Can't extract results from solution

[AleBastos25]

Trying to run this,

`using ModelingToolkit, MethodOfLines, OrdinaryDiffEq, DomainSets, LinearAlgebra, Dierckx, NonlinearSolve

theta = 0:pi/20:pi
xs = cos.(theta)
ys = sin.(theta)
points = [xs ys]

fchapBA = .1
fchapBF = .05


interp_extra0 = Spline1D(points[end : -1 : 1, 1],points[end: -1 :1, 2])
interp_extra1 = Spline1D(points[end : -1 : 1, 1],points[end: -1 :1, 2])

extra0(x) = interp_extra0(x)
extra1(x) = interp_extra1(x)

@register_symbolic extra0(x)
@register_symbolic extra1(x)

@parameters x y 
@variables z(..) Dy_z(..)

Dx = Differential(x)
Dy = Differential(y)
Dxx = Differential(x)^2
Dyy = Differential(y)^2

eqs = [
    ((1+Dx(z(x,y))^2)*Dyy(z(x,y)) + 2*Dx(z(x,y))*Dy_z(x,y)*Dx(Dy_z(x,y)) + (1+Dy_z(x,y)^2)*Dxx(z(x,y))) ~ 0,
    Dy_z(x,y) ~ Dy(z(x, y))
]
   
domains = [x ∈ Interval(0, 1),
           y ∈ Interval(0, 1)]

bcs = [
    z(0, y) ~ extra0(fchapBA),
    z(1, y) ~ extra0(1-fchapBF),
    z(x, 0) ~ extra0(x),
    z(x, 1) ~ extra1(x),
    ]

@named pdesys = PDESystem(eqs, bcs, domains, [x,y], [z(x, y), Dy_z(x, y)])

N = 20

dx = 0.05
dy = 0.05

order = 2

discretization = MOLFiniteDifference([x=>dx, y=>dy], nothing, approx_order=order)


@time prob = discretize(pdesys, discretization)


println("Solve:")
@time sol = NonlinearSolve.solve(prob, NewtonRaphson())


grid = get_discrete(pdesys, discretization)
discrete_x = grid[x]
discrete_y = grid[y]
z_sol = map(d -> sol[d][1], grid[z(x, y)])
`

And this error shows up

ERROR: ArgumentError: Cannot find the parent of var"Dy_z[22]ˍnothing". Stacktrace: [1] getparent @ C:\Users\Alexandre.julia\packages\Symbolics\4VdEG\src\variable.jl:420 [inlined] [2] getparent @ C:\Users\Alexandre.julia\packages\Symbolics\4VdEG\src\variable.jl:412 [inlined] [3] _getname(x::Sym{Real, Nothing}, val::Dict{Any, Any}) @ Symbolics C:\Users\Alexandre.julia\packages\Symbolics\4VdEG\src\variable.jl:401 [4] getname(x::Sym{Real, Nothing}, val::Dict{Any, Any}) (repeats 2 times) @ Symbolics C:\Users\Alexandre.julia\packages\Symbolics\4VdEG\src\variable.jl:409 [5] renamespace(sys::NonlinearSystem, x::Sym{Real, Nothing}) @ ModelingToolkit C:\Users\Alexandre.julia\packages\ModelingToolkit\9ppm9\src\systems\abstractsystem.jl:362 [6] states(sys::NonlinearSystem, v::Sym{Real, Nothing}) @ ModelingToolkit C:\Users\Alexandre.julia\packages\ModelingToolkit\9ppm9\src\systems\abstractsystem.jl:469 [7] (::ModelingToolkit.var"#315#320"{NonlinearSystem})(x::Sym{Real, Nothing}) @ ModelingToolkit .\none:0 [8] iterate @ .\generator.jl:47 [inlined] [9] _all(f::Base.var"#282#284", itr::Base.Generator{Vector{SymbolicUtils.Symbolic{Real}}, ModelingToolkit.var"#315#320"{NonlinearSystem}}, #unused#::Colon) @ Base .\reduce.jl:930 [10] all @ .\reduce.jl:918 [inlined] [11] Dict(kv::Base.Generator{Vector{SymbolicUtils.Symbolic{Real}}, ModelingToolkit.var"#315#320"{NonlinearSystem}}) @ Base .\dict.jl:131 [12] build_explicit_observed_function(sys::NonlinearSystem, ts::Num; expression::Bool, output_type::Type, checkbounds::Bool) @ ModelingToolkit C:\Users\Alexandre.julia\packages\ModelingToolkit\9ppm9\src\systems\diffeqs\odesystem.jl:290 [13] build_explicit_observed_function @ C:\Users\Alexandre.julia\packages\ModelingToolkit\9ppm9\src\systems\diffeqs\odesystem.jl:276 [inlined] [14] #596 @ C:\Users\Alexandre.julia\packages\ModelingToolkit\9ppm9\src\systems\nonlinear\nonlinearsystem.jl:229 [inlined] [15] get!(default::ModelingToolkit.var"#596#602"{Num, NonlinearSystem}, h::Dict{Any, Any}, key::Term{Real, Nothing}) @ Base .\dict.jl:465 [16] (::ModelingToolkit.var"#generated_observed#601"{NonlinearSystem, Dict{Any, Any}})(obsvar::Num, u::Vector{Float64}, p::Nothing) @ ModelingToolkit C:\Users\Alexandre.julia\packages\ModelingToolkit\9ppm9\src\systems\nonlinear\nonlinearsystem.jl:228 [17] observed @ C:\Users\Alexandre.julia\packages\SciMLBase\YasGG\src\solutions\solution_interface.jl:135 [inlined] [18] getindex(A::SciMLBase.NonlinearSolution{Float64, 1, Vector{Float64}, Vector{Float64}, NonlinearProblem{Vector{Float64}, true, Nothing, NonlinearFunction{true, ModelingToolkit.var"#f#598"{RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋arg1, :ˍ₋arg2), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xd8992cee, 0x0c2228ac, 0xe0732ac6, 0xf23f344c, 0x8a9d5dcf)}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :ˍ₋arg1, :ˍ₋arg2), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x11d077a5, 0xb1dec8fb, 0xc28cc637, 0xb621f640, 0xa3e24f28)}}, UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Vector{Symbol}, ModelingToolkit.var"#generated_observed#601"{NonlinearSystem, Dict{Any, Any}}, Nothing}, Base.Iterators.Pairs{Union{}, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}}, NewtonRaphson{12, true, DataType, NonlinearSolve.DefaultLinSolve}, Nothing, Nothing}, sym::Num) @ SciMLBase C:\Users\Alexandre.julia\packages\SciMLBase\YasGG\src\solutions\solution_interface.jl:128 [19] (::var"#117#118")(d::Num) @ Main c:\Users\Alexandre\DownloadOFF\GitHub\KF\test.jl:84 [20] iterate @ .\generator.jl:47 [inlined] [21] _collect(c::Matrix{Num}, itr::Base.Generator{Matrix{Num}, var"#117#118"}, #unused#::Base.EltypeUnknown, isz::Base.HasShape{2}) @ Base .\array.jl:695 [22] collect_similar(cont::Matrix{Num}, itr::Base.Generator{Matrix{Num}, var"#117#118"}) @ Base .\array.jl:606 [23] map(f::Function, A::Matrix{Num}) @ Base .\abstractarray.jl:2294 [24] top-level scope @ c:\Users\Alexandre\DownloadOFF\GitHub\KF\test.jl:84

caused by: ArgumentError: Cannot find the parent of var"Dy_z[22]ˍnothing". Stacktrace: [1] getparent @ C:\Users\Alexandre.julia\packages\Symbolics\4VdEG\src\variable.jl:420 [inlined] [2] getparent @ C:\Users\Alexandre.julia\packages\Symbolics\4VdEG\src\variable.jl:412 [inlined] [3] _getname(x::Sym{Real, Nothing}, val::Dict{Any, Any}) @ Symbolics C:\Users\Alexandre.julia\packages\Symbolics\4VdEG\src\variable.jl:401 [4] getname(x::Sym{Real, Nothing}, val::Dict{Any, Any}) (repeats 2 times) @ Symbolics C:\Users\Alexandre.julia\packages\Symbolics\4VdEG\src\variable.jl:409 [5] renamespace(sys::NonlinearSystem, x::Sym{Real, Nothing}) @ ModelingToolkit C:\Users\Alexandre.julia\packages\ModelingToolkit\9ppm9\src\systems\abstractsystem.jl:362 [6] states(sys::NonlinearSystem, v::Sym{Real, Nothing}) @ ModelingToolkit C:\Users\Alexandre.julia\packages\ModelingToolkit\9ppm9\src\systems\abstractsystem.jl:469 [7] (::ModelingToolkit.var"#315#320"{NonlinearSystem})(x::Sym{Real, Nothing}) @ ModelingToolkit .\none:0 [8] iterate @ .\generator.jl:47 [inlined] [9] grow_to!(dest::Dict{Term{Real, Nothing}, Term{Real, Nothing}}, itr::Base.Generator{Vector{SymbolicUtils.Symbolic{Real}}, ModelingToolkit.var"#315#320"{NonlinearSystem}}, st::Int64) @ Base .\dict.jl:162 [10] grow_to!(dest::Dict{Any, Any}, itr::Base.Generator{Vector{SymbolicUtils.Symbolic{Real}}, ModelingToolkit.var"#315#320"{NonlinearSystem}})
@ Base .\dict.jl:145 [11] dict_with_eltype @ .\abstractdict.jl:545 [inlined] [12] Dict(kv::Base.Generator{Vector{SymbolicUtils.Symbolic{Real}}, ModelingToolkit.var"#315#320"{NonlinearSystem}}) @ Base .\dict.jl:129 [13] build_explicit_observed_function(sys::NonlinearSystem, ts::Num; expression::Bool, output_type::Type, checkbounds::Bool) @ ModelingToolkit C:\Users\Alexandre.julia\packages\ModelingToolkit\9ppm9\src\systems\diffeqs\odesystem.jl:290 [14] build_explicit_observed_function @ C:\Users\Alexandre.julia\packages\ModelingToolkit\9ppm9\src\systems\diffeqs\odesystem.jl:276 [inlined] [15] #596 @ C:\Users\Alexandre.julia\packages\ModelingToolkit\9ppm9\src\systems\nonlinear\nonlinearsystem.jl:229 [inlined] [16] get!(default::ModelingToolkit.var"#596#602"{Num, NonlinearSystem}, h::Dict{Any, Any}, key::Term{Real, Nothing}) @ Base .\dict.jl:465 [17] (::ModelingToolkit.var"#generated_observed#601"{NonlinearSystem, Dict{Any, Any}})(obsvar::Num, u::Vector{Float64}, p::Nothing) @ ModelingToolkit C:\Users\Alexandre.julia\packages\ModelingToolkit\9ppm9\src\systems\nonlinear\nonlinearsystem.jl:228 [18] observed @ C:\Users\Alexandre.julia\packages\SciMLBase\YasGG\src\solutions\solution_interface.jl:135 [inlined] [19] getindex(A::SciMLBase.NonlinearSolution{Float64, 1, Vector{Float64}, Vector{Float64}, NonlinearProblem{Vector{Float64}, true, Nothing, NonlinearFunction{true, ModelingToolkit.var"#f#598"{RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋arg1, :ˍ₋arg2), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0xd8992cee, 0x0c2228ac, 0xe0732ac6, 0xf23f344c, 0x8a9d5dcf)}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :ˍ₋arg1, :ˍ₋arg2), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x11d077a5, 0xb1dec8fb, 0xc28cc637, 0xb621f640, 0xa3e24f28)}}, UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Vector{Symbol}, ModelingToolkit.var"#generated_observed#601"{NonlinearSystem, Dict{Any, Any}}, Nothing}, Base.Iterators.Pairs{Union{}, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}}, NewtonRaphson{12, true, DataType, NonlinearSolve.DefaultLinSolve}, Nothing, Nothing}, sym::Num) @ SciMLBase C:\Users\Alexandre.julia\packages\SciMLBase\YasGG\src\solutions\solution_interface.jl:128 [20] (::var"#117#118")(d::Num) @ Main c:\Users\Alexandre\DownloadOFF\GitHub\KF\test.jl:84 [21] iterate @ .\generator.jl:47 [inlined] [22] _collect(c::Matrix{Num}, itr::Base.Generator{Matrix{Num}, var"#117#118"}, #unused#::Base.EltypeUnknown, isz::Base.HasShape{2}) @ Base .\array.jl:695 [23] collect_similar(cont::Matrix{Num}, itr::Base.Generator{Matrix{Num}, var"#117#118"}) @ Base .\array.jl:606 [24] map(f::Function, A::Matrix{Num}) @ Base .\abstractarray.jl:2294 [25] top-level scope @ c:\Users\Alexandre\DownloadOFF\GitHub\KF\test.jl:84

julia>

[xtalax]

This looks like a problem in NonlinearSolve, are you running with latest versions? Can you retry after running Pkg.update()?

[AleBastos25]

Got the same error after the update and with Tsit5() algorithm

[ChrisRackauckas]

Solving what with Tsit5? There's no ODEs?

[AleBastos25]

Can't I use Tsit5 for PDE? Anyway NonlinearSolve continue with this error after the update

[ChrisRackauckas]

For time-dependent PDEs, yes. If your PDE isn't time dependent, or is discretized in all dimensions, then you get a NonlinearProblem instead of an ODEProblem.

[AleBastos25]

Well, so what did I do wrong? I can't map the solution z_sol = map(d -> sol[d][1], grid[z(x, y)])

[ChrisRackauckas]

sys = symbolic_discretize(pdesys, discretization)[1]
simpsys = structural_simplify(sys)

Gives something odd.

julia> println(states(sys))
Term{Real, Nothing}[Dy_z[1, 1], Dy_z[2, 1], Dy_z[3, 1], Dy_z[4, 1], Dy_z[5, 1], Dy_z[6, 1], Dy_z[7, 1], Dy_z[8, 1], Dy_z[9, 1], Dy_z[10, 1], Dy_z[11, 1], Dy_z[12, 1], Dy_z[13, 1], Dy_z[14, 1], Dy_z[15, 1], Dy_z[16, 1], Dy_z[17, 1], Dy_z[18, 1], Dy_z[19, 1], Dy_z[20, 1], Dy_z[21, 1], Dy_z[1, 2], Dy_z[2, 2], Dy_z[3, 2], Dy_z[4, 2], Dy_z[5, 2], Dy_z[6, 2], Dy_z[7, 2], Dy_z[8, 2], Dy_z[9, 2], Dy_z[10, 2], Dy_z[11, 2], Dy_z[12, 2], Dy_z[13, 2], Dy_z[14, 2], Dy_z[15, 2], Dy_z[16, 2], Dy_z[17, 2], Dy_z[18, 2], Dy_z[19, 2], Dy_z[20, 2], Dy_z[21, 2], Dy_z[1, 3], Dy_z[2, 3], Dy_z[3, 3], Dy_z[4, 3], Dy_z[5, 3], Dy_z[6, 3], Dy_z[7, 3], Dy_z[8, 3], Dy_z[9, 3], Dy_z[10, 3], Dy_z[11, 3], Dy_z[12, 3], Dy_z[13, 3], Dy_z[14, 3], Dy_z[15, 3], Dy_z[16, 3], Dy_z[17, 3], Dy_z[18, 3], Dy_z[19, 3], Dy_z[20, 3], Dy_z[21, 3], Dy_z[1, 4], Dy_z[2, 4], Dy_z[3, 4], Dy_z[4, 4], Dy_z[5, 4], Dy_z[6, 4], Dy_z[7, 4], Dy_z[8, 4], Dy_z[9, 4], Dy_z[10, 4], Dy_z[11, 4], Dy_z[12, 4], Dy_z[13, 4], Dy_z[14, 4], Dy_z[15, 4], Dy_z[16, 4], Dy_z[17, 4], Dy_z[18, 4], Dy_z[19, 4], Dy_z[20, 4], Dy_z[21, 4], Dy_z[1, 5], Dy_z[2, 5], Dy_z[3, 5], Dy_z[4, 5], Dy_z[5, 5], Dy_z[6, 5], Dy_z[7, 5], Dy_z[8, 5], Dy_z[9, 5], Dy_z[10, 5], Dy_z[11, 5], Dy_z[12, 5], Dy_z[13, 5], Dy_z[14, 5], Dy_z[15, 5], Dy_z[16, 5], Dy_z[17, 5], Dy_z[18, 5], Dy_z[19, 5], Dy_z[20, 5], Dy_z[21, 5], Dy_z[1, 6], Dy_z[2, 6], Dy_z[3, 6], Dy_z[4, 6], Dy_z[5, 6], Dy_z[6, 6], Dy_z[7, 6], Dy_z[8, 6], Dy_z[9, 6], Dy_z[10, 6], Dy_z[11, 6], Dy_z[12, 6], Dy_z[13, 6], Dy_z[14, 6], Dy_z[15, 6], Dy_z[16, 6], Dy_z[17, 6], Dy_z[18, 6], Dy_z[19, 6], Dy_z[20, 6], Dy_z[21, 6], Dy_z[1, 7], Dy_z[2, 7], Dy_z[3, 7], Dy_z[4, 7], Dy_z[5, 7], Dy_z[6, 7], Dy_z[7, 7], Dy_z[8, 7], Dy_z[9, 7], Dy_z[10, 7], Dy_z[11, 7], Dy_z[12, 7], Dy_z[13, 7], Dy_z[14, 7], Dy_z[15, 7], Dy_z[16, 7], Dy_z[17, 7], Dy_z[18, 7], Dy_z[19, 7], Dy_z[20, 7], Dy_z[21, 7], Dy_z[1, 8], Dy_z[2, 8], Dy_z[3, 8], Dy_z[4, 8], Dy_z[5, 8], Dy_z[6, 8], Dy_z[7, 8], Dy_z[8, 8], Dy_z[9, 8], Dy_z[10, 8], Dy_z[11, 8], Dy_z[12, 8], Dy_z[13, 8], Dy_z[14, 8], Dy_z[15, 8], Dy_z[16, 8], Dy_z[17, 8], Dy_z[18, 8], Dy_z[19, 8], Dy_z[20, 8], Dy_z[21, 8], Dy_z[1, 9], Dy_z[2, 9], Dy_z[3, 9], Dy_z[4, 9], Dy_z[5, 9], Dy_z[6, 9], Dy_z[7, 9], Dy_z[8, 9], Dy_z[9, 9], Dy_z[10, 9], Dy_z[11, 9], Dy_z[12, 9], Dy_z[13, 9], Dy_z[14, 9], Dy_z[15, 9], Dy_z[16, 9], Dy_z[17, 9], Dy_z[18, 9], Dy_z[19, 9], Dy_z[20, 9], Dy_z[21, 9], Dy_z[1, 10], Dy_z[2, 10], Dy_z[3, 10], Dy_z[4, 10], Dy_z[5, 10], Dy_z[6, 10], Dy_z[7, 10], Dy_z[8, 10], Dy_z[9, 10], Dy_z[10, 10], Dy_z[11, 10], Dy_z[12, 10], Dy_z[13, 10], Dy_z[14, 10], Dy_z[15, 10], Dy_z[16, 10], Dy_z[17, 10], Dy_z[18, 10], Dy_z[19, 10], Dy_z[20, 10], Dy_z[21, 10], Dy_z[1, 11], Dy_z[2, 11], Dy_z[3, 11], Dy_z[4, 11], Dy_z[5, 11], Dy_z[6, 11], Dy_z[7, 11], Dy_z[8, 11], Dy_z[9, 11], Dy_z[10, 11], Dy_z[11, 11], Dy_z[12, 11], Dy_z[13, 11], Dy_z[14, 11], Dy_z[15, 11], Dy_z[16, 11], Dy_z[17, 11], Dy_z[18, 11], Dy_z[19, 11], Dy_z[20, 11], Dy_z[21, 11], Dy_z[1, 12], Dy_z[2, 12], Dy_z[3, 12], Dy_z[4, 12], Dy_z[5, 12], Dy_z[6, 12], Dy_z[7, 12], Dy_z[8, 12], Dy_z[9, 12], Dy_z[10, 12], Dy_z[11, 12], Dy_z[12, 12], Dy_z[13, 12], Dy_z[14, 12], Dy_z[15, 12], Dy_z[16, 12], Dy_z[17, 12], Dy_z[18, 12], Dy_z[19, 12], Dy_z[20, 12], Dy_z[21, 12], Dy_z[1, 13], Dy_z[2, 13], Dy_z[3, 13], Dy_z[4, 13], Dy_z[5, 13], Dy_z[6, 13], Dy_z[7, 13], Dy_z[8, 13], Dy_z[9, 13], Dy_z[10, 13], Dy_z[11, 13], Dy_z[12, 13], Dy_z[13, 13], Dy_z[14, 13], Dy_z[15, 13], Dy_z[16, 13], Dy_z[17, 13], Dy_z[18, 13], Dy_z[19, 13], Dy_z[20, 13], Dy_z[21, 13], Dy_z[1, 14], Dy_z[2, 14], Dy_z[3, 14], Dy_z[4, 14], Dy_z[5, 14], Dy_z[6, 14], Dy_z[7, 14], Dy_z[8, 14], Dy_z[9, 14], Dy_z[10, 14], Dy_z[11, 14], Dy_z[12, 14], Dy_z[13, 14], Dy_z[14, 14], Dy_z[15, 14], Dy_z[16, 14], Dy_z[17, 14], Dy_z[18, 14], Dy_z[19, 14], Dy_z[20, 14], Dy_z[21, 14], Dy_z[1, 15], Dy_z[2, 15], Dy_z[3, 15], Dy_z[4, 15], Dy_z[5, 15], Dy_z[6, 15], Dy_z[7, 15], Dy_z[8, 15], Dy_z[9, 15], Dy_z[10, 15], Dy_z[11, 15], Dy_z[12, 15], Dy_z[13, 15], Dy_z[14, 15], Dy_z[15, 15], Dy_z[16, 15], Dy_z[17, 15], Dy_z[18, 15], Dy_z[19, 15], Dy_z[20, 15], Dy_z[21, 15], Dy_z[1, 16], Dy_z[2, 16], Dy_z[3, 16], Dy_z[4, 16], Dy_z[5, 16], Dy_z[6, 16], Dy_z[7, 16], Dy_z[8, 16], Dy_z[9, 16], Dy_z[10, 16], Dy_z[11, 16], Dy_z[12, 16], Dy_z[13, 16], Dy_z[14, 16], Dy_z[15, 16], Dy_z[16, 16], Dy_z[17, 16], Dy_z[18, 16], Dy_z[19, 16], Dy_z[20, 16], Dy_z[21, 16], Dy_z[1, 17], Dy_z[2, 17], Dy_z[3, 17], Dy_z[4, 17], Dy_z[5, 17], Dy_z[6, 17], Dy_z[7, 17], Dy_z[8, 17], Dy_z[9, 17], Dy_z[10, 17], Dy_z[11, 17], Dy_z[12, 17], Dy_z[13, 17], Dy_z[14, 17], Dy_z[15, 17], Dy_z[16, 17], Dy_z[17, 17], Dy_z[18, 17], Dy_z[19, 17], Dy_z[20, 17], Dy_z[21, 17], Dy_z[1, 18], Dy_z[2, 18], Dy_z[3, 18], Dy_z[4, 18], Dy_z[5, 18], Dy_z[6, 18], Dy_z[7, 18], Dy_z[8, 18], Dy_z[9, 18], Dy_z[10, 18], Dy_z[11, 18], Dy_z[12, 18], Dy_z[13, 18], Dy_z[14, 18], Dy_z[15, 18], Dy_z[16, 18], Dy_z[17, 18], Dy_z[18, 18], Dy_z[19, 18], Dy_z[20, 18], Dy_z[21, 18], Dy_z[1, 19], Dy_z[2, 19], Dy_z[3, 19], Dy_z[4, 19], Dy_z[5, 19], Dy_z[6, 19], Dy_z[7, 19], Dy_z[8, 19], Dy_z[9, 19], Dy_z[10, 19], Dy_z[11, 19], Dy_z[12, 19], Dy_z[13, 19], Dy_z[14, 19], Dy_z[15, 19], Dy_z[16, 19], Dy_z[17, 19], Dy_z[18, 19], Dy_z[19, 19], Dy_z[20, 19], Dy_z[21, 19], Dy_z[1, 20], Dy_z[2, 20], Dy_z[3, 20], Dy_z[4, 20], Dy_z[5, 20], Dy_z[6, 20], Dy_z[7, 20], Dy_z[8, 20], Dy_z[9, 20], Dy_z[10, 20], Dy_z[11, 20], Dy_z[12, 20], Dy_z[13, 20], Dy_z[14, 20], Dy_z[15, 20], Dy_z[16, 20], Dy_z[17, 20], Dy_z[18, 20], Dy_z[19, 20], Dy_z[20, 20], Dy_z[21, 20], Dy_z[1, 21], Dy_z[2, 21], Dy_z[3, 21], Dy_z[4, 21], Dy_z[5, 21], Dy_z[6, 21], Dy_z[7, 21], Dy_z[8, 21], Dy_z[9, 21], Dy_z[10, 21], Dy_z[11, 21], Dy_z[12, 21], Dy_z[13, 21], Dy_z[14, 21], Dy_z[15, 21], Dy_z[16, 21], Dy_z[17, 21], Dy_z[18, 21], Dy_z[19, 21], Dy_z[20, 21], Dy_z[21, 21], z[1, 1], z[2, 1], z[3, 1], z[4, 1], z[5, 1], z[6, 1], z[7, 1], z[8, 1], z[9, 1], z[10, 1], z[11, 1], z[12, 1], z[13, 1], z[14, 1], z[15, 1], z[16, 1], z[17, 1], z[18, 1], z[19, 1], z[20, 1], z[21, 1], z[1, 2], z[2, 2], z[3, 2], z[4, 2], z[5, 2], z[6, 2], z[7, 2], z[8, 2], z[9, 2], z[10, 2], z[11, 2], z[12, 2], z[13, 2], z[14, 2], z[15, 2], z[16, 2], z[17, 2], z[18, 2], z[19, 2], z[20, 2], z[21, 2], z[1, 3], z[2, 3], z[3, 3], z[4, 3], z[5, 3], z[6, 3], z[7, 3], z[8, 3], z[9, 3], z[10, 3], z[11, 3], z[12, 3], z[13, 3], z[14, 3], z[15, 3], z[16, 3], z[17, 3], z[18, 3], z[19, 3], z[20, 3], z[21, 3], z[1, 4], z[2, 4], z[3, 4], z[4, 4], z[5, 4], z[6, 4], z[7, 4], z[8, 4], z[9, 4], z[10, 4], z[11, 4], z[12, 4], z[13, 4], z[14, 4], z[15, 4], z[16, 4], z[17, 4], z[18, 4], z[19, 4], z[20, 4], z[21, 4], z[1, 5], z[2, 5], z[3, 5], z[4, 5], z[5, 5], z[6, 5], z[7, 5], z[8, 5], z[9, 5], z[10, 5], z[11, 5], z[12, 5], z[13, 5], z[14, 5], z[15, 5], z[16, 5], z[17, 5], z[18, 5], z[19, 5], z[20, 5], z[21, 5], z[1, 6], z[2, 6], z[3, 6], z[4, 6], z[5, 6], z[6, 6], z[7, 6], z[8, 6], z[9, 6], z[10, 6], z[11, 6], z[12, 6], z[13, 6], z[14, 6], z[15, 6], z[16, 6], z[17, 6], z[18, 6], z[19, 6], z[20, 6], z[21, 6], z[1, 7], z[2, 7], z[3, 7], z[4, 7], z[5, 7], z[6, 7], z[7, 7], z[8, 7], z[9, 7], z[10, 7], z[11, 7], z[12, 7], z[13, 7], z[14, 7], z[15, 7], z[16, 7], z[17, 7], z[18, 7], z[19, 7], z[20, 7], z[21, 7], z[1, 8], z[2, 8], z[3, 8], z[4, 8], z[5, 8], z[6, 8], z[7, 8], z[8, 8], z[9, 8], z[10, 8], z[11, 8], z[12, 8], z[13, 8], z[14, 8], z[15, 8], z[16, 8], z[17, 8], z[18, 8], z[19, 8], z[20, 8], z[21, 8], z[1, 9], z[2, 9], z[3, 9], z[4, 9], z[5, 9], z[6, 9], z[7, 9], z[8, 9], z[9, 9], z[10, 9], z[11, 9], z[12, 9], z[13, 9], z[14, 9], z[15, 9], z[16, 9], z[17, 9], z[18, 9], z[19, 9], z[20, 9], z[21, 9], z[1, 10], z[2, 10], z[3, 10], z[4, 10], z[5, 10], z[6, 10], z[7, 10], z[8, 10], z[9, 10], z[10, 10], z[11, 10], z[12, 10], z[13, 10], z[14, 10], z[15, 10], z[16, 10], z[17, 10], z[18, 10], z[19, 10], z[20, 10], z[21, 10], z[1, 11], z[2, 11], z[3, 11], z[4, 11], z[5, 11], z[6, 11], z[7, 11], z[8, 11], z[9, 11], z[10, 11], z[11, 11], z[12, 11], z[13, 11], z[14, 11], z[15, 11], z[16, 11], z[17, 11], z[18, 11], z[19, 11], z[20, 11], z[21, 11], z[1, 12], z[2, 12], z[3, 12], z[4, 12], z[5, 12], z[6, 12], z[7, 12], z[8, 12], z[9, 12], z[10, 12], z[11, 12], z[12, 12], z[13, 12], z[14, 12], z[15, 12], z[16, 12], z[17, 12], z[18, 12], z[19, 12], z[20, 12], z[21, 12], z[1, 13], z[2, 13], z[3, 13], z[4, 13], z[5, 13], z[6, 13], z[7, 13], z[8, 13], z[9, 13], z[10, 13], z[11, 13], z[12, 13], z[13, 13], z[14, 13], z[15, 13], z[16, 13], z[17, 13], z[18, 13], z[19, 13], z[20, 13], z[21, 13], z[1, 14], z[2, 14], z[3, 14], z[4, 14], z[5, 14], z[6, 14], z[7, 14], z[8, 14], z[9, 14], z[10, 14], z[11, 14], z[12, 14], z[13, 14], z[14, 14], z[15, 14], z[16, 14], z[17, 14], z[18, 14], z[19, 14], z[20, 14], z[21, 14], z[1, 15], z[2, 15], z[3, 15], z[4, 15], z[5, 15], z[6, 15], z[7, 15], z[8, 15], z[9, 15], z[10, 15], z[11, 15], z[12, 15], z[13, 15], z[14, 15], z[15, 15], z[16, 15], z[17, 15], z[18, 15], z[19, 15], z[20, 15], z[21, 15], z[1, 16], z[2, 16], z[3, 16], z[4, 16], z[5, 16], z[6, 16], z[7, 16], z[8, 16], z[9, 16], z[10, 16], z[11, 16], z[12, 16], z[13, 16], z[14, 16], z[15, 16], z[16, 16], z[17, 16], z[18, 16], z[19, 16], z[20, 16], z[21, 16], z[1, 17], z[2, 17], z[3, 17], z[4, 17], z[5, 17], z[6, 17], z[7, 17], z[8, 17], z[9, 17], z[10, 17], z[11, 17], z[12, 17], z[13, 17], z[14, 17], z[15, 17], z[16, 17], z[17, 17], z[18, 17], z[19, 17], z[20, 17], z[21, 17], z[1, 18], z[2, 18], z[3, 18], z[4, 18], z[5, 18], z[6, 18], z[7, 18], z[8, 18], z[9, 18], z[10, 18], z[11, 18], z[12, 18], z[13, 18], z[14, 18], z[15, 18], z[16, 18], z[17, 18], z[18, 18], z[19, 18], z[20, 18], z[21, 18], z[1, 19], z[2, 19], z[3, 19], z[4, 19], z[5, 19], z[6, 19], z[7, 19], z[8, 19], z[9, 19], z[10, 19], z[11, 19], z[12, 19], z[13, 19], z[14, 19], z[15, 19], z[16, 19], z[17, 19], z[18, 19], z[19, 19], z[20, 19], z[21, 19], z[1, 20], z[2, 20], z[3, 20], z[4, 20], z[5, 20], z[6, 20], z[7, 20], z[8, 20], z[9, 20], z[10, 20], z[11, 20], z[12, 20], z[13, 20], z[14, 20], z[15, 20], z[16, 20], z[17, 20], z[18, 20], z[19, 20], z[20, 20], z[21, 20], z[1, 21], z[2, 21], z[3, 21], z[4, 21], z[5, 21], z[6, 21], z[7, 21], z[8, 21], z[9, 21], z[10, 21], z[11, 21], z[12, 21], z[13, 21], z[14, 21], z[15, 21], z[16, 21], z[17, 21], z[18, 21], z[19, 21], z[20, 21], z[21, 21]]

julia> states(simpsys)
722-element Vector{SymbolicUtils.Symbolic{Real}}:
 Dy_z[2, 2]
 Dy_z[3, 2]
 Dy_z[4, 2]
 Dy_z[5, 2]
 Dy_z[6, 2]
 ⋮
 var"Dy_z[1720]ˍnothing"
 var"Dy_z[1820]ˍnothing"
 var"Dy_z[1920]ˍnothing"
 var"Dy_z[2020]ˍnothing"

julia> println(states(simpsys))
SymbolicUtils.Symbolic{Real}[Dy_z[2, 2], Dy_z[3, 2], Dy_z[4, 2], Dy_z[5, 2], Dy_z[6, 2], Dy_z[7, 2], Dy_z[8, 2], Dy_z[9, 2], Dy_z[10, 2], Dy_z[11, 2], Dy_z[12, 2], Dy_z[13, 2], Dy_z[14, 2], Dy_z[15, 2], Dy_z[16, 2], Dy_z[17, 2], Dy_z[18, 2], Dy_z[19, 2], Dy_z[20, 2], Dy_z[2, 3], Dy_z[3, 3], Dy_z[4, 3], Dy_z[5, 3], Dy_z[6, 3], Dy_z[7, 3], Dy_z[8, 3], Dy_z[9, 3], Dy_z[10, 3], Dy_z[11, 3], Dy_z[12, 3], Dy_z[13, 3], Dy_z[14, 3], Dy_z[15, 3], Dy_z[16, 3], Dy_z[17, 3], Dy_z[18, 3], Dy_z[19, 3], Dy_z[20, 3], Dy_z[2, 4], Dy_z[3, 4], Dy_z[4, 4], Dy_z[5, 4], Dy_z[6, 4], Dy_z[7, 4], Dy_z[8, 4], Dy_z[9, 4], Dy_z[10, 4], Dy_z[11, 4], Dy_z[12, 4], Dy_z[13, 4], Dy_z[14, 4], Dy_z[15, 4], Dy_z[16, 4], Dy_z[17, 4], Dy_z[18, 4], Dy_z[19, 4], Dy_z[20, 4], Dy_z[2, 5], Dy_z[3, 5], Dy_z[4, 5], Dy_z[5, 5], Dy_z[6, 5], Dy_z[7, 5], Dy_z[8, 5], Dy_z[9, 5], Dy_z[10, 5], Dy_z[11, 5], Dy_z[12, 5], Dy_z[13, 5], Dy_z[14, 5], Dy_z[15, 5], Dy_z[16, 5], Dy_z[17, 5], Dy_z[18, 5], Dy_z[19, 5], Dy_z[20, 5], Dy_z[2, 6], Dy_z[3, 6], Dy_z[4, 6], Dy_z[5, 6], Dy_z[6, 6], Dy_z[7, 6], Dy_z[8, 6], Dy_z[9, 6], Dy_z[10, 6], Dy_z[11, 6], Dy_z[12, 6], Dy_z[13, 6], Dy_z[14, 6], Dy_z[15, 6], Dy_z[16, 6], Dy_z[17, 6], Dy_z[18, 6], Dy_z[19, 6], Dy_z[20, 6], Dy_z[2, 7], Dy_z[3, 7], Dy_z[4, 7], Dy_z[5, 7], Dy_z[6, 7], Dy_z[7, 7], Dy_z[8, 7], Dy_z[9, 7], Dy_z[10, 7], Dy_z[11, 7], Dy_z[12, 7], Dy_z[13, 7], Dy_z[14, 7], Dy_z[15, 7], Dy_z[16, 7], Dy_z[17, 7], Dy_z[18, 7], Dy_z[19, 7], Dy_z[20, 7], Dy_z[2, 8], Dy_z[3, 8], Dy_z[4, 8], Dy_z[5, 8], Dy_z[6, 8], Dy_z[7, 8], Dy_z[8, 8], Dy_z[9, 8], Dy_z[10, 8], Dy_z[11, 8], Dy_z[12, 8], Dy_z[13, 8], Dy_z[14, 8], Dy_z[15, 8], Dy_z[16, 8], Dy_z[17, 8], Dy_z[18, 8], Dy_z[19, 8], Dy_z[20, 8], Dy_z[2, 9], Dy_z[3, 9], Dy_z[4, 9], Dy_z[5, 9], Dy_z[6, 9], Dy_z[7, 9], Dy_z[8, 9], Dy_z[9, 9], Dy_z[10, 9], Dy_z[11, 9], Dy_z[12, 9], Dy_z[13, 9], Dy_z[14, 9], Dy_z[15, 9], Dy_z[16, 9], Dy_z[17, 9], Dy_z[18, 9], Dy_z[19, 9], Dy_z[20, 9], Dy_z[2, 10], Dy_z[3, 10], Dy_z[4, 10], Dy_z[5, 10], Dy_z[6, 10], Dy_z[7, 10], Dy_z[8, 10], Dy_z[9, 10], Dy_z[10, 10], Dy_z[11, 10], Dy_z[12, 10], Dy_z[13, 10], Dy_z[14, 10], Dy_z[15, 10], Dy_z[16, 10], Dy_z[17, 10], Dy_z[18, 10], Dy_z[19, 10], Dy_z[20, 10], Dy_z[2, 11], Dy_z[3, 11], Dy_z[4, 11], Dy_z[5, 11], Dy_z[6, 11], Dy_z[7, 11], Dy_z[8, 11], Dy_z[9, 11], Dy_z[10, 11], Dy_z[11, 11], Dy_z[12, 11], Dy_z[13, 11], Dy_z[14, 11], Dy_z[15, 11], Dy_z[16, 11], Dy_z[17, 11], Dy_z[18, 11], Dy_z[19, 11], Dy_z[20, 11], Dy_z[2, 12], Dy_z[3, 12], Dy_z[4, 12], Dy_z[5, 12], Dy_z[6, 12], Dy_z[7, 12], Dy_z[8, 12], Dy_z[9, 12], Dy_z[10, 12], Dy_z[11, 12], Dy_z[12, 12], Dy_z[13, 12], Dy_z[14, 12], Dy_z[15, 12], Dy_z[16, 12], Dy_z[17, 12], Dy_z[18, 12], Dy_z[19, 12], Dy_z[20, 12], Dy_z[2, 13], Dy_z[3, 13], Dy_z[4, 13], Dy_z[5, 13], Dy_z[6, 13], Dy_z[7, 13], Dy_z[8, 13], Dy_z[9, 13], Dy_z[10, 13], Dy_z[11, 13], Dy_z[12, 13], Dy_z[13, 13], Dy_z[14, 13], Dy_z[15, 13], Dy_z[16, 13], Dy_z[17, 13], Dy_z[18, 13], Dy_z[19, 13], Dy_z[20, 13], Dy_z[2, 14], Dy_z[3, 14], Dy_z[4, 14], Dy_z[5, 14], Dy_z[6, 14], Dy_z[7, 14], Dy_z[8, 14], Dy_z[9, 14], Dy_z[10, 14], Dy_z[11, 14], Dy_z[12, 14], Dy_z[13, 14], Dy_z[14, 14], Dy_z[15, 14], Dy_z[16, 14], Dy_z[17, 14], Dy_z[18, 14], Dy_z[19, 14], Dy_z[20, 14], Dy_z[2, 15], Dy_z[3, 15], Dy_z[4, 15], Dy_z[5, 15], Dy_z[6, 15], Dy_z[7, 15], Dy_z[8, 15], Dy_z[9, 15], Dy_z[10, 15], Dy_z[11, 15], Dy_z[12, 15], Dy_z[13, 15], Dy_z[14, 15], Dy_z[15, 15], Dy_z[16, 15], Dy_z[17, 15], Dy_z[18, 15], Dy_z[19, 15], Dy_z[20, 15], Dy_z[2, 16], Dy_z[3, 16], Dy_z[4, 16], Dy_z[5, 16], Dy_z[6, 16], Dy_z[7, 16], Dy_z[8, 16], Dy_z[9, 16], Dy_z[10, 16], Dy_z[11, 16], Dy_z[12, 16], Dy_z[13, 16], Dy_z[14, 16], Dy_z[15, 16], Dy_z[16, 16], Dy_z[17, 16], Dy_z[18, 16], Dy_z[19, 16], Dy_z[20, 16], Dy_z[2, 17], Dy_z[3, 17], Dy_z[4, 17], Dy_z[5, 17], Dy_z[6, 17], Dy_z[7, 17], Dy_z[8, 17], Dy_z[9, 17], Dy_z[10, 17], Dy_z[11, 17], Dy_z[12, 17], Dy_z[13, 17], Dy_z[14, 17], Dy_z[15, 17], Dy_z[16, 17], Dy_z[17, 17], Dy_z[18, 17], Dy_z[19, 17], Dy_z[20, 17], Dy_z[2, 18], Dy_z[3, 18], Dy_z[4, 18], Dy_z[5, 18], Dy_z[6, 18], Dy_z[7, 18], Dy_z[8, 18], Dy_z[9, 18], Dy_z[10, 18], Dy_z[11, 18], Dy_z[12, 18], Dy_z[13, 18], Dy_z[14, 18], Dy_z[15, 18], Dy_z[16, 18], Dy_z[17, 18], Dy_z[18, 18], Dy_z[19, 18], Dy_z[20, 18], Dy_z[2, 19], Dy_z[3, 19], Dy_z[4, 19], Dy_z[5, 19], Dy_z[6, 19], Dy_z[7, 19], Dy_z[8, 19], Dy_z[9, 19], Dy_z[10, 19], Dy_z[11, 19], Dy_z[12, 19], Dy_z[13, 19], Dy_z[14, 19], Dy_z[15, 19], Dy_z[16, 19], Dy_z[17, 19], Dy_z[18, 19], Dy_z[19, 19], Dy_z[20, 19], Dy_z[2, 20], Dy_z[3, 20], Dy_z[4, 20], Dy_z[5, 20], Dy_z[6, 20], Dy_z[7, 20], Dy_z[8, 20], Dy_z[9, 20], Dy_z[10, 20], Dy_z[11, 20], Dy_z[12, 20], Dy_z[13, 20], Dy_z[14, 20], Dy_z[15, 20], Dy_z[16, 20], Dy_z[17, 20], Dy_z[18, 20], Dy_z[19, 20], Dy_z[20, 20], var"Dy_z[22]ˍnothing", var"Dy_z[32]ˍnothing", var"Dy_z[42]ˍnothing", var"Dy_z[52]ˍnothing", var"Dy_z[62]ˍnothing", var"Dy_z[72]ˍnothing", var"Dy_z[82]ˍnothing", var"Dy_z[92]ˍnothing", var"Dy_z[102]ˍnothing", var"Dy_z[112]ˍnothing", var"Dy_z[122]ˍnothing", var"Dy_z[132]ˍnothing", var"Dy_z[142]ˍnothing", var"Dy_z[152]ˍnothing", var"Dy_z[162]ˍnothing", var"Dy_z[172]ˍnothing", var"Dy_z[182]ˍnothing", var"Dy_z[192]ˍnothing", var"Dy_z[202]ˍnothing", var"Dy_z[23]ˍnothing", var"Dy_z[33]ˍnothing", var"Dy_z[43]ˍnothing", var"Dy_z[53]ˍnothing", var"Dy_z[63]ˍnothing", var"Dy_z[73]ˍnothing", var"Dy_z[83]ˍnothing", var"Dy_z[93]ˍnothing", var"Dy_z[103]ˍnothing", var"Dy_z[113]ˍnothing", var"Dy_z[123]ˍnothing", var"Dy_z[133]ˍnothing", var"Dy_z[143]ˍnothing", var"Dy_z[153]ˍnothing", var"Dy_z[163]ˍnothing", var"Dy_z[173]ˍnothing", var"Dy_z[183]ˍnothing", var"Dy_z[193]ˍnothing", var"Dy_z[203]ˍnothing", var"Dy_z[24]ˍnothing", var"Dy_z[34]ˍnothing", var"Dy_z[44]ˍnothing", var"Dy_z[54]ˍnothing", var"Dy_z[64]ˍnothing", var"Dy_z[74]ˍnothing", var"Dy_z[84]ˍnothing", var"Dy_z[94]ˍnothing", var"Dy_z[104]ˍnothing", var"Dy_z[114]ˍnothing", var"Dy_z[124]ˍnothing", var"Dy_z[134]ˍnothing", var"Dy_z[144]ˍnothing", var"Dy_z[154]ˍnothing", var"Dy_z[164]ˍnothing", var"Dy_z[174]ˍnothing", var"Dy_z[184]ˍnothing", var"Dy_z[194]ˍnothing", var"Dy_z[204]ˍnothing", var"Dy_z[25]ˍnothing", var"Dy_z[35]ˍnothing", var"Dy_z[45]ˍnothing", var"Dy_z[55]ˍnothing", var"Dy_z[65]ˍnothing", var"Dy_z[75]ˍnothing", var"Dy_z[85]ˍnothing", var"Dy_z[95]ˍnothing", var"Dy_z[105]ˍnothing", var"Dy_z[115]ˍnothing", var"Dy_z[125]ˍnothing", var"Dy_z[135]ˍnothing", var"Dy_z[145]ˍnothing", var"Dy_z[155]ˍnothing", var"Dy_z[165]ˍnothing", var"Dy_z[175]ˍnothing", var"Dy_z[185]ˍnothing", var"Dy_z[195]ˍnothing", var"Dy_z[205]ˍnothing", var"Dy_z[26]ˍnothing", var"Dy_z[36]ˍnothing", var"Dy_z[46]ˍnothing", var"Dy_z[56]ˍnothing", var"Dy_z[66]ˍnothing", var"Dy_z[76]ˍnothing", var"Dy_z[86]ˍnothing", var"Dy_z[96]ˍnothing", var"Dy_z[106]ˍnothing", var"Dy_z[116]ˍnothing", var"Dy_z[126]ˍnothing", var"Dy_z[136]ˍnothing", var"Dy_z[146]ˍnothing", var"Dy_z[156]ˍnothing", var"Dy_z[166]ˍnothing", var"Dy_z[176]ˍnothing", var"Dy_z[186]ˍnothing", 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@YingboMa I think the dummy derivative pass is being applied on NonlinearSystems and that causes this oddity?