# Vector equations LHS/RHS missing with MTK and MethodOfLines

I’ve been trying to generate a system of equations in vector format using MTK and MOL, and I keep getting errors related to broadcast-created equations missing LHS/RHS. I’ve adapted a tutorial problem to show the issue.

``````using DifferentialEquations, ModelingToolkit, MethodOfLines, DomainSets, DataInterpolations

# Parameters, variables, and derivatives
n_comp = 2
@parameters p[1:n_comp]
@variables t, x, u(..)[1:n_comp]
Dt = Differential(t)
Dx = Differential(x)
Dxx = Differential(x)^2
params = [p => [1.5, 2.0]]
# 1D PDE and boundary conditions

eq  = Dt.(u(t, x)) .~ p .* Dxx.(u(t, x))
eqs_collected = vcat(collect.(eq)...) #tried with and without vcat(collect.()...)
bcs = [u(0, x) .~ p .* cos(x),
u(t, 0) .~ sin(t),
u(t, 1) .~ exp(-t) * cos(1),
Dx.(u(t,0)) .~ 0.0]
bcs_collected = vcat(collect.(bcs)...)

# Space and time domains
domains = [t ∈ Interval(0.0, 1.0),
x ∈ Interval(0.0, 1.0)]

# PDE system

@named pdesys = PDESystem(eqs_collected, bcs_collected, domains, [t, x], [u(t, x)], params)

# Method of lines discretization
dx = 0.1
order = 2
discretization = MOLFiniteDifference([x => dx], t)

# Convert the PDE problem into an ODE problem
prob = discretize(pdesys,discretization) #error actually occurs here when running

# Solve ODE problem
using OrdinaryDiffEq
sol = solve(prob, Tsit5(), saveat=0.2)
``````

The actual error I get is

``````ERROR: type Term has no field lhs.
Stacktrace:
[1] error(s::String)
@ Base .\error.jl:35
[2] throw_no_field(#unused#::Val{:Term}, s::Symbol)
@ Unityper \.julia\packages\Unityper\vtKYP\src\compactify.jl:481
[3] getproperty(x::SymbolicUtils.BasicSymbolic{Any}, s::Symbol)
@ SymbolicUtils \.julia\packages\Unityper\vtKYP\src\compactify.jl:290
[4] cardinalize_eqs!(pdesys::PDESystem)
@ MethodOfLines \.julia\packages\MethodOfLines\jB2jr\src\system_parsing\pde_system_transformation.jl:39
[5] symbolic_discretize(pdesys::PDESystem, discretization::MOLFiniteDifference{MethodOfLines.CenterAlignedGrid, MethodOfLines.ScalarizedDiscretization})
@ MethodOfLines \.julia\packages\MethodOfLines\jB2jr\src\MOL_discretization.jl:29
[6] discretize(pdesys::PDESystem, discretization::MOLFiniteDifference{MethodOfLines.CenterAlignedGrid, MethodOfLines.ScalarizedDiscretization}; analytic::Nothing, kwargs::Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}})
@ MethodOfLines \.julia\packages\MethodOfLines\jB2jr\src\MOL_discretization.jl:132
[7] discretize(pdesys::PDESystem, discretization::MOLFiniteDifference{MethodOfLines.CenterAlignedGrid, MethodOfLines.ScalarizedDiscretization})
@ MethodOfLines \.julia\packages\MethodOfLines\jB2jr\src\MOL_discretization.jl:131
[8] top-level scope
@ Untitled-1:34

``````

I found this thread(Cannot use a set of equations in ODESystem with variables that are vectors · Issue #1196 · SciML/ModelingToolkit.jl · GitHub) , which suggested using

``````eqs_collected = vcat(collect.(eqs)...)
``````

But unfortunately, that didn’t fix the issue for the equations.

The boundary conditions form a very nice vector of equations even when they contain a differential which I thought was the issue for a while, but the equations themselves stay messy and actually cause the error.

eqs_collected looks like:

``````2-element Vector{SymbolicUtils.BasicSymbolic{Any}}:

``````

while bcs_collected looks like:

``````8-element Vector{Equation}:
(u(0, x))[1] ~ cos(x)*p[1]
(u(0, x))[2] ~ cos(x)*p[2]
(u(t, 0))[1] ~ sin(t)
(u(t, 0))[2] ~ sin(t)
(u(t, 1))[1] ~ 0.5403023058681398exp(-t)
(u(t, 1))[2] ~ 0.5403023058681398exp(-t)
Differential(x)((u(t, 0))[1]) ~ 0.0
Differential(x)((u(t, 0))[2]) ~ 0.0

``````

Am I making a dumb mistake somewhere, or is there a better way to do this?
edit: fixed some typos

Share `]st` and `]st -m`?

]st

`````` [6e4b80f9] BenchmarkTools v1.3.2
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[9e88b42a] Serialization

``````

]st -m

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[ae81ac8f] ASL_jll v0.1.3+0
[7b86fcea] ATK_jll v2.36.1+0
[e21ec000] Antic_jll v0.201.500+0
[d9960996] Arb_jll v200.2300.0+0
[6e34b625] Bzip2_jll v1.0.8+0
[83423d85] Cairo_jll v1.16.1+1
[fcfa6d1b] Calcium_jll v0.401.100+0
[ee1fde0b] Dbus_jll v1.12.16+3
[cd4c43a9] Dierckx_jll v0.1.0+0
⌅ [7cc45869] Enzyme_jll v0.0.48+1
[2e619515] Expat_jll v2.4.8+0
[b22a6f82] FFMPEG_jll v4.4.2+2
[f5851436] FFTW_jll v3.3.10+0
[e134572f] FLINT_jll v200.900.5+0
[a3f928ae] Fontconfig_jll v2.13.93+0
[d7e528f0] FreeType2_jll v2.10.4+0
[559328eb] FriBidi_jll v1.0.10+0
[0656b61e] GLFW_jll v3.3.8+0
[d2c73de3] GR_jll v0.72.0+0
[77ec8976] GTK3_jll v3.24.31+0
[78b55507] Gettext_jll v0.21.0+0
[7746bdde] Glib_jll v2.74.0+2
[3b182d85] Graphite2_jll v1.3.14+0
[2e76f6c2] HarfBuzz_jll v2.8.1+1
[1d5cc7b8] IntelOpenMP_jll v2018.0.3+2
⌅ [9cc047cb] Ipopt_jll v300.1400.400+0
[aacddb02] JpegTurbo_jll v2.1.91+0
[c1c5ebd0] LAME_jll v3.100.1+0
[88015f11] LERC_jll v3.0.0+1
[dd4b983a] LZO_jll v2.10.1+0
[42c93a91] Libepoxy_jll v1.5.10+0
⌅ [e9f186c6] Libffi_jll v3.2.2+1
[d4300ac3] Libgcrypt_jll v1.8.7+0
[7e76a0d4] Libglvnd_jll v1.6.0+0
[94ce4f54] Libiconv_jll v1.16.1+2
[4b2f31a3] Libmount_jll v2.35.0+0
[925c91fb] Librsvg_jll v2.54.5+0
[89763e89] Libtiff_jll v4.4.0+0
[38a345b3] Libuuid_jll v2.36.0+0
[d00139f3] METIS_jll v5.1.2+0
[856f044c] MKL_jll v2022.2.0+0
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[079eb43e] NLopt_jll v2.7.1+0
[e7412a2a] Ogg_jll v1.3.5+1
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[ec84b674] Xorg_libXrandr_jll v1.5.2+4
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[12413925] Xorg_xcb_util_image_jll v0.4.0+1
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[0d47668e] Xorg_xcb_util_renderutil_jll v0.3.9+1
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[35661453] Xorg_xkbcomp_jll v1.4.2+4
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[c5fb5394] Xorg_xtrans_jll v1.4.0+3
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⌅ [214eeab7] fzf_jll v0.29.0+0
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[a4ae2306] libaom_jll v3.4.0+0
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[b53b4c65] libpng_jll v1.6.38+0
[f27f6e37] libvorbis_jll v1.3.7+1
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[d8fb68d0] xkbcommon_jll v1.4.1+0
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[8ba89e20] Distributed
[7b1f6079] FileWatching
[9fa8497b] Future
[b77e0a4c] InteractiveUtils
[4af54fe1] LazyArtifacts
[b27032c2] LibCURL v0.6.3
[76f85450] LibGit2
[8f399da3] Libdl
[37e2e46d] LinearAlgebra
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[9a3f8284] Random
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[9e88b42a] Serialization
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[6462fe0b] Sockets
[2f01184e] SparseArrays
[10745b16] Statistics
[4607b0f0] SuiteSparse
[fa267f1f] TOML v1.0.0
[a4e569a6] Tar v1.10.1
[8dfed614] Test
[cf7118a7] UUIDs
[4ec0a83e] Unicode
[e66e0078] CompilerSupportLibraries_jll v1.0.1+0
[781609d7] GMP_jll v6.2.1+2
[deac9b47] LibCURL_jll v7.84.0+0
[29816b5a] LibSSH2_jll v1.10.2+0
[3a97d323] MPFR_jll v4.1.1+1
[c8ffd9c3] MbedTLS_jll v2.28.0+0
[14a3606d] MozillaCACerts_jll v2022.2.1
[4536629a] OpenBLAS_jll v0.3.20+0
[05823500] OpenLibm_jll v0.8.1+0
[efcefdf7] PCRE2_jll v10.40.0+0
[bea87d4a] SuiteSparse_jll v5.10.1+0
[83775a58] Zlib_jll v1.2.12+3
[8e850b90] libblastrampoline_jll v5.1.1+0
[8e850ede] nghttp2_jll v1.48.0+0
[3f19e933] p7zip_jll v17.4.0+0
``````

Looks like Symbolics is wrapping your broadcasted collect, if you collect in a generator expression this will work

I think I’ve figured out part of the issue, but I’ve uncovered a new question.

For people from the future, the equations can be safely formatted by enclosing them in brackets.

``````#this doesn't work
eq1 = Dt.(u(t,x)) ~ p .* Dxx.(u(t,x))
eqs_collected1 = vcat(collect.(eq1)...)

#this works
eq2  = [Dt.(u(t, x)) ~ p .* Dxx.(u(t, x))]
eqs2_collected = vcat(collect.(eq2)...)
``````

Unfortunately, even with all equations and BCs “properly” formed into a vector, the problem cannot be discretized, and the following error appears.

``````ERROR: MethodError: no method matching operation(::Symbolics.Arr{Num, 1})
Closest candidates are:
operation(!Matched::ArrayMaker) at \.julia\packages\Symbolics\bYtrk\src\arrays.jl:757
operation(!Matched::PolyForm) at \.julia\packages\SymbolicUtils\1JRDc\src\polyform.jl:184
...
Stacktrace:

(::MethodOfLines.var"#65#66")(u::Symbolics.Arr{Num, 1}) at \.julia\packages\MethodOfLines\jB2jr\src\MOL_symbolic_utils.jl

iterate at .\generator.jl

_collect at .\array.jl

collect_similar at .\array.jl

map at .\abstractarray.jl

get_ops at \.julia\packages\MethodOfLines\jB2jr\src\MOL_symbolic_utils.jl

MethodOfLines.VariableMap(eqs::Vector{Equation}, depvars::Vector{Symbolics.Arr{Num, 1}}, domain::Vector{Symbolics.VarDomainPairing}, time::Num, ps::Vector{Pair{Symbolics.Arr{Num, 1}, Vector{Float64}}}) at \.julia\packages\MethodOfLines\jB2jr\src\system_parsing\variable_map.jl

MethodOfLines.VariableMap(pdesys::PDESystem, t::Num) at \.julia\packages\MethodOfLines\jB2jr\src\system_parsing\variable_map.jl

symbolic_discretize(pdesys::PDESystem, discretization::MOLFiniteDifference{MethodOfLines.CenterAlignedGrid, MethodOfLines.ScalarizedDiscretization}) at \.julia\packages\MethodOfLines\jB2jr\src\MOL_discretization.jl

discretize(pdesys::PDESystem, discretization::MOLFiniteDifference{MethodOfLines.CenterAlignedGrid, MethodOfLines.ScalarizedDiscretization}; analytic::Nothing, kwargs::Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}) at \.julia\packages\MethodOfLines\jB2jr\src\MOL_discretization.jl

discretize(pdesys::PDESystem, discretization::MOLFiniteDifference{MethodOfLines.CenterAlignedGrid, MethodOfLines.ScalarizedDiscretization}) at \.julia\packages\MethodOfLines\jB2jr\src\MOL_discretization.jl

top-level scope at \test_for_debug.jl

``````

You need to write [collect(eq) for eq in eqs]

Sorry, I’m having some trouble understanding.

`eqs_collected = [collect(eq) for eq in eqs]` returns

``````1-element Vector{Vector{Equation}}:
[Differential(t)((u(t, x))[1]) ~ Differential(x)(Differential(x)((u(t, x))[1]))*p[1], Differential(t)((u(t, x))[2]) ~ Differential(x)(Differential(x)((u(t, x))[2]))*p[2]]
``````

This has the same no LHS error as in the original problem.

`eqs_collected = vcat(collect.(eqs)...)` returns

``````2-element Vector{Equation}:
Differential(t)((u(t, x))[1]) ~ Differential(x)(Differential(x)((u(t, x))[1]))*p[1]
Differential(t)((u(t, x))[2]) ~ Differential(x)(Differential(x)((u(t, x))[2]))*p[2]
``````

This returns the “new” method error related to
`operation(::Symbolics.Arr{Num, 1})`

running `eqs_collected2 = [collect(eq) for eq in eqs_collected]` where eqs_collected is the `2-element Vector{Equation}` returns the following error:

``````ERROR: MethodError: no method matching length(::Equation)
Closest candidates are:
length(!Matched::Union{Base.KeySet, Base.ValueIterator}) at abstractdict.jl:58
length(!Matched::Union{ArrayInterface.BidiagonalIndex, ArrayInterface.TridiagonalIndex}) at \.julia\packages\ArrayInterface\RKU7b\src\ArrayInterface.jl:808
length(!Matched::Union{Tables.AbstractColumns, Tables.AbstractRow}) at \.julia\packages\Tables\AcRIE\src\Tables.jl:180
...
Stacktrace:

_similar_shape(itr::Equation, #unused#::Base.HasLength) at .\array.jl

_collect(cont::UnitRange{Int64}, itr::Equation, #unused#::Base.HasEltype, isz::Base.HasLength) at .\array.jl

collect(itr::Equation) at .\array.jl

(::var"#27#28")(eq::Equation) at .\none

iterate at .\generator.jl

collect(itr::Base.Generator{Vector{Equation}, var"#27#28"}) at .\array.jl

top-level scope at \test_for_debug.jl

``````

Ah, reduce the generator with vcat and it will work, you want a vector of equations

My apologies, I am not at my computer, I will write a more detailed answer when I get home

That is giving me the same method error related to `operation(::Symbolics.Arr{Num, 1})`

`````` eqs_collected = [collect(eq) for eq in eqs]
eqs_collected2 = vcat(eqs_collected...)
``````

`eqs_collected2 == eqs_collected3` where `eqs_collected3 = vcat(collect.(eqs)...) `returns true, so I’m pretty sure both methods end up doing the same thing, though you would know better than I would whether there are more nuanced differences in terms of generalizability of the technique.

Thanks for your help, I really appreciate it!

I can tell you that this is mostly due to unintegrated Symbolics.jl Array variable support. I’ll get this in to my environment tomorrow and properly work the problem to get this solving. You may be able to avoid with `Symbolics.scalarize` instead of `collect`, but if that doesn’t work I’m going to need to see where exactly in the stack this fails to tell you exactly what needs to happen.

My apologies, but I’m sure we’ll be able to get your model working tomorrow.

1 Like

Symbolics.scalarize doesn’t fix the issue when I replace collect (returns the same MethodError as collect methods) so I’ll assume it’s not working properly for now. I’ve got plenty of other things to work on in the meantime, so no rush!

Thanks!

Hi, I have found a method that works, but it is not as elegant. Your post has brought to light an oversight that I will fix, but for now this code works:

``````# Parameters, variables, and derivatives
n_comp = 2
@parameters t, x, p[1:n_comp]
@variables u[1:n_comp](..)
Dt = Differential(t)
Dx = Differential(x)
Dxx = Differential(x)^2
params = p .=> [1.5, 2.0]
# 1D PDE and boundary conditions

eqs  = [Dt(u[i](t, x)) ~ p[i] * Dxx(u[i](t, x)) for i in 1:n_comp]

bcs = [[u[i](0, x) ~ p[i] * cos(x),
u[i](t, 0) ~ sin(t),
u[i](t, 1) ~ exp(-t) * cos(1),
Dx(u[i](t,0)) ~ 0.0] for i in 1:n_comp]
bcs_collected = reduce(vcat, bcs)

# Space and time domains
domains = [t ∈ Interval(0.0, 1.0),
x ∈ Interval(0.0, 1.0)]

# PDE system

@named pdesys = PDESystem(eqs, bcs_collected, domains, [t, x], [u[i](t, x) for i in 1:n_comp], scalarize(params))

``````

In general be very careful with things like `map`, `broadcast` and `sum` with symbolics, while array variable support is improving it is still incomplete, especially in MethodOfLines - for now it’s best to prefer generators to guarantee the typing of the inputs.

Glad to have been able to provide a test case to work with. I had been using for loop style constructions previously, but I had hoped to be able to simplify the appearance of the code a bit. I’ll go back to the for loops and look forward to array variable related updates!

Thanks!

I’m sorry for reopening this, but I realized I was not using the preferred updated syntax `u(..)[1:n]` since `u[1:n](..)` is slated for deprecation. When I modify this in the code, I get a new error.

``````using DifferentialEquations, ModelingToolkit, MethodOfLines, DomainSets, DataInterpolations

# Parameters, variables, and derivatives
n_comp = 2
@parameters t, x, p[1:n_comp], q[1:n_comp]
@variables u(..)[1:n_comp]
Dt = Differential(t)
Dx = Differential(x)
Dxx = Differential(x)^2
params = Symbolics.scalarize(reduce(vcat,[p .=> [1.5, 2.0], q .=> [1.2, 1.8]]))
# 1D PDE and boundary conditions

eqs  = [Dt(u(t, x)[i]) ~ p[i] * Dxx(u(t, x)[i]) for i in 1:n_comp]

bcs = [[u(0, x)[i] ~ q[i] * cos(x),
u(t, 0)[i] ~ sin(t),
u(t, 1)[i] ~ exp(-t) * cos(1),
Dx(u(t,0)[i]) ~ 0.0] for i in 1:n_comp]
bcs_collected = reduce(vcat, bcs)

# Space and time domains
domains = [t ∈ Interval(0.0, 1.0),
x ∈ Interval(0.0, 1.0)]

# PDE system

@named pdesys = PDESystem(eqs, bcs_collected, domains, [t, x], [u(t, x)[i] for i in 1:n_comp], Symbolics.scalarize(params))

# Method of lines discretization
dx = 0.1
order = 2
discretization = MOLFiniteDifference([x => dx], t; approx_order = order)

# Convert the PDE problem into an ODE problem
prob = discretize(pdesys,discretization) #error occurs here

# Solve ODE problem
sol = solve(prob, Tsit5(), saveat=0.2)
``````

The error I get from attempting discretization is:

``````ERROR: ArgumentError: invalid index: nothing of type Nothing
Stacktrace:
[1] to_index(i::Nothing)
@ Base .\indices.jl:300
[2] to_index(A::Vector{Symbolics.VarDomainPairing}, i::Nothing)
@ Base .\indices.jl:277
[3] to_indices
@ .\indices.jl:333 [inlined]
[4] to_indices
@ .\indices.jl:325 [inlined]
[5] getindex
@ .\abstractarray.jl:1241 [inlined]
[6] (::MethodOfLines.var"#225#234"{Vector{Symbolics.VarDomainPairing}})(x::SymbolicUtils.BasicSymbolic{Vector{Real}})
@ MethodOfLines \.julia\packages\MethodOfLines\jB2jr\src\system_parsing\variable_map.jl:30
[7] iterate
@ .\generator.jl:47 [inlined]
[8] _collect(c::Vector{Any}, itr::Base.Generator{Vector{Any}, MethodOfLines.var"#225#234"{Vector{Symbolics.VarDomainPairing}}}, #unused#::Base.EltypeUnknown, isz::Base.HasShape{1})
@ Base .\array.jl:807
[9] collect_similar(cont::Vector{Any}, itr::Base.Generator{Vector{Any}, MethodOfLines.var"#225#234"{Vector{Symbolics.VarDomainPairing}}})
@ Base .\array.jl:716
[10] map(f::Function, A::Vector{Any})
@ Base .\abstractarray.jl:2933
[11] MethodOfLines.VariableMap(eqs::Vector{Equation}, depvars::Vector{Num}, domain::Vector{Symbolics.VarDomainPairing}, time::Num, ps::Vector{Pair{SymbolicUtils.BasicSymbolic{Real}, Float64}})
@ MethodOfLines \.julia\packages\MethodOfLines\jB2jr\src\system_parsing\variable_map.jl:29
[12] MethodOfLines.VariableMap(pdesys::PDESystem, t::Num)
@ MethodOfLines \.julia\packages\MethodOfLines\jB2jr\src\system_parsing\variable_map.jl:41
[13] symbolic_discretize(pdesys::PDESystem, discretization::MOLFiniteDifference{MethodOfLines.CenterAlignedGrid, MethodOfLines.ScalarizedDiscretization})
@ MethodOfLines \.julia\packages\MethodOfLines\jB2jr\src\MOL_discretization.jl:35
[14] discretize(pdesys::PDESystem, discretization::MOLFiniteDifference{MethodOfLines.CenterAlignedGrid, MethodOfLines.ScalarizedDiscretization}; analytic::Nothing, kwargs::Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}})
@ MethodOfLines \.julia\packages\MethodOfLines\jB2jr\src\MOL_discretization.jl:132
[15] discretize(pdesys::PDESystem, discretization::MOLFiniteDifference{MethodOfLines.CenterAlignedGrid, MethodOfLines.ScalarizedDiscretization})
@ MethodOfLines \.julia\packages\MethodOfLines\jB2jr\src\MOL_discretization.jl:131
[16] top-level scope
@ test_for_debug.jl:36

``````