# MTK SDDE ArgumentError when Connecting two Components
**URL:** https://discourse.julialang.org/t/mtk-sdde-argumenterror-when-connecting-two-components/138861
**Category:** Numerics
**Tags:** modelingtoolkit, differentialequation
**Created:** [August 17, 2026, 7:26am UTC](https://discourse.julialang.org/t/mtk-sdde-argumenterror-when-connecting-two-components/138861 "2026-08-17T07:26:13Z")
**Posts on this page:** 8
**Page:** 1
### Author:  [@bebrunn](https://discourse.julialang.org/u/bebrunn)
#### Post date: [August 17, 2026, 7:26am UTC](https://discourse.julialang.org/t/mtk-sdde-argumenterror-when-connecting-two-components/138861/1 "2026-08-17T07:26:14Z")
Hi,
I am trying to connect two MTK `components` and then solve the resulting `SDDE` system. However, I am getting an `ArgumentsError` that I don’t understand.
```Julia
using ModelingToolkit
using DifferentialEquations
using ModelingToolkit: t_nounits as t, D_nounits as D
using StochasticDiffEq
@component function StochasticLV(;name)
@variables x(t) = 0.9 y(t) = 0.9
@parameters begin
α = 2/3
β = 4/3
γ = 1
δ = 1
end
@brownians η
eqs = [
D(x) ~ α * x - β * x * y + η
D(y) ~ -γ * y + δ * x * y
]
System(eqs, t; name)
end
@component function SomethingElse(;name, τ)
@variables z(t) = 0 x(..)
@parameters θ = 0.1 τ = τ
@brownians ξ
eqs = [
D(z) ~ -θ * x(t - τ) + ξ
]
System(eqs, t; name)
end
@named lv = StochasticLV()
@named sth = SomethingElse(τ = 3)
connection_eqs = [
sth.x ~ lv.x
]
@named connected_model = System(connection_eqs, t, [], []; systems = [lv, sth])
connected = mtkcompile(connected_model)
prob = SDDEProblem(connected, [], (0.0, 1.0))
sol = solve(prob, ImplicitEM())
```
**Stacktrace:**
```Julia
ERROR: ArgumentError: sth₊x(-sth₊τ + t) is present in the system but sth₊x(-sth₊τ + t) is not an unknown.
Stacktrace:
[1]
@ ModelingToolkitTearing ~/.julia/packages/ModelingToolkitTearing/ZusxN/src/tearingstate.jl:298
[2] TearingState
@ ~/.julia/packages/ModelingToolkitTearing/ZusxN/src/tearingstate.jl:149 [inlined]
[3] __mtkcompile(sys::System; inputs::OrderedCollections.OrderedSet{…}, outputs::OrderedCollections.OrderedSet{…}, disturbance_inputs::OrderedCollections.OrderedSet{…}, sort_eqs::Bool, kwargs::@Kwargs{…})
@ ModelingToolkit ~/.julia/packages/ModelingToolkit/GtdTx/src/systems/systems.jl:34
[4] __mtkcompile
@ ~/.julia/packages/ModelingToolkit/GtdTx/src/systems/systems.jl:23 [inlined]
[5] _mtkcompile(sys::System; kwargs::@Kwargs{…})
@ ModelingToolkitBase ~/.julia/packages/ModelingToolkitBase/gJDou/src/systems/systems.jl:155
[6] _mtkcompile
@ ~/.julia/packages/ModelingToolkitBase/gJDou/src/systems/systems.jl:128 [inlined]
[7] mtkcompile(sys::System; additional_passes::Tuple{}, inputs::Vector{…}, outputs::Vector{…}, disturbance_inputs::Vector{…}, split::Bool, kwargs::@Kwargs{…})
@ ModelingToolkitBase ~/.julia/packages/ModelingToolkitBase/gJDou/src/systems/systems.jl:100
[8] mtkcompile
@ ~/.julia/packages/ModelingToolkitBase/gJDou/src/systems/systems.jl:84 [inlined]
[9] InitializationProblem{…}(sys::System, t::Float64, op::ModelingToolkitBase.AtomicArrayDict{…}; fast_path::Bool, guesses::Dict{…}, check_length::Nothing, warn_initialize_determined::Bool, initialization_eqs::Vector{…}, fully_determined::Nothing, check_units::Bool, allow_incomplete::Bool, algebraic_only::Bool, time_dependent_init::Bool, initsys_mtkcompile_kwargs::@NamedTuple{}, is_steadystateprob::Bool, kwargs::@Kwargs{…})
@ ModelingToolkitBase ~/.julia/packages/ModelingToolkitBase/gJDou/src/problems/initializationproblem.jl:97
[10] InitializationProblem
@ ~/.julia/packages/ModelingToolkitBase/gJDou/src/problems/initializationproblem.jl:25 [inlined]
[11] #_#910
@ ./none:0 [inlined]
[12] maybe_build_initialization_problem(sys::System, iip::Bool, op::ModelingToolkitBase.AtomicArrayDict{…}, t::Float64, guesses::Dict{…}; time_dependent_init::Bool, u0_constructor::Function, p_constructor::Function, floatT::Type, initialization_eqs::Vector{…}, use_scc::Bool, eval_expression::Bool, eval_module::Module, missing_guess_value::ModelingToolkitBase.MissingGuessValue.var"typeof(MissingGuessValue)", implicit_dae::Bool, is_steadystateprob::Bool, expression::Type, kwargs::@Kwargs{…})
@ ModelingToolkitBase ~/.julia/packages/ModelingToolkitBase/gJDou/src/systems/problem_utils.jl:1610
[13] __process_SciMLProblem(constructor::Type, sys::System, op::Dict{…}; floatT::Type, u0Type::Type, u0_eltype::Type, build_initializeprob::Bool, implicit_dae::Bool, t::Float64, guesses::Dict{…}, warn_initialize_determined::Bool, initialization_eqs::Vector{…}, eval_expression::Bool, eval_module::Module, fully_determined::Nothing, check_initialization_units::Bool, tofloat::Bool, u0_constructor::typeof(identity), p_constructor::typeof(identity), check_length::Bool, symbolic_u0::Bool, warn_cyclic_dependency::Bool, circular_dependency_max_cycle_length::Int64, circular_dependency_max_cycles::Int64, initsys_mtkcompile_kwargs::@NamedTuple{}, substitution_limit::Int64, use_scc::Bool, time_dependent_init::Bool, algebraic_only::Bool, missing_guess_value::ModelingToolkitBase.MissingGuessValue.var"typeof(MissingGuessValue)", allow_incomplete::Bool, is_initializeprob::Bool, is_steadystateprob::Bool, return_operating_point::Bool, compiler_options::CompilerOptions, init_compiler_options::CompilerOptions, kwargs::@Kwargs{…})
@ ModelingToolkitBase ~/.julia/packages/ModelingToolkitBase/gJDou/src/systems/problem_utils.jl:2016
[14] process_SciMLProblem(constructor::Any, sys::System, op::Any; u0_eltype::Nothing, u0_constructor::Function, p_constructor::Function, symbolic_u0::Bool, kwargs::@Kwargs{…})
@ ModelingToolkitBase ~/.julia/packages/ModelingToolkitBase/gJDou/src/systems/problem_utils.jl:1965
[15] (SDDEProblem{…})(sys::System, op::Vector{…}, tspan::Tuple{…}; callback::Nothing, check_length::Bool, checkbounds::Bool, eval_expression::Bool, eval_module::Module, check_compatibility::Bool, u0_constructor::typeof(identity), sparse::Bool, sparsenoise::Bool, expression::Type, kwargs::@Kwargs{})
@ ModelingToolkitBase ~/.julia/packages/ModelingToolkitBase/gJDou/src/problems/sddeproblem.jl:74
[16] SDDEProblem
@ ~/.julia/packages/ModelingToolkitBase/gJDou/src/problems/sddeproblem.jl:63 [inlined]
[17] SDDEProblem
@ ./none:0 [inlined]
[18] SDDEProblem(sys::System, op::Vector{Any}, tspan::Tuple{Float64, Float64})
@ ModelingToolkitBase ./none:0
[19] top-level scope
@ ~/Documents/SomeProject/src/models/test.jl:42
Some type information was truncated. Use `show(err)` to see complete types.
```
Calling `mtkcompile()` on the `connected_model` removes the `sth₊x(t)` unknown.
```Julia
unknowns(connected_model)
4-element Vector{SymbolicUtils.BasicSymbolicImpl.var"typeof(BasicSymbolicImpl)"{SymReal}}:
lv₊x(t)
lv₊y(t)
sth₊z(t)
sth₊x(t)
```
```Julia
unknowns(connected)
3-element Vector{SymbolicUtils.BasicSymbolicImpl.var"typeof(BasicSymbolicImpl)"{SymReal}}:
sth₊z(t)
lv₊y(t)
lv₊x(t)
```
I’d appreciate any help regarding this issue. Thanks!
---
### Author:  [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)
#### Post date: [August 17, 2026, 8:06am UTC](https://discourse.julialang.org/t/mtk-sdde-argumenterror-when-connecting-two-components/138861/2 "2026-08-17T08:06:46Z")
Open an issue for this.
---
### Author:  [@bebrunn](https://discourse.julialang.org/u/bebrunn)
#### Post date: [August 17, 2026, 9:27am UTC](https://discourse.julialang.org/t/mtk-sdde-argumenterror-when-connecting-two-components/138861/3 "2026-08-17T09:27:25Z")
Hi Chris, I created the [issue](https://github.com/SciML/ModelingToolkit.jl/issues/4985). Thanks for the reply!
---
### Author:  [@kahliburke](https://discourse.julialang.org/u/kahliburke)
#### Post date: [August 17, 2026, 1:10pm UTC](https://discourse.julialang.org/t/mtk-sdde-argumenterror-when-connecting-two-components/138861/4 "2026-08-17T13:10:31Z")
> [@bebrunn](#):
>
> I am trying to connect two MTK `components` and then solve the resulting `SDDE` system. However, I am getting an `ArgumentsError` that I don’t understand.
I’m hopeful that this document might help you work around the issue. It also details more about why it’s happening.
> **[Delayed signals between ModelingToolkit components](https://discourse-answers.pages.dev/delayed-signals-between-modelingtoolkit-components/)**
>
> Notes on SciML/ModelingToolkit.jl4985(https://github.com/SciML/ModelingToolkit.jl/issues/4985)
---
### Author:  [@bebrunn](https://discourse.julialang.org/u/bebrunn)
#### Post date: [August 18, 2026, 7:31am UTC](https://discourse.julialang.org/t/mtk-sdde-argumenterror-when-connecting-two-components/138861/5 "2026-08-18T07:31:57Z")
Thank you very much for the detailed reply! I read the document and am currently implementing the work around.
---
### Author:  [@bebrunn](https://discourse.julialang.org/u/bebrunn)
#### Post date: [August 18, 2026, 9:46am UTC](https://discourse.julialang.org/t/mtk-sdde-argumenterror-when-connecting-two-components/138861/6 "2026-08-18T09:46:29Z")
The solution works and I could make the example run. However, when translating the MRE to a more complex problem I observed slightly deviating solutions when setting tau = 0 (SDDE with t = 0 vs. SDE solution). I employ the same random seed and the deviations are marginal, however, is that something which is expected?
---
### Author:  [@kahliburke](https://discourse.julialang.org/u/kahliburke)
#### Post date: [August 18, 2026, 10:02am UTC](https://discourse.julialang.org/t/mtk-sdde-argumenterror-when-connecting-two-components/138861/7 "2026-08-18T10:02:01Z")
> [@bebrunn](#):
>
> I observed slightly deviating solutions when setting tau = 0
Yes: it’s expected, because seed doesn’t give you the same Brownian path across an SDE and an SDDE (they build their noise processes independently), so compare deterministically with the brownians dropped instead, where τ=0 matches the ODE to 1e-9.
---
### Author:  [@bebrunn](https://discourse.julialang.org/u/bebrunn)
#### Post date: [August 18, 2026, 11:38am UTC](https://discourse.julialang.org/t/mtk-sdde-argumenterror-when-connecting-two-components/138861/8 "2026-08-18T11:38:45Z")
Great. Thank you for your help!