOfLines.DiscreteSpace{2, 4, MethodOfLines.CenterAlignedGrid}, Vector{Any}, PDEBase.HigherOrderInterfaceBoundary, Dict{SymbolicUtils.BasicSymbolic{Real}, Int64}, Equation}})
    @ Base .\array.jl:711
 [13] map(f::Function, A::Vector{CartesianIndex{1}})
    @ Base .\abstractarray.jl:3263
 [14] generate_bc_eqs(s::MethodOfLines.DiscreteSpace{2, 4, MethodOfLines.CenterAlignedGrid}, boundaryvalfuncs::Vector{Any}, boundary::PDEBase.HigherOrderInterfaceBoundary, interiormap::MethodOfLines.InteriorMap, indexmap::Dict{SymbolicUtils.BasicSymbolic{Real}, Int64})
    @ MethodOfLines C:\Users\bozdoc\.julia\packages\MethodOfLines\qu7lv\src\discretization\generate_bc_eqs.jl:225
 [15] generate_bc_eqs!(disc_state::PDEBase.EquationState, s::MethodOfLines.DiscreteSpace{2, 4, MethodOfLines.CenterAlignedGrid}, boundaryvalfuncs::Vector{Any}, interiormap::MethodOfLines.InteriorMap, boundary::PDEBase.HigherOrderInterfaceBoundary)
    @ MethodOfLines C:\Users\bozdoc\.julia\packages\MethodOfLines\qu7lv\src\discretization\generate_bc_eqs.jl:27
 [16] discretize_equation!(disc_state::PDEBase.EquationState, pde::Equation, interiormap::MethodOfLines.InteriorMap, eqvar::SymbolicUtils.BasicSymbolic{Real}, bcmap::Dict{SymbolicUtils.BasicSymbolic{SymbolicUtils.FnType{Tuple, Real}}, Dict{SymbolicUtils.BasicSymbolic{Real}, Vector{Any}}}, depvars::Vector{Any}, s::MethodOfLines.DiscreteSpace{2, 4, MethodOfLines.CenterAlignedGrid}, derivweights::MethodOfLines.DifferentialDiscretizer{Pair{SymbolicUtils.BasicSymbolic{Real}, Vector{Int64}}, Dict{Function, MethodOfLines.DerivativeOperator{Float64, Nothing, false, Float64, StaticArraysCore.SVector{3, Float64}, S2, S3, Nothing, Nothing} where {S2, S3}}, UpwindScheme}, indexmap::Dict{SymbolicUtils.BasicSymbolic{Real}, Int64}, discretization::MOLFiniteDifference{MethodOfLines.CenterAlignedGrid, MethodOfLines.ScalarizedDiscretization})
    @ MethodOfLines C:\Users\bozdoc\.julia\packages\MethodOfLines\qu7lv\src\scalar_discretization.jl:9
 [17] symbolic_discretize(pdesys::PDESystem, discretization::MOLFiniteDifference{MethodOfLines.CenterAlignedGrid, MethodOfLines.ScalarizedDiscretization})
    @ PDEBase C:\Users\bozdoc\.julia\packages\PDEBase\Aqj4G\src\symbolic_discretize.jl:80
 [18] discretize(pdesys::PDESystem, discretization::MOLFiniteDifference{MethodOfLines.CenterAlignedGrid, MethodOfLines.ScalarizedDiscretization}; analytic::Nothing, kwargs::Base.Pairs{Symbol, 
Union{}, Tuple{}, NamedTuple{(), Tuple{}}})
    @ PDEBase C:\Users\bozdoc\.julia\packages\PDEBase\Aqj4G\src\discretization_state.jl:58
 [19] discretize(pdesys::PDESystem, discretization::MOLFiniteDifference{MethodOfLines.CenterAlignedGrid, MethodOfLines.ScalarizedDiscretization})
    @ PDEBase C:\Users\bozdoc\.julia\packages\PDEBase\Aqj4G\src\discretization_state.jl:55
 [20] top-level scope
    @ c:\Users\bozdoc\Desktop\CanRepo\Phase-2\src\minimal-example.jl:82

Environment

• Output of using Pkg; Pkg.status()

julia> Pkg.status()
Status `C:\Users\bozdoc\Desktop\CanRepo\MyJuliaProject\Project.toml`
  [70b36510] AutomaticDocstrings v1.0.5
  [336ed68f] CSV v0.10.11
  [052768ef] CUDA v5.1.1
  [c3611d14] ColorVectorSpace v0.10.0
  [a93c6f00] DataFrames v1.6.1
  [31a5f54b] Debugger v0.7.8
  [071ae1c0] DiffEqGPU v3.3.0
  [0c46a032] DifferentialEquations v7.11.0
  [31c24e10] Distributions v0.25.104
  [ffbed154] DocStringExtensions v0.9.3
⌅ [28b8d3ca] GR v0.72.10
  [5903a43b] Infiltrator v1.6.4
  [2fda8390] LsqFit v0.15.0
  [94925ecb] MethodOfLines v0.10.4
⌃ [961ee093] ModelingToolkit v8.73.2
  [a03496cd] PlotlyBase v0.8.19
  [f0f68f2c] PlotlyJS v0.18.11
  [91a5bcdd] Plots v1.39.0
  [aea7be01] PrecompileTools v1.2.0
  [92933f4c] ProgressMeter v1.9.0
  [6303bc30] Signals v1.2.0
  [c3572dad] Sundials v4.22.1
⌃ [fce5fe82] Turing v0.29.3
  [ea0860ee] TuringCallbacks v0.4.0
  [b8865327] UnicodePlots v3.6.0
  [fa267f1f] TOML v1.0.3

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

julia> Pkg.status(; mode = PKGMODE_MANIFEST)
Status `C:\Users\bozdoc\Desktop\CanRepo\MyJuliaProject\Manifest.toml`
  [47edcb42] ADTypes v0.2.5
  [c3fe647b] AbstractAlgebra v0.34.5
  [621f4979] AbstractFFTs v1.5.0
⌅ [80f14c24] AbstractMCMC v4.4.2
⌅ [7a57a42e] AbstractPPL v0.6.2
  [1520ce14] AbstractTrees v0.4.4
  [7d9f7c33] Accessors v0.1.33
⌅ [79e6a3ab] Adapt v3.7.2
⌅ [0bf59076] AdvancedHMC v0.4.4
⌅ [5b7e9947] AdvancedMH v0.7.5
⌅ [576499cb] AdvancedPS v0.4.3
  [b5ca4192] AdvancedVI v0.2.4
  [dce04be8] ArgCheck v2.3.0
  [ec485272] ArnoldiMethod v0.2.0
  [4fba245c] ArrayInterface v7.7.0
  [4c555306] ArrayLayouts v1.4.5
  [bf4720bc] AssetRegistry v0.1.0
  [a9b6321e] Atomix v0.1.0
  [70b36510] AutomaticDocstrings v1.0.5
⌃ [13072b0f] AxisAlgorithms v1.0.1
  [39de3d68] AxisArrays v0.4.7
  [ab4f0b2a] BFloat16s v0.4.2
  [aae01518] BandedMatrices v1.4.0
  [198e06fe] BangBang v0.3.39
  [9718e550] Baselet v0.1.1
  [e2ed5e7c] Bijections v0.1.6
  [76274a88] Bijectors v0.13.8
  [d1d4a3ce] BitFlags v0.1.8
  [62783981] BitTwiddlingConvenienceFunctions v0.1.5
  [ad839575] Blink v0.12.8
  [764a87c0] BoundaryValueDiffEq v5.6.0
  [e1450e63] BufferedStreams v1.2.1
  [fa961155] CEnum v0.5.0
  [2a0fbf3d] CPUSummary v0.2.4
  [00ebfdb7] CSTParser v3.3.6
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⌃ [bcd4f6db] DelayDiffEq v5.44.0
  [8bb1440f] DelimitedFiles v1.9.1
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⌃ [459566f4] DiffEqCallbacks v2.35.0
  [071ae1c0] DiffEqGPU v3.3.0
  [77a26b50] DiffEqNoiseProcess v5.20.0
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  [0c46a032] DifferentialEquations v7.11.0
  [b4f34e82] Distances v0.10.11
  [31c24e10] Distributions v0.25.104
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⌅ [5b8099bc] DomainSets v0.6.7
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⌅ [366bfd00] DynamicPPL v0.23.21
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  [9aa1b823] FastClosures v0.3.2
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  [5789e2e9] FileIO v1.16.1
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  [6a86dc24] FiniteDiff v2.21.1
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  [f6369f11] ForwardDiff v0.10.36
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  [de31a74c] FunctionalCollections v0.5.0
  [d9f16b24] Functors v0.4.5
⌅ [0c68f7d7] GPUArrays v9.1.0
⌅ [46192b85] GPUArraysCore v0.1.5
  [61eb1bfa] GPUCompiler v0.25.0
⌅ [28b8d3ca] GR v0.72.10
  [c145ed77] GenericSchur v0.5.3
  [c27321d9] Glob v1.3.1
  [a2bd30eb] Graphics v1.1.2
  [86223c79] Graphs v1.9.0
  [42e2da0e] Grisu v1.0.2
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⌅ [d5909c97] GroupsCore v0.4.2
  [cd3eb016] HTTP v1.10.1
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⌅ [a09fc81d] ImageCore v0.8.22
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⌅ [a98d9a8b] Interpolations v0.14.7
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  [e80e1ace] MLJModelInterface v1.9.3
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  [d125e4d3] ManualMemory v0.1.8
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  [299715c1] MarchingCubes v0.1.9
  [a3b82374] MatrixFactorizations v2.1.0
  [739be429] MbedTLS v1.1.9
  [442fdcdd] Measures v0.3.2
  [94925ecb] MethodOfLines v0.10.4
  [128add7d] MicroCollections v0.1.4
  [e1d29d7a] Missings v1.1.0
⌃ [961ee093] ModelingToolkit v8.73.2
  [e94cdb99] MosaicViews v0.3.4
  [46d2c3a1] MuladdMacro v0.2.4
  [102ac46a] MultivariatePolynomials v0.5.3
  [ffc61752] Mustache v1.0.19
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  [a975b10e] Mux v1.0.1
  [d41bc354] NLSolversBase v7.8.3
  [2774e3e8] NLsolve v4.5.1
  [872c559c] NNlib v0.9.9
  [5da4648a] NVTX v0.3.3
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⌅ [8913a72c] NonlinearSolve v2.8.2
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⌃ [1dea7af3] OrdinaryDiffEq v6.59.3
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  [1d0040c9] PolyesterWeave v0.2.1
  [2dfb63ee] PooledArrays v1.4.3
  [85a6dd25] PositiveFactorizations v0.2.4
  [d236fae5] PreallocationTools v0.4.13
  [aea7be01] PrecompileTools v1.2.0
  [21216c6a] Preferences v1.4.1
  [08abe8d2] PrettyTables v2.3.1
  [27ebfcd6] Primes v0.5.5
  [33c8b6b6] ProgressLogging v0.1.4
  [92933f4c] ProgressMeter v1.9.0
  [3349acd9] ProtoBuf v1.0.14
  [1fd47b50] QuadGK v2.9.1
  [8a4e6c94] QuasiMonteCarlo v0.3.3
  [74087812] Random123 v1.6.2
  [fb686558] RandomExtensions v0.4.4
  [e6cf234a] RandomNumbers v1.5.3
  [b3c3ace0] RangeArrays v0.3.2
  [c84ed2f1] Ratios v0.4.5
  [c1ae055f] RealDot v0.1.0
  [3cdcf5f2] RecipesBase v1.3.4
  [01d81517] RecipesPipeline v0.6.12
⌅ [731186ca] RecursiveArrayTools v2.38.10
  [f2c3362d] RecursiveFactorization v0.2.21
  [189a3867] Reexport v1.2.2
  [05181044] RelocatableFolders v1.0.1
  [ae029012] Requires v1.3.0
  [ae5879a3] ResettableStacks v1.1.1
  [79098fc4] Rmath v0.7.1
  [f2b01f46] Roots v2.0.22
  [7e49a35a] RuntimeGeneratedFunctions v0.5.12
  [fdea26ae] SIMD v3.4.6
  [94e857df] SIMDTypes v0.1.0
  [476501e8] SLEEFPirates v0.6.42
⌃ [0bca4576] SciMLBase v2.10.0
  [e9a6253c] SciMLNLSolve v0.1.9
  [c0aeaf25] SciMLOperators v0.3.7
  [30f210dd] ScientificTypesBase v3.0.0
  [6c6a2e73] Scratch v1.2.1
  [91c51154] SentinelArrays v1.4.1
  [efcf1570] Setfield v1.1.1
  [992d4aef] Showoff v1.0.3
  [6303bc30] Signals v1.2.0
  [777ac1f9] SimpleBufferStream v1.1.0
  [05bca326] SimpleDiffEq v1.11.0
⌅ [727e6d20] SimpleNonlinearSolve v0.1.25
  [699a6c99] SimpleTraits v0.9.4
  [ce78b400] SimpleUnPack v1.1.0
  [ed01d8cd] Sobol v1.5.0
  [a2af1166] SortingAlgorithms v1.2.0
  [47a9eef4] SparseDiffTools v2.15.0
  [dc90abb0] SparseInverseSubset v0.1.2
  [e56a9233] Sparspak v0.3.9
  [276daf66] SpecialFunctions v2.3.1
  [171d559e] SplittablesBase v0.1.15
  [cae243ae] StackViews v0.1.1
  [aedffcd0] Static v0.8.8
  [0d7ed370] StaticArrayInterface v1.5.0
  [90137ffa] StaticArrays v1.8.1
  [1e83bf80] StaticArraysCore v1.4.2
  [64bff920] StatisticalTraits v3.2.0
  [82ae8749] StatsAPI v1.7.0
⌅ [2913bbd2] StatsBase v0.33.21
  [4c63d2b9] StatsFuns v1.3.0
⌅ [9672c7b4] SteadyStateDiffEq v1.16.1
  [789caeaf] StochasticDiffEq v6.64.0
  [7792a7ef] StrideArraysCore v0.5.2
  [892a3eda] StringManipulation v0.3.4
  [09ab397b] StructArrays v0.6.16
  [c3572dad] Sundials v4.22.1
⌅ [2efcf032] SymbolicIndexingInterface v0.2.2
⌃ [d1185830] SymbolicUtils v1.4.0
⌃ [0c5d862f] Symbolics v5.11.0
  [3783bdb8] TableTraits v1.0.1
  [bd369af6] Tables v1.11.1
  [899adc3e] TensorBoardLogger v0.1.23
  [62fd8b95] TensorCore v0.1.1
  [8ea1fca8] TermInterface v0.3.3
  [5d786b92] TerminalLoggers v0.1.7
  [8290d209] ThreadingUtilities v0.5.2
  [a759f4b9] TimerOutputs v0.5.23
  [0796e94c] Tokenize v0.5.26
  [9f7883ad] Tracker v0.2.30
⌅ [3bb67fe8] TranscodingStreams v0.9.13
  [28d57a85] Transducers v0.4.79
  [d5829a12] TriangularSolve v0.1.20
  [410a4b4d] Tricks v0.1.8
  [781d530d] TruncatedStacktraces v1.4.0
⌃ [fce5fe82] Turing v0.29.3
  [ea0860ee] TuringCallbacks v0.4.0
  [5c2747f8] URIs v1.5.1
  [3a884ed6] UnPack v1.0.2
  [1cfade01] UnicodeFun v0.4.1
  [b8865327] UnicodePlots v3.6.0
  [1986cc42] Unitful v1.19.0
  [45397f5d] UnitfulLatexify v1.6.3
  [a7c27f48] Unityper v0.1.6
  [013be700] UnsafeAtomics v0.2.1
  [d80eeb9a] UnsafeAtomicsLLVM v0.1.3
  [41fe7b60] Unzip v0.2.0
  [3d5dd08c] VectorizationBase v0.21.65
  [19fa3120] VertexSafeGraphs v0.2.0
  [ea10d353] WeakRefStrings v1.4.2
  [0f1e0344] WebIO v0.8.21
  [104b5d7c] WebSockets v1.6.0
  [cc8bc4a8] Widgets v0.6.6
⌅ [efce3f68] WoodburyMatrices v0.5.6
  [76eceee3] WorkerUtilities v1.6.1
  [700de1a5] ZygoteRules v0.2.4
  [6e34b625] Bzip2_jll v1.0.8+0
  [4ee394cb] CUDA_Driver_jll v0.7.0+0
⌅ [76a88914] CUDA_Runtime_jll v0.10.1+0
  [83423d85] Cairo_jll v1.16.1+1
  [2702e6a9] EpollShim_jll v0.0.20230411+0
  [2e619515] Expat_jll v2.5.0+0
  [b22a6f82] FFMPEG_jll v4.4.4+1
  [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
  [0656b61e] GLFW_jll v3.3.8+0
⌅ [d2c73de3] GR_jll v0.72.10+0
  [78b55507] Gettext_jll v0.21.0+0
  [7746bdde] Glib_jll v2.76.5+0
  [3b182d85] Graphite2_jll v1.3.14+0
  [2e76f6c2] HarfBuzz_jll v2.8.1+1
  [1d5cc7b8] IntelOpenMP_jll v2024.0.0+0
  [aacddb02] JpegTurbo_jll v3.0.1+0
  [9c1d0b0a] JuliaNVTXCallbacks_jll v0.2.1+0
  [f7e6163d] Kaleido_jll v0.2.1+0
  [c1c5ebd0] LAME_jll v3.100.1+0
  [88015f11] LERC_jll v3.0.0+1
  [dad2f222] LLVMExtra_jll v0.0.27+1
  [1d63c593] LLVMOpenMP_jll v15.0.4+0
  [dd4b983a] LZO_jll v2.10.1+0
⌅ [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 v4.5.1+1
  [38a345b3] Libuuid_jll v2.36.0+0
  [856f044c] MKL_jll v2024.0.0+0
  [e98f9f5b] NVTX_jll v3.1.0+2
  [e7412a2a] Ogg_jll v1.3.5+1
  [458c3c95] OpenSSL_jll v3.0.12+0
  [efe28fd5] OpenSpecFun_jll v0.5.5+0
  [91d4177d] Opus_jll v1.3.2+0
  [30392449] Pixman_jll v0.42.2+0
  [c0090381] Qt6Base_jll v6.5.3+1
  [f50d1b31] Rmath_jll v0.4.0+0
⌅ [fb77eaff] Sundials_jll v5.2.1+0
  [a44049a8] Vulkan_Loader_jll v1.3.243+0
  [a2964d1f] Wayland_jll v1.21.0+1
  [2381bf8a] Wayland_protocols_jll v1.25.0+0
  [02c8fc9c] XML2_jll v2.12.2+0
  [aed1982a] XSLT_jll v1.1.34+0
  [ffd25f8a] XZ_jll v5.4.5+0
  [f67eecfb] Xorg_libICE_jll v1.0.10+1
  [c834827a] Xorg_libSM_jll v1.2.3+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
  [e920d4aa] Xorg_xcb_util_cursor_jll v0.1.4+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
  [35ca27e7] eudev_jll v3.2.9+0
  [214eeab7] fzf_jll v0.43.0+0
  [1a1c6b14] gperf_jll v3.1.1+0
  [a4ae2306] libaom_jll v3.4.0+0
  [0ac62f75] libass_jll v0.15.1+0
  [2db6ffa8] libevdev_jll v1.11.0+0
  [f638f0a6] libfdk_aac_jll v2.0.2+0
  [36db933b] libinput_jll v1.18.0+0
  [b53b4c65] libpng_jll v1.6.40+0
  [f27f6e37] libvorbis_jll v1.3.7+1
  [009596ad] mtdev_jll v1.1.6+0
  [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 v1.9.2
  [de0858da] Printf
  [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 v1.0.5+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 v5.8.0+0
  [8e850ede] nghttp2_jll v1.48.0+0
  [3f19e933] p7zip_jll v17.4.0+0

versioninfo():

julia> versioninfo()
Julia Version 1.9.3
Commit bed2cd540a (2023-08-24 14:43 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Windows (x86_64-w64-mingw32)
  CPU: 8 × Intel(R) Core(TM) i7-7700HQ CPU @ 2.80GHz
  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 = 1