Better error for exponential parameters in structural identifiability extension

[TorkelE]

Currently, StructuralIdentifiability.jl cannot assess identifiability for models where there is a parameter in an exponent. When using the package directly, there is an error when trying to create such a model. However, for ModelingToolkit, there error happens when assess_identifiability is called, and is rather non-intuitive. I.e.

using Catalyst, StructuralIdentifiability
rn = @reaction_network begin
    X^n, ∅ --> X
    d, X --> 0
end
assess_identifiability(rn; measured_quantities = [:X])

yields a

ERROR: MethodError: no method matching isless(::Int64, ::Nemo.QQMPolyRingElem)
The function `isless` exists, but no method is defined for this combination of argument types.

Closest candidates are:
  isless(::Integer, ::ForwardDiff.Dual{Ty}) where Ty
   @ ForwardDiff ~/.julia/packages/ForwardDiff/UBbGT/src/dual.jl:149
  isless(::Real, ::Num)
   @ Symbolics ~/.julia/packages/Symbolics/sc64L/src/num.jl:140
  isless(::Real, ::ForwardDiff.Dual{Ty}) where Ty
   @ ForwardDiff ~/.julia/packages/ForwardDiff/UBbGT/src/dual.jl:149
  ...

Stacktrace:
  [1] <(x::Int64, y::Nemo.QQMPolyRingElem)
    @ Base ./operators.jl:353
  [2] <=(x::Int64, y::Nemo.QQMPolyRingElem)
    @ Base ./operators.jl:402
  [3] >=(x::Nemo.QQMPolyRingElem, y::Int64)
    @ Base ./operators.jl:426
  [4] eval_at_nemo(e::SymbolicUtils.BasicSymbolic{Real}, vals::Dict{SymbolicUtils.BasicSymbolic{Real}, Nemo.QQMPolyRingElem})
    @ ModelingToolkitSIExt ~/.julia/packages/StructuralIdentifiability/r7Tss/ext/ModelingToolkitSIExt.jl:45
  [5] (::ModelingToolkitSIExt.var"#1#2"{Dict{…}})(a::SymbolicUtils.BasicSymbolic{Real})
    @ ModelingToolkitSIExt ~/.julia/packages/StructuralIdentifiability/r7Tss/ext/ModelingToolkitSIExt.jl:37
  [6] iterate
    @ ./generator.jl:48 [inlined]
  [7] _collect(c::SymbolicUtils.SmallVec{…}, itr::Base.Generator{…}, ::Base.EltypeUnknown, isz::Base.HasShape{…})
    @ Base ./array.jl:811
  [8] collect_similar(cont::SymbolicUtils.SmallVec{…}, itr::Base.Generator{…})
    @ Base ./array.jl:720
  [9] map(f::Function, A::SymbolicUtils.SmallVec{Any, Vector{Any}})
    @ Base ./abstractarray.jl:3371
 [10] eval_at_nemo(e::SymbolicUtils.BasicSymbolic{Real}, vals::Dict{SymbolicUtils.BasicSymbolic{Real}, Nemo.QQMPolyRingElem})
    @ ModelingToolkitSIExt ~/.julia/packages/StructuralIdentifiability/r7Tss/ext/ModelingToolkitSIExt.jl:36
 [11] __mtk_to_si(de::ODESystem, measured_quantities::Vector{Tuple{String, SymbolicUtils.BasicSymbolic{Real}}})
    @ ModelingToolkitSIExt ~/.julia/packages/StructuralIdentifiability/r7Tss/ext/ModelingToolkitSIExt.jl:259
 [12] mtk_to_si(de::ODESystem, measured_quantities::Vector{Equation})
    @ ModelingToolkitSIExt ~/.julia/packages/StructuralIdentifiability/r7Tss/ext/ModelingToolkitSIExt.jl:111
 [13] _assess_identifiability(ode::ODESystem; measured_quantities::Vector{…}, funcs_to_check::Vector{…}, known_ic::Vector{…}, prob_threshold::Float64)
    @ ModelingToolkitSIExt ~/.julia/packages/StructuralIdentifiability/r7Tss/ext/ModelingToolkitSIExt.jl:411
 [14] _assess_identifiability
    @ ~/.julia/packages/StructuralIdentifiability/r7Tss/ext/ModelingToolkitSIExt.jl:404 [inlined]
 [15] SciML/ModelingToolkit.jl#56
    @ ~/.julia/packages/StructuralIdentifiability/r7Tss/ext/ModelingToolkitSIExt.jl:394 [inlined]
 [16] with_logstate(f::ModelingToolkitSIExt.var"#56#57"{…}, logstate::Base.CoreLogging.LogState)
    @ Base.CoreLogging ./logging/logging.jl:522
 [17] with_logger
    @ ./logging/logging.jl:632 [inlined]
 [18] assess_identifiability(ode::ODESystem; measured_quantities::Vector{…}, funcs_to_check::Vector{…}, known_ic::Vector{…}, prob_threshold::Float64, loglevel::Base.CoreLogging.LogLevel)
    @ ModelingToolkitSIExt ~/.julia/packages/StructuralIdentifiability/r7Tss/ext/ModelingToolkitSIExt.jl:393
 [19] assess_identifiability(::ReactionSystem{…}; measured_quantities::Vector{…}, known_p::Vector{…}, funcs_to_check::Vector{…}, remove_conserved::Bool, ignore_no_measured_warn::Bool, kwargs::@Kwargs{})
    @ CatalystStructuralIdentifiabilityExtension ~/.julia/packages/Catalyst/8qDWw/ext/CatalystStructuralIdentifiabilityExtension/structural_identifiability_extension.jl:118

For someone not rather familiar with the package, there is more or less not way to figure out what the issue with this case is.

[pogudingleb]

Good point, I will fix it, thanks!

[TorkelE]

The native SI error could probably be improved a bit also. Right now it just say something like ^ is not defined for certain arguments. But maybe one could write a custom one explicitly saying that parameters in exponents are currently not supported?