I am trying to describe a second order stochastic differential equation with something like:
using ModelingToolkit
import ModelingToolkit: t_nounits as t, D_nounits as D
function NoisyHarmonic(; name, x0, ω, Q)
@parameters ω=ω Q=Q
@variables x(t) = x0
@brownians B
System([D(D(x)) + ω/Q * D(x) + + ω^2 * x ~ B], t; name)
end
@mtkcompile osc = NoisyHarmonic(; x0 = 1.0, ω = 1.0, Q = 100.0)Which I would expect to "just work", however, I get a Differential(t, 1)(xˍt(t)) isn't handled. error from it. Removing the brownian parameter works, manually "first-orderizing" the differential is of course possible, but not as ergonomic as I would expect ModelingToolkit wants to be.
Error & Stacktrace ⚠️
julia> show(err)
1-element ExceptionStack:
LoadError: Differential(t, 1)(xˍt(t)) isn't handled.
Stacktrace:
[1] error(s::String)
@ Base ./error.jl:44
[2] __mtkcompile(sys::System; inputs::OrderedCollections.OrderedSet{SymbolicUtils.BasicSymbolicImpl.var"typeof(BasicSymbolicImpl)"{SymReal}}, outputs::OrderedCollections.OrderedSet{SymbolicUtils.BasicSymbolicImpl.var"typeof(BasicSymbolicImpl)"{SymReal}}, disturbance_inputs::OrderedCollections.OrderedSet{SymbolicUtils.BasicSymbolicImpl.var"typeof(BasicSymbolicImpl)"{SymReal}}, sort_eqs::Bool, kwargs::@Kwargs{additional_passes::Tuple{}})
@ ModelingToolkit ~/.julia/packages/ModelingToolkit/GtdTx/src/systems/systems.jl:100
[3] __mtkcompile
@ ~/.julia/packages/ModelingToolkit/GtdTx/src/systems/systems.jl:23 [inlined]
[4] simplify_sde_system(sys::System; kwargs::@Kwargs{inputs::OrderedCollections.OrderedSet{SymbolicUtils.BasicSymbolicImpl.var"typeof(BasicSymbolicImpl)"{SymReal}}, outputs::OrderedCollections.OrderedSet{SymbolicUtils.BasicSymbolicImpl.var"typeof(BasicSymbolicImpl)"{SymReal}}, disturbance_inputs::OrderedCollections.OrderedSet{SymbolicUtils.BasicSymbolicImpl.var"typeof(BasicSymbolicImpl)"{SymReal}}, additional_passes::Tuple{}})
@ ModelingToolkit ~/.julia/packages/ModelingToolkit/GtdTx/src/systems/systems.jl:151
[5] simplify_sde_system
@ ~/.julia/packages/ModelingToolkit/GtdTx/src/systems/systems.jl:150 [inlined]
[6] _mtkcompile(sys::System; kwargs::@Kwargs{inputs::OrderedCollections.OrderedSet{SymbolicUtils.BasicSymbolicImpl.var"typeof(BasicSymbolicImpl)"{SymReal}}, outputs::OrderedCollections.OrderedSet{SymbolicUtils.BasicSymbolicImpl.var"typeof(BasicSymbolicImpl)"{SymReal}}, disturbance_inputs::OrderedCollections.OrderedSet{SymbolicUtils.BasicSymbolicImpl.var"typeof(BasicSymbolicImpl)"{SymReal}}, additional_passes::Tuple{}})
@ ModelingToolkitBase ~/.julia/packages/ModelingToolkitBase/tQDig/src/systems/systems.jl:153
[7] _mtkcompile
@ ~/.julia/packages/ModelingToolkitBase/tQDig/src/systems/systems.jl:128 [inlined]
[8] mtkcompile(sys::System; additional_passes::Tuple{}, inputs::Vector{SymbolicUtils.BasicSymbolicImpl.var"typeof(BasicSymbolicImpl)"{SymReal}}, outputs::Vector{SymbolicUtils.BasicSymbolicImpl.var"typeof(BasicSymbolicImpl)"{SymReal}}, disturbance_inputs::Vector{SymbolicUtils.BasicSymbolicImpl.var"typeof(BasicSymbolicImpl)"{SymReal}}, split::Bool, kwargs::@Kwargs{})
@ ModelingToolkitBase ~/.julia/packages/ModelingToolkitBase/tQDig/src/systems/systems.jl:100
[9] mtkcompile(sys::System)
@ ModelingToolkitBase ~/.julia/packages/ModelingToolkitBase/tQDig/src/systems/systems.jl:84Environment (please complete the following information):
This is in a clean, temporary environment with just ModelingToolkit installed:
- Output of
using Pkg; Pkg.status()
Status `/private/var/folders/gy/vxg0vt315071jkrhkhxj8_4w0000gn/T/jl_FW2TQc/Project.toml`
[961ee093] ModelingToolkit v11.38.0
Output of `using Pkg; Pkg.status(; mode = PKGMODE_MANIFEST)`
Status `/private/var/folders/gy/vxg0vt315071jkrhkhxj8_4w0000gn/T/jl_FW2TQc/Manifest.toml`
[47edcb42] ADTypes v1.22.3
[14f7f29c] AMD v0.5.3
[6e696c72] AbstractPlutoDingetjes v1.4.0
[1520ce14] AbstractTrees v0.4.5
[7d9f7c33] Accessors v0.1.45
[79e6a3ab] Adapt v4.7.0
[ec485272] ArnoldiMethod v0.4.0
[4fba245c] ArrayInterface v7.28.1
[4c555306] ArrayLayouts v1.12.2
[aae01518] BandedMatrices v1.11.0
[e2ed5e7c] Bijections v0.2.2
[b2a6c25c] BinaryHeaps v1.0.4
[caf10ac8] BipartiteGraphs v0.1.10
[8e7c35d0] BlockArrays v1.10.0
[70df07ce] BracketingNonlinearSolve v1.12.4
⌅ [861a8166] Combinatorics v1.0.2 [loaded: v1.1.0]
[38540f10] CommonSolve v0.2.12
[bbf7d656] CommonSubexpressions v0.3.1
[f70d9fcc] CommonWorldInvalidations v1.1.2
[34da2185] Compat v4.18.1
[b152e2b5] CompositeTypes v0.1.4
[a33af91c] CompositionsBase v0.1.2
[2569d6c7] ConcreteStructs v0.2.7
[187b0558] ConstructionBase v1.6.0
[a8cc5b0e] Crayons v4.2.0 [loaded: v4.1.1]
[9a962f9c] DataAPI v1.16.0
[864edb3b] DataStructures v0.19.6
[e2d170a0] DataValueInterfaces v1.0.0
[2b5f629d] DiffEqBase v7.10.0
[459566f4] DiffEqCallbacks v4.19.0
[163ba53b] DiffResults v1.1.0
[b552c78f] DiffRules v1.16.0
[a0c0ee7d] DifferentiationInterface v0.7.20
[ffbed154] DocStringExtensions v0.9.5
[5b8099bc] DomainSets v0.8.1
[7c1d4256] DynamicPolynomials v0.6.6
[4e289a0a] EnumX v1.0.7
[f151be2c] EnzymeCore v0.8.21
[e2ba6199] ExprTools v0.1.11
[55351af7] ExproniconLite v0.10.14
[7034ab61] FastBroadcast v1.3.5
[9aa1b823] FastClosures v0.3.2
[a4df4552] FastPower v1.4.0
[1a297f60] FillArrays v1.17.0
[64ca27bc] FindFirstFunctions v3.2.1
[6a86dc24] FiniteDiff v2.32.0
[f6369f11] ForwardDiff v1.4.4
[a85aefff] FunctionMaps v0.1.2
[069b7b12] FunctionWrappers v1.1.3
[77dc65aa] FunctionWrappersWrappers v1.12.0
[46192b85] GPUArraysCore v0.2.0
[86223c79] Graphs v1.14.0
[3263718b] ImplicitDiscreteSolve v2.1.5
[d25df0c9] Inflate v0.1.5
[18e54dd8] IntegerMathUtils v0.1.4
[8197267c] IntervalSets v0.7.14
[3587e190] InverseFunctions v0.1.17
[92d709cd] IrrationalConstants v0.2.6
[82899510] IteratorInterfaceExtensions v1.0.0
[692b3bcd] JLLWrappers v1.8.0
[ae98c720] Jieko v0.2.1
[ccbc3e58] JumpProcesses v9.29.2
[ba0b0d4f] Krylov v0.10.9
[b964fa9f] LaTeXStrings v1.4.0
[87fe0de2] LineSearch v0.1.12
[7ed4a6bd] LinearSolve v5.4.0
[2ab3a3ac] LogExpFunctions v1.0.1
[e6f89c97] LoggingExtras v1.2.0
[1914dd2f] MacroTools v0.5.16
[bb5d69b7] MaybeInplace v0.1.7
[961ee093] ModelingToolkit v11.38.0
[7771a370] ModelingToolkitBase v1.59.0
[6bb917b9] ModelingToolkitTearing v1.20.4
[2e0e35c7] Moshi v0.3.12
[46d2c3a1] MuladdMacro v0.2.7
[102ac46a] MultivariatePolynomials v0.5.19
[d8a4904e] MutableArithmetics v1.8.0
[77ba4419] NaNMath v1.1.4
[be0214bd] NonlinearSolveBase v2.39.1
[5959db7a] NonlinearSolveFirstOrder v2.2.3
[6fe1bfb0] OffsetArrays v1.17.0
⌅ [bac558e1] OrderedCollections v1.8.2
[bbf590c4] OrdinaryDiffEqCore v4.12.0
[e409e4f3] PoissonRandom v0.4.13
[d236fae5] PreallocationTools v1.4.0
[aea7be01] PrecompileTools v1.3.4
[21216c6a] Preferences v1.5.2
[08abe8d2] PrettyTables v3.4.4
[27ebfcd6] Primes v0.5.7
[0c0d3e7f] PureKLU v1.2.0
[988b38a3] ReadOnlyArrays v0.2.0
[795d4caa] ReadOnlyDicts v1.0.1
[3cdcf5f2] RecipesBase v1.3.4
[731186ca] RecursiveArrayTools v4.3.5
[189a3867] Reexport v1.2.2
[9fe22ead] RespecializeParams v1.2.0
[7e49a35a] RuntimeGeneratedFunctions v0.5.24
[9dfe8606] SCCNonlinearSolve v1.14.0
[0bca4576] SciMLBase v3.41.0
[19f34311] SciMLJacobianOperators v0.1.16
[a6db7da4] SciMLLogging v2.0.3
[c0aeaf25] SciMLOperators v1.26.0
[431bcebd] SciMLPublic v1.2.4
[53ae85a6] SciMLStructures v1.10.4
[efcf1570] Setfield v1.1.2
[727e6d20] SimpleNonlinearSolve v2.13.1
[699a6c99] SimpleTraits v0.9.6
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[276daf66] SpecialFunctions v2.8.1
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[10745b16] Statistics v1.11.1
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[d1185830] SymbolicUtils v4.44.0
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[3783bdb8] TableTraits v1.0.1
[bd369af6] Tables v1.13.0
[ed4db957] TaskLocalValues v0.1.3
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[1317d2d5] oneTBB_jll v2022.3.0+0
[0dad84c5] ArgTools v1.1.2
[56f22d72] Artifacts v1.11.0
[2a0f44e3] Base64 v1.11.0
[ade2ca70] Dates v1.11.0
[8ba89e20] Distributed v1.11.0
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[9fa8497b] Future v1.11.0
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[56ddb016] Logging v1.11.0
[d6f4376e] Markdown v1.11.0
[ca575930] NetworkOptions v1.3.0
[44cfe95a] Pkg v1.12.1
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[3fa0cd96] REPL v1.11.0
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Julia Version 1.12.6
Commit 15346901f00 (2026-04-09 19:20 UTC)
Build Info:
Official https://julialang.org release
Platform Info:
OS: macOS (arm64-apple-darwin24.0.0)
CPU: 16 × Apple M4 Max
WORD_SIZE: 64
LLVM: libLLVM-18.1.7 (ORCJIT, apple-m4)
GC: Built with stock GC
Threads: 1 default, 1 interactive, 1 GC (on 12 virtual cores)
Environment:
JULIA_PKG_USE_CLI_GIT = true
JULIA_EDITOR = nvim
I am trying to describe a second order stochastic differential equation with something like:
Which I would expect to "just work", however, I get a
Differential(t, 1)(xˍt(t)) isn't handled.error from it. Removing the brownian parameter works, manually "first-orderizing" the differential is of course possible, but not as ergonomic as I would expectModelingToolkitwants to be.Error & Stacktrace⚠️
Environment (please complete the following information):
This is in a clean, temporary environment with just
ModelingToolkitinstalled:using Pkg; Pkg.status()Output of `using Pkg; Pkg.status(; mode = PKGMODE_MANIFEST)`
versioninfo()