BifurcationProblem drops observed variables from ODESystem

[mjowen]

Describe the bug 🐞

Using observed variables in the RHS of an ODESystem leads to errors when computing bifurcation diagrams.

Expected behavior

A bifurcation diagram should be plotted, instead an error is thrown because the observed variable is not defined.

Minimal Reproducible Example 👇

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

@mtkmodel FOL begin
    @parameters begin
        τ # parameters
    end
    @variables begin
        x(t) # dependent variables
        RHS(t)
    end
    @equations begin
        RHS ~ (1 - x) / τ
        D(x) ~ RHS
    end
end

@mtkbuild fol = FOL()

par = [fol.τ => 1.]
u0 = [fol.x => 1.]
prob = ODEProblem(fol, u0, (0.0, 1.), par)

bif_par = fol.τ

bp = BifurcationProblem(fol, u0, par, bif_par)

opts_br = ContinuationPar(p_min = 0.5,
    p_max = 2.)

bf = bifurcationdiagram(bp, PALC(), 2, opts_br)

Error & Stacktrace ⚠️

ERROR: UndefVarError: `RHS` not defined
Stacktrace:
  [1] macro expansion
    @ C:\Users\pmzmo\.julia\packages\SymbolicUtils\EGhOJ\src\code.jl:468 [inlined]
  [2] macro expansion
    @ C:\Users\pmzmo\.julia\packages\RuntimeGeneratedFunctions\M9ZX8\src\RuntimeGeneratedFunctions.jl:163 [inlined]
  [3] macro expansion
    @ .\none:0 [inlined]
  [4] generated_callfunc
    @ .\none:0 [inlined]
  [5] (::RuntimeGeneratedFunctions.RuntimeGeneratedFunction{…})(::Vector{…}, ::Vector{…})
    @ RuntimeGeneratedFunctions C:\Users\pmzmo\.julia\packages\RuntimeGeneratedFunctions\M9ZX8\src\RuntimeGeneratedFunctions.jl:150
  [6] f
    @ C:\Users\pmzmo\.julia\packages\ModelingToolkit\U2JaS\src\systems\nonlinear\nonlinearsystem.jl:289 [inlined]
  [7] residual
    @ C:\Users\pmzmo\.julia\packages\BifurcationKit\2LYxR\src\Problems.jl:69 [inlined]
  [8] residual
    @ C:\Users\pmzmo\.julia\packages\BifurcationKit\2LYxR\src\Problems.jl:269 [inlined]
  [9] _newton(prob::BifurcationProblem{…}, x0::Vector{…}, p0::Vector{…}, options::NewtonPar{…}; normN::typeof(LinearAlgebra.norm), callback::typeof(BifurcationKit.cb_default), kwargs::@Kwargs{…})
    @ BifurcationKit C:\Users\pmzmo\.julia\packages\BifurcationKit\2LYxR\src\Newton.jl:75
 [10] _newton
    @ C:\Users\pmzmo\.julia\packages\BifurcationKit\2LYxR\src\Newton.jl:67 [inlined]
 [11] newton
    @ C:\Users\pmzmo\.julia\packages\BifurcationKit\2LYxR\src\Newton.jl:146 [inlined]
 [12] iterate(it::ContIterable{…}; _verbosity::UInt8)
    @ BifurcationKit C:\Users\pmzmo\.julia\packages\BifurcationKit\2LYxR\src\Continuation.jl:357
 [13] iterate
    @ C:\Users\pmzmo\.julia\packages\BifurcationKit\2LYxR\src\Continuation.jl:338 [inlined]
 [14] continuation(it::ContIterable{…})
    @ BifurcationKit C:\Users\pmzmo\.julia\packages\BifurcationKit\2LYxR\src\Continuation.jl:570
 [15] continuation(prob::BifurcationProblem{…}, alg::PALC{…}, contparams::ContinuationPar{…}; linear_algo::Nothing, bothside::Bool, kwargs::@Kwargs{})
    @ BifurcationKit C:\Users\pmzmo\.julia\packages\BifurcationKit\2LYxR\src\Continuation.jl:648
 [16] continuation
    @ C:\Users\pmzmo\.julia\packages\BifurcationKit\2LYxR\src\Continuation.jl:618 [inlined]
 [17] bifurcationdiagram(prob::BifurcationProblem{…}, alg::PALC{…}, level::Int64, options::BifurcationKit.var"#717#718"{…}; linear_algo::Nothing, kwargs::@Kwargs{})
    @ BifurcationKit C:\Users\pmzmo\.julia\packages\BifurcationKit\2LYxR\src\bifdiagram\BifurcationDiagram.jl:108
 [18] bifurcationdiagram
    @ C:\Users\pmzmo\.julia\packages\BifurcationKit\2LYxR\src\bifdiagram\BifurcationDiagram.jl:101 [inlined]
 [19] #bifurcationdiagram#716
    @ C:\Users\pmzmo\.julia\packages\BifurcationKit\2LYxR\src\bifdiagram\BifurcationDiagram.jl:120 [inlined]
 [20] bifurcationdiagram(prob::BifurcationProblem{…}, alg::PALC{…}, level::Int64, options::ContinuationPar{…})
    @ BifurcationKit C:\Users\pmzmo\.julia\packages\BifurcationKit\2LYxR\src\bifdiagram\BifurcationDiagram.jl:115
 [21] top-level scope
    @ c:\Users\pmzmo\OneDrive - The University of Nottingham\Documents\Julia\ContinuationForOptimisation\mre.jl:32
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 `C:\Users\pmzmo\.julia\environments\v1.10\Project.toml`
  [0f109fa4] BifurcationKit v0.3.6
  [03cb29e0] CellMLToolkit v2.12.0
  [187b0558] ConstructionBase v1.5.5
  [0c46a032] DifferentialEquations v7.13.0
  [61744808] DynamicalSystems v3.3.17
  [961ee093] ModelingToolkit v9.24.0
  [d96e819e] Parameters v0.12.3
  [91a5bcdd] Plots v1.40.5
  [295af30f] Revise v3.5.15

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

Status `C:\Users\pmzmo\.julia\environments\v1.10\Manifest.toml`
  [47edcb42] ADTypes v1.6.1
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  [13072b0f] AxisAlgorithms v1.1.0
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  [aed1982a] XSLT_jll v1.1.41+0
  [ffd25f8a] XZ_jll v5.4.6+0
  [f67eecfb] Xorg_libICE_jll v1.1.1+0
  [c834827a] Xorg_libSM_jll v1.2.4+0
  [4f6342f7] Xorg_libX11_jll v1.8.6+0
  [0c0b7dd1] Xorg_libXau_jll v1.0.11+0
  [935fb764] Xorg_libXcursor_jll v1.2.0+4
  [a3789734] Xorg_libXdmcp_jll v1.1.4+0
  [1082639a] Xorg_libXext_jll v1.3.6+0
  [d091e8ba] Xorg_libXfixes_jll v5.0.3+4
  [a51aa0fd] Xorg_libXi_jll v1.7.10+4
  [d1454406] Xorg_libXinerama_jll v1.1.4+4
  [ec84b674] Xorg_libXrandr_jll v1.5.2+4
  [ea2f1a96] Xorg_libXrender_jll v0.9.11+0
  [14d82f49] Xorg_libpthread_stubs_jll v0.1.1+0
  [c7cfdc94] Xorg_libxcb_jll v1.17.0+0
  [cc61e674] Xorg_libxkbfile_jll v1.1.2+0
  [e920d4aa] Xorg_xcb_util_cursor_jll v0.1.4+0
  [12413925] Xorg_xcb_util_image_jll v0.4.0+1
  [2def613f] Xorg_xcb_util_jll v0.4.0+1
  [975044d2] Xorg_xcb_util_keysyms_jll v0.4.0+1
  [0d47668e] Xorg_xcb_util_renderutil_jll v0.3.9+1
  [c22f9ab0] Xorg_xcb_util_wm_jll v0.4.1+1
  [35661453] Xorg_xkbcomp_jll v1.4.6+0
  [33bec58e] Xorg_xkeyboard_config_jll v2.39.0+0
  [c5fb5394] Xorg_xtrans_jll v1.5.0+0
  [3161d3a3] Zstd_jll v1.5.6+0
  [35ca27e7] eudev_jll v3.2.9+0
⌅ [214eeab7] fzf_jll v0.43.0+0
  [1a1c6b14] gperf_jll v3.1.1+0
  [a4ae2306] libaom_jll v3.9.0+0
  [0ac62f75] libass_jll v0.15.1+0
  [2db6ffa8] libevdev_jll v1.11.0+0
  [f638f0a6] libfdk_aac_jll v2.0.2+0
  [36db933b] libinput_jll v1.18.0+0
  [b53b4c65] libpng_jll v1.6.43+1
  [f27f6e37] libvorbis_jll v1.3.7+1
  [009596ad] mtdev_jll v1.1.6+0
  [1317d2d5] oneTBB_jll v2021.12.0+0
  [1270edf5] x264_jll v2021.5.5+0
  [dfaa095f] x265_jll v3.5.0+0
  [d8fb68d0] xkbcommon_jll v1.4.1+1
  [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
  [deac9b47] LibCURL_jll v8.4.0+0
  [e37daf67] LibGit2_jll v1.6.4+0
  [29816b5a] LibSSH2_jll v1.11.0+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
  [efcefdf7] PCRE2_jll v10.42.0+1
  [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 48d4fd4843 (2024-06-04 10:41 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Windows (x86_64-w64-mingw32)
  CPU: 4 × Intel(R) Core(TM) i3-8130U CPU @ 2.20GHz
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-15.0.7 (ORCJIT, skylake)
Threads: 1 default, 0 interactive, 1 GC (on 4 virtual cores)
Environment:
  JULIA_EDITOR = code
  JULIA_NUM_THREADS =

Additional context

When an ODESystem is used to construct a BifurcationProblem, only the equations, parameters and unknowns are included. If an observed variable, with its own equations, if used in the RHS of any of the ODEs, then it will be undefined in the resulting NonlinearSystem.

The following code provides a workaround by ensuring ALL observed variables and equations are included in the NonlinearSystem (and skipping the ODESystem conversion step). This also requires including initial guesses for the observed variables.

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

@mtkmodel FOL begin
    @parameters begin
        τ # parameters
    end
    @variables begin
        x(t) # dependent variables
        RHS(t)
    end
    @equations begin
        RHS ~ (1 - x) / τ
        D(x) ~ RHS
    end
end

@mtkbuild fol = FOL()

par = [fol.τ => 1.]
u0 = [fol.x => 1.]
prob = ODEProblem(fol, u0, (0.0, 1.), par)

bif_par = fol.τ

# Define the NonlinearSystem to include observed variables
nsys = NonlinearSystem([[0 ~ eq.rhs for eq in equations(fol)]; [eq for eq in observed(fol)]],
    [unknowns(fol); [eq.lhs for eq in observed(fol)]],
    parameters(fol);
    name = nameof(fol))
# This means observed variables are now unknowns and so need initial guesses
u0 = [u0; [fol.RHS => (1 - 1.) / 1.]]

bp = BifurcationProblem(complete(nsys), u0, par, bif_par)

opts_br = ContinuationPar(p_min = 0.5,
    p_max = 2.)

bf = bifurcationdiagram(bp, PALC(), 2, opts_br)

Not sure if its best to have a system like this (where observed variables and their equations are included separately), but with a check to make sure the observed variables actually need including. Or if its better to unfurl any observed variables that are used in the RHS.

[ChrisRackauckas]

The codegen probably just needs to be using full_equations.