Parameter identifiability example from docs fails

[moble]

Describe the bug 🐞

Following the example on this page results in

ERROR: Measured quantities (output functions) were not provided and no outputs were found.

I'm not sure that this package is really to blame. Maybe @pogudingleb could provide some insight?

Expected behavior

I would have thought that marking y1(t) and y2(t) with [output = true] would be enough to communicate that these are outputs.

Minimal Reproducible Example 👇

I've just copied the example code, but run it in a temp environment:

using Pkg
Pkg.activate(; temp=true)
Pkg.add(["StructuralIdentifiability", "ModelingToolkit"])


using StructuralIdentifiability, ModelingToolkit
using ModelingToolkit: t_nounits as t, D_nounits as D

@mtkmodel Biohydrogenation begin
    @variables begin
        x4(t)
        x5(t)
        x6(t)
        x7(t)
        y1(t), [output = true]
        y2(t), [output = true]
    end
    @parameters begin
        k5
        k6
        k7
        k8
        k9
        k10
    end
    # define equations
    @equations begin
        D(x4) ~ -k5 * x4 / (k6 + x4)
        D(x5) ~ k5 * x4 / (k6 + x4) - k7 * x5 / (k8 + x5 + x6)
        D(x6) ~ k7 * x5 / (k8 + x5 + x6) - k9 * x6 * (k10 - x6) / k10
        D(x7) ~ k9 * x6 * (k10 - x6) / k10
        y1 ~ x4
        y2 ~ x5
    end
end

# define the system
@mtkbuild de = Biohydrogenation()

# query local identifiability
# we pass the ode-system
local_id_all = assess_local_identifiability(de, prob_threshold = 0.99)

Error & Stacktrace ⚠️

ERROR: Measured quantities (output functions) were not provided and no outputs were found.
Stacktrace:
 [1] error(s::String)
   @ Base ./error.jl:35
 [2] macro expansion
   @ ~/.julia/packages/StructuralIdentifiability/GXfvN/ext/ModelingToolkitSIExt.jl:299 [inlined]
 [3] _assess_local_identifiability(ode::ODESystem; measured_quantities::Vector{…}, funcs_to_check::Vector{…}, prob_threshold::Float64, type::Symbol)
   @ ModelingToolkitSIExt ~/.julia/packages/TimerOutputs/Lw5SP/src/TimerOutput.jl:237
 [4] _assess_local_identifiability
   @ ~/.julia/packages/TimerOutputs/Lw5SP/src/TimerOutput.jl:230 [inlined]
 [5] (::ModelingToolkitSIExt.var"#42#43"{Vector{Array{Equation}}, Vector{Array}, Float64, Symbol, ODESystem})()
   @ ModelingToolkitSIExt ~/.julia/packages/StructuralIdentifiability/GXfvN/ext/ModelingToolkitSIExt.jl:274
 [6] with_logstate(f::Function, logstate::Any)
   @ Base.CoreLogging ./logging.jl:515
 [7] with_logger
   @ ./logging.jl:627 [inlined]
 [8] assess_local_identifiability(ode::ODESystem; measured_quantities::Vector{…}, funcs_to_check::Vector{…}, prob_threshold::Float64, type::Symbol, loglevel::Base.CoreLogging.LogLevel)
   @ ModelingToolkitSIExt ~/.julia/packages/StructuralIdentifiability/GXfvN/ext/ModelingToolkitSIExt.jl:273
 [9] top-level scope
   @ ~/.julia/dev/PostNewtonian/notes/modeling_toolkit/structural_identifiability_bug.jl:42
Some type information was truncated. Use `show(err)` to see complete types.

Environment (please complete the following information):

• Output of using Pkg; Pkg.status()

Status `/private/var/folders/bh/rg4bdsl965l0572z3vtmwkr40000gn/T/jl_B1llWc/Project.toml`
  [961ee093] ModelingToolkit v9.25.0
  [220ca800] StructuralIdentifiability v0.5.8

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

Status `/private/var/folders/bh/rg4bdsl965l0572z3vtmwkr40000gn/T/jl_B1llWc/Manifest.toml`
  [47edcb42] ADTypes v1.6.1
⌅ [c3fe647b] AbstractAlgebra v0.41.10
  [1520ce14] AbstractTrees v0.4.5
  [7d9f7c33] Accessors v0.1.36
  [79e6a3ab] Adapt v4.0.4
  [66dad0bd] AliasTables v1.1.3
  [ec485272] ArnoldiMethod v0.4.0
  [4fba245c] ArrayInterface v7.12.0
  [4c555306] ArrayLayouts v1.10.2
  [a9b6321e] Atomix v0.1.0
  [e2ed5e7c] Bijections v0.1.7
  [62783981] BitTwiddlingConvenienceFunctions v0.1.6
  [2a0fbf3d] CPUSummary v0.2.6
  [00ebfdb7] CSTParser v3.4.3
  [49dc2e85] Calculus v0.5.1
  [d360d2e6] ChainRulesCore v1.24.0
  [fb6a15b2] CloseOpenIntervals v0.1.13
  [861a8166] Combinatorics v1.0.2
  [a80b9123] CommonMark v0.8.12
  [38540f10] CommonSolve v0.2.4
  [bbf7d656] CommonSubexpressions v0.3.0
  [f70d9fcc] CommonWorldInvalidations v1.0.0
  [34da2185] Compat v4.15.0
  [b152e2b5] CompositeTypes v0.1.4
  [a33af91c] CompositionsBase v0.1.2
  [2569d6c7] ConcreteStructs v0.2.3
  [187b0558] ConstructionBase v1.5.5
  [adafc99b] CpuId v0.3.1
  [a8cc5b0e] Crayons v4.1.1
  [9a962f9c] DataAPI v1.16.0
  [864edb3b] DataStructures v0.18.20
  [e2d170a0] DataValueInterfaces v1.0.0
  [2b5f629d] DiffEqBase v6.151.5
  [459566f4] DiffEqCallbacks v3.6.2
  [163ba53b] DiffResults v1.1.0
  [b552c78f] DiffRules v1.15.1
  [a0c0ee7d] DifferentiationInterface v0.5.9
  [31c24e10] Distributions v0.25.109
  [ffbed154] DocStringExtensions v0.9.3
  [5b8099bc] DomainSets v0.7.14
  [fa6b7ba4] DualNumbers v0.6.8
⌅ [7c1d4256] DynamicPolynomials v0.5.7
⌅ [06fc5a27] DynamicQuantities v0.13.2
  [4e289a0a] EnumX v1.0.4
  [f151be2c] EnzymeCore v0.7.7
  [e2ba6199] ExprTools v0.1.10
  [7034ab61] FastBroadcast v0.3.4
  [9aa1b823] FastClosures v0.3.2
  [29a986be] FastLapackInterface v2.0.4
  [1a297f60] FillArrays v1.11.0
  [64ca27bc] FindFirstFunctions v1.2.0
  [6a86dc24] FiniteDiff v2.23.1
  [1fa38f19] Format v1.3.7
  [f6369f11] ForwardDiff v0.10.36
  [069b7b12] FunctionWrappers v1.1.3
  [77dc65aa] FunctionWrappersWrappers v0.1.3
  [d9f16b24] Functors v0.4.11
  [46192b85] GPUArraysCore v0.1.6
  [c27321d9] Glob v1.3.1
  [86223c79] Graphs v1.11.2
  [0b43b601] Groebner v0.7.5
  [3e5b6fbb] HostCPUFeatures v0.1.17
  [34004b35] HypergeometricFunctions v0.3.23
  [615f187c] IfElse v0.1.1
  [d25df0c9] Inflate v0.1.5
  [18e54dd8] IntegerMathUtils v0.1.2
  [8197267c] IntervalSets v0.7.10
  [3587e190] InverseFunctions v0.1.15
  [92d709cd] IrrationalConstants v0.2.2
  [c8e1da08] IterTools v1.10.0
  [82899510] IteratorInterfaceExtensions v1.0.0
  [692b3bcd] JLLWrappers v1.5.0
  [682c06a0] JSON v0.21.4
  [98e50ef6] JuliaFormatter v1.0.58
  [ccbc3e58] JumpProcesses v9.11.1
  [ef3ab10e] KLU v0.6.0
  [ba0b0d4f] Krylov v0.9.6
  [b964fa9f] LaTeXStrings v1.3.1
  [2ee39098] LabelledArrays v1.16.0
  [984bce1d] LambertW v0.4.6
  [23fbe1c1] Latexify v0.16.4
  [10f19ff3] LayoutPointers v0.1.17
  [5078a376] LazyArrays v2.1.9
  [d3d80556] LineSearches v7.2.0
  [7ed4a6bd] LinearSolve v2.30.2
  [2ab3a3ac] LogExpFunctions v0.3.28
  [bdcacae8] LoopVectorization v0.12.171
  [d8e11817] MLStyle v0.4.17
  [1914dd2f] MacroTools v0.5.13
  [d125e4d3] ManualMemory v0.1.8
  [bb5d69b7] MaybeInplace v0.1.3
  [e1d29d7a] Missings v1.2.0
  [961ee093] ModelingToolkit v9.25.0
  [46d2c3a1] MuladdMacro v0.2.4
  [102ac46a] MultivariatePolynomials v0.5.6
  [d8a4904e] MutableArithmetics v1.4.5
  [d41bc354] NLSolversBase v7.8.3
  [77ba4419] NaNMath v1.0.2
⌅ [2edaba10] Nemo v0.45.7
  [8913a72c] NonlinearSolve v3.13.1
  [6fe1bfb0] OffsetArrays v1.14.1
  [bac558e1] OrderedCollections v1.6.3
  [90014a1f] PDMats v0.11.31
  [65ce6f38] PackageExtensionCompat v1.0.2
  [3e851597] ParamPunPam v0.4.1
  [d96e819e] Parameters v0.12.3
  [69de0a69] Parsers v2.8.1
  [e409e4f3] PoissonRandom v0.4.4
  [f517fe37] Polyester v0.7.15
  [1d0040c9] PolyesterWeave v0.2.2
  [d236fae5] PreallocationTools v0.4.22
  [aea7be01] PrecompileTools v1.2.1
  [21216c6a] Preferences v1.4.3
  [08abe8d2] PrettyTables v2.3.2
  [27ebfcd6] Primes v0.5.6
  [92933f4c] ProgressMeter v1.10.2
  [43287f4e] PtrArrays v1.2.0
  [1fd47b50] QuadGK v2.9.4
  [fb686558] RandomExtensions v0.4.4
  [e6cf234a] RandomNumbers v1.5.3
  [3cdcf5f2] RecipesBase v1.3.4
  [731186ca] RecursiveArrayTools v3.26.0
  [f2c3362d] RecursiveFactorization v0.2.23
  [189a3867] Reexport v1.2.2
  [ae029012] Requires v1.3.0
  [79098fc4] Rmath v0.7.1
  [7e49a35a] RuntimeGeneratedFunctions v0.5.13
  [94e857df] SIMDTypes v0.1.0
  [476501e8] SLEEFPirates v0.6.43
  [0bca4576] SciMLBase v2.43.0
  [c0aeaf25] SciMLOperators v0.3.8
  [53ae85a6] SciMLStructures v1.4.1
  [efcf1570] Setfield v1.1.1
  [727e6d20] SimpleNonlinearSolve v1.10.1
  [699a6c99] SimpleTraits v0.9.4
  [a2af1166] SortingAlgorithms v1.2.1
  [47a9eef4] SparseDiffTools v2.19.0
  [0a514795] SparseMatrixColorings v0.3.5
  [e56a9233] Sparspak v0.3.9
  [276daf66] SpecialFunctions v2.4.0
  [aedffcd0] Static v1.1.1
  [0d7ed370] StaticArrayInterface v1.5.1
  [90137ffa] StaticArrays v1.9.7
  [1e83bf80] StaticArraysCore v1.4.3
  [82ae8749] StatsAPI v1.7.0
  [2913bbd2] StatsBase v0.34.3
  [4c63d2b9] StatsFuns v1.3.1
  [7792a7ef] StrideArraysCore v0.5.7
  [892a3eda] StringManipulation v0.3.4
  [220ca800] StructuralIdentifiability v0.5.8
  [2efcf032] SymbolicIndexingInterface v0.3.26
  [19f23fe9] SymbolicLimits v0.2.1
  [d1185830] SymbolicUtils v2.1.2
  [0c5d862f] Symbolics v5.34.0
  [3783bdb8] TableTraits v1.0.1
  [bd369af6] Tables v1.12.0
⌅ [8ea1fca8] TermInterface v0.4.1
  [8290d209] ThreadingUtilities v0.5.2
  [a759f4b9] TimerOutputs v0.5.24
  [0796e94c] Tokenize v0.5.29
  [d5829a12] TriangularSolve v0.2.1
  [410a4b4d] Tricks v0.1.8
  [781d530d] TruncatedStacktraces v1.4.0
  [5c2747f8] URIs v1.5.1
  [3a884ed6] UnPack v1.0.2
  [1986cc42] Unitful v1.21.0
  [a7c27f48] Unityper v0.1.6
  [013be700] UnsafeAtomics v0.2.1
  [3d5dd08c] VectorizationBase v0.21.70
  [19fa3120] VertexSafeGraphs v0.2.0
  [e134572f] FLINT_jll v300.100.300+0
  [1d5cc7b8] IntelOpenMP_jll v2024.2.0+0
  [856f044c] MKL_jll v2024.2.0+0
⌅ [656ef2d0] OpenBLAS32_jll v0.3.24+0
  [efe28fd5] OpenSpecFun_jll v0.5.5+0
  [f50d1b31] Rmath_jll v0.4.2+0
  [1317d2d5] oneTBB_jll v2021.12.0+0
  [0dad84c5] ArgTools v1.1.1
  [56f22d72] Artifacts
  [2a0f44e3] Base64
  [ade2ca70] Dates
  [8ba89e20] Distributed
  [f43a241f] Downloads v1.6.0
  [7b1f6079] FileWatching
  [9fa8497b] Future
  [b77e0a4c] InteractiveUtils
  [4af54fe1] LazyArtifacts
  [b27032c2] LibCURL v0.6.4
  [76f85450] LibGit2
  [8f399da3] Libdl
  [37e2e46d] LinearAlgebra
  [56ddb016] Logging
  [d6f4376e] Markdown
  [a63ad114] Mmap
  [ca575930] NetworkOptions v1.2.0
  [44cfe95a] Pkg v1.10.0
  [de0858da] Printf
  [3fa0cd96] REPL
  [9a3f8284] Random
  [ea8e919c] SHA v0.7.0
  [9e88b42a] Serialization
  [1a1011a3] SharedArrays
  [6462fe0b] Sockets
  [2f01184e] SparseArrays v1.10.0
  [10745b16] Statistics v1.10.0
  [4607b0f0] SuiteSparse
  [fa267f1f] TOML v1.0.3
  [a4e569a6] Tar v1.10.0
  [8dfed614] Test
  [cf7118a7] UUIDs
  [4ec0a83e] Unicode
  [e66e0078] CompilerSupportLibraries_jll v1.1.1+0
  [781609d7] GMP_jll v6.2.1+6
  [deac9b47] LibCURL_jll v8.4.0+0
  [e37daf67] LibGit2_jll v1.6.4+0
  [29816b5a] LibSSH2_jll v1.11.0+1
  [3a97d323] MPFR_jll v4.2.0+1
  [c8ffd9c3] MbedTLS_jll v2.28.2+1
  [14a3606d] MozillaCACerts_jll v2023.1.10
  [4536629a] OpenBLAS_jll v0.3.23+4
  [05823500] OpenLibm_jll v0.8.1+2
  [bea87d4a] SuiteSparse_jll v7.2.1+1
  [83775a58] Zlib_jll v1.2.13+1
  [8e850b90] libblastrampoline_jll v5.8.0+1
  [8e850ede] nghttp2_jll v1.52.0+1
  [3f19e933] p7zip_jll v17.4.0+2
Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated -m`

• Output of versioninfo()

Julia Version 1.10.4
Commit 48d4fd48430 (2024-06-04 10:41 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: macOS (arm64-apple-darwin22.4.0)
  CPU: 12 × Apple M2 Max
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-15.0.7 (ORCJIT, apple-m1)
Threads: 8 default, 0 interactive, 4 GC (on 8 virtual cores)
Environment:
  JULIA_EDITOR = code

[pogudingleb]

@moble
Thanks for reporting! This is indeed a big in the interface, this particular way of defining models does not quite work in the current versions. I am refactoring right now ModelingToolkit interface, I will fix this as well.

For the time being, you can just pass the observed quantities to the function directly like this

using StructuralIdentifiability, ModelingToolkit
using ModelingToolkit: t_nounits as t, D_nounits as D

@mtkmodel Biohydrogenation begin
    @variables begin
        x4(t)
        x5(t)
        x6(t)
        x7(t)
        y1(t), [output = true]
        y2(t), [output = true]
    end
    @parameters begin
        k5
        k6
        k7
        k8
        k9
        k10
    end
    # define equations
    @equations begin
        D(x4) ~ -k5 * x4 / (k6 + x4)
        D(x5) ~ k5 * x4 / (k6 + x4) - k7 * x5 / (k8 + x5 + x6)
        D(x6) ~ k7 * x5 / (k8 + x5 + x6) - k9 * x6 * (k10 - x6) / k10
        D(x7) ~ k9 * x6 * (k10 - x6) / k10
    end
end

# define the system
@mtkbuild de = Biohydrogenation()

x4, x5, x6, x7 = unknowns(de)

# query local identifiability
# we pass the ode-system
local_id_all = assess_local_identifiability(de, measured_quantities = [x4, x5], prob_threshold = 0.99)

[moble]

Thanks for looking into this, Gleb! Since posting this, I took a look too and found ModelingToolkit.observed. Is this what you need? In particular, could you change the signatures in your extension to use that as a default value, like this:

function StructuralIdentifiability.find_identifiable_functions(
    ode::ModelingToolkit.ODESystem;
    measured_quantities = ModelingToolkit.observed(ode),

Thanks for your help!

[pogudingleb]

Thanks for looking into this, Gleb! Since posting this, I took a look too and found ModelingToolkit.observed. Is this what you need? In particular, could you change the signatures in your extension to use that as a default value, like this:

function StructuralIdentifiability.find_identifiable_functions(
    ode::ModelingToolkit.ODESystem;
    measured_quantities = ModelingToolkit.observed(ode),

Thanks for your help!

Thanks! We indeed used observed before (but in a less nice way as you proposed) but this code was lost in some transformations and, apparently, was not covered in the tests. I will fix this for the next release.

[pogudingleb]

@moble Thanks again for reporting this!
The example should work with the new release of StructuralIdentifiability (0.5.9) as you wrote it originally.

[moble]

Works like a charm. Thanks!