Helpful error for missing guesses has disappeared

[hersle]

Solving an ODE that needs a guess in initialization, like

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

@variables x(t) y(t)
@named sys = ODESystem([x^2 + y^2 ~ 25, D(x) ~ 1], t)
ssys = structural_simplify(sys)
prob = ODEProblem(ssys, [x => 3], (0, 1), [] #=; guesses = [y => 5]=#)

gives the bad error

ERROR: LoadError: MethodError: no method matching AbstractFloat(::Type{SymbolicUtils.BasicSymbolic{Real}})

Closest candidates are:
  AbstractFloat(::Bool)
   @ Base float.jl:264
  AbstractFloat(::UInt32)
   @ Base float.jl:272
  AbstractFloat(::UInt8)
   @ Base float.jl:270
  ...

Stacktrace:
  [1] float(x::Type)
    @ Base .\float.jl:294
  [2] promote_to_concrete(vs::Vector{SymbolicUtils.BasicSymbolic{Real}}; tofloat::Bool, use_union::Bool)
    @ ModelingToolkit c:\Users\herma\.julia\dev\Symboltz\dev\ModelingToolkit\src\utils.jl:657
  [3] varmap_to_vars(varmap::Dict{…}, varlist::Vector{…}; defaults::Dict{…}, check::Bool, toterm::Function, promotetoconcrete::Nothing, tofloat::Bool, use_union::Bool)
    @ ModelingToolkit c:\Users\herma\.julia\dev\Symboltz\dev\ModelingToolkit\src\variables.jl:165
  [4] get_u0(sys::NonlinearSystem, u0map::Dict{Any, Any}, parammap::Vector{Pair{…}}; symbolic_u0::Bool, toterm::Function)
    @ ModelingToolkit c:\Users\herma\.julia\dev\Symboltz\dev\ModelingToolkit\src\systems\diffeqs\abstractodesystem.jl:742
  [5] get_u0
    @ c:\Users\herma\.julia\dev\Symboltz\dev\ModelingToolkit\src\systems\diffeqs\abstractodesystem.jl:719 [inlined]
  [6] process_NonlinearProblem(constructor::Type, sys::NonlinearSystem, u0map::Dict{…}, parammap::Vector{…}; version::Nothing, jac::Bool, checkbounds::Bool, sparse::Bool, simplify::Bool, linenumbers::Bool, parallel::Symbolics.SerialForm, eval_expression::Bool, eval_module::Module, use_union::Bool, tofloat::Bool, kwargs::@Kwargs{…})
    @ ModelingToolkit c:\Users\herma\.julia\dev\Symboltz\dev\ModelingToolkit\src\systems\nonlinear\nonlinearsystem.jl:391

I believe it used to give something much nicer saying which variables have missing guesses. What happened to that?

[hersle]

I think this is the core issue:

• varmap_to_vars() calls _varmap_to_vars() to try to calculate an initial value of y using a varmap of x => 3 (from u0) and t => 0 (from tspan).
• fixpoint_sub() (blue line) substitutes t => 0 into y(t), so it becomes y(0). The next line detects that y has changed, and adds it to the dictionary of "successfully changed" variables.
• missingvars does not contain y (because it "successfully changed"), so the MissingVariablesError is not thrown.
• promote_to_concrete() tries to promote y(0) to a concrete value, and rightfully throws up.

This can be reproduced with simply

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

@variables x(t) y(t)
ModelingToolkit._varmap_to_vars(Dict(t => 0), [y]) # changes y(t) to y(0)

[ChrisRackauckas]

fixpoint_sub() (blue line) substitutes t => 0 into y(t), so it becomes y(0). The next line detects that y has changed, and adds it to the dictionary of "successfully changed" variables.

Yeah I've noticed that in the error message. I have thought that should probably be removed, but it's a bit tricky. We do want t => 0 so that non-autonomous DAEs with algebraic equations that explicitly have t know how to handle it during initialization, i.e. x ~ 2t is a fine initialization equation since you know what t is, but the substitution to y(0) is an unintended side effect. It seems to only happen when you miss a variable so it's "okay" in the sense it doesn't make anything not work, but indeed you get the worst error message so I've wanted to fix this but haven't thought of a great way to do it.

At a high level, the fix is to just not substitute t=>0 into the dependent variables. But I'm not sure there's a symbolics utility that helps with that.

[hersle]

Indeed. ?fixpoint_sub() says that

The operator keyword can be specified to prevent substitution of expressions inside operators of the given type.

Can this be used to shield t from substitutions when it is an argument of a dependent variable (not in cos(t), for example)?