Handling of null differential equations

[dodoplus]

The following code:

using ModelingToolkit, OrdinaryDiffEq

@variables t, x(t)
eqs = [x ~ 0]
@named model = ODESystem(eqs, t, [], [])
sys = structural_simplify(model)
prob = ODAEProblem(sys, [], (0, 2.0))
sol = solve(prob, Tsit5())

Generates this extremely unhelpful error message:

MethodError: no method matching oneunit(::Type{Any})
Closest candidates are:
  oneunit(::Type{Union{Missing, T}}) where T at missing.jl:105
  oneunit(::Type{T}) where T at number.jl:358
  oneunit(::T) where T at number.jl:357
  ...

Stacktrace:
  [1] oneunit(#unused#::Type{Any})
    @ Base ./missing.jl:106
  [2] __init(prob::ODEProblem{Nothing, Tuple{Float64, Float64}, true, Nothing, ODEFunction{true, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(Symbol("##out#335"), Symbol("##arg#8441539597060760774"), Symbol("##arg#8441539597060760774"), :t), ModelingToolkit.StructuralTransformations.var"#_RGF_ModTag", ModelingToolkit.StructuralTransformations.var"#_RGF_ModTag", (0x6b5e1fad, 0x6ae8718d, 0xb753908c, 0x3897280c, 0xad418a6d)}, LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, SparseArrays.SparseMatrixCSC{Bool, Int64}, Nothing, Nothing, Nothing, Vector{Symbol}, Nothing, ModelingToolkit.StructuralTransformations.var"#generated_observed#226"{Bool, ModelingToolkit.BipartiteGraphs.Matching{ModelingToolkit.BipartiteGraphs.Unassigned, Vector{Union{ModelingToolkit.BipartiteGraphs.Unassigned, Int64}}}, TearingState{ODESystem}, Dict{Any, Any}, BitVector, Vector{Any}, Tuple{Vector{Int64}, Vector{BitSet}}, SymbolicUtils.Code.LazyState, Dict{Any, Int64}}, Nothing}, Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}, alg::Tsit5{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!), Static.False}, timeseries_init::Tuple{}, ts_init::Tuple{}, ks_init::Tuple{}, recompile::Type{Val{true}}; saveat::Tuple{}, tstops::Tuple{}, d_discontinuities::Tuple{}, save_idxs::Nothing, save_everystep::Bool, save_on::Bool, save_start::Bool, save_end::Nothing, callback::Nothing, dense::Bool, calck::Bool, dt::Float64, dtmin::Nothing, dtmax::Float64, force_dtmin::Bool, adaptive::Bool, gamma::Rational{Int64}, abstol::Nothing, reltol::Nothing, qmin::Rational{Int64}, qmax::Int64, qsteady_min::Int64, qsteady_max::Int64, beta1::Nothing, beta2::Nothing, qoldinit::Rational{Int64}, controller::Nothing, fullnormalize::Bool, failfactor::Int64, maxiters::Int64, internalnorm::typeof(DiffEqBase.ODE_DEFAULT_NORM), internalopnorm::typeof(LinearAlgebra.opnorm), isoutofdomain::typeof(DiffEqBase.ODE_DEFAULT_ISOUTOFDOMAIN), unstable_check::typeof(DiffEqBase.ODE_DEFAULT_UNSTABLE_CHECK), verbose::Bool, timeseries_errors::Bool, dense_errors::Bool, advance_to_tstop::Bool, stop_at_next_tstop::Bool, initialize_save::Bool, progress::Bool, progress_steps::Int64, progress_name::String, progress_message::typeof(DiffEqBase.ODE_DEFAULT_PROG_MESSAGE), userdata::Nothing, allow_extrapolation::Bool, initialize_integrator::Bool, alias_u0::Bool, alias_du0::Bool, initializealg::OrdinaryDiffEq.DefaultInit, kwargs::Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}})
    @ OrdinaryDiffEq ~/.julia/packages/OrdinaryDiffEq/irVAX/src/solve.jl:159
  [3] __init(prob::ODEProblem{Nothing, Tuple{Float64, Float64}, true, Nothing, ODEFunction{true, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(Symbol("##out#335"), Symbol("##arg#8441539597060760774"), Symbol("##arg#8441539597060760774"), :t), ModelingToolkit.StructuralTransformations.var"#_RGF_ModTag", ModelingToolkit.StructuralTransformations.var"#_RGF_ModTag", (0x6b5e1fad, 0x6ae8718d, 0xb753908c, 0x3897280c, 0xad418a6d)}, LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, SparseArrays.SparseMatrixCSC{Bool, Int64}, Nothing, Nothing, Nothing, Vector{Symbol}, Nothing, ModelingToolkit.StructuralTransformations.var"#generated_observed#226"{Bool, ModelingToolkit.BipartiteGraphs.Matching{ModelingToolkit.BipartiteGraphs.Unassigned, Vector{Union{ModelingToolkit.BipartiteGraphs.Unassigned, Int64}}}, TearingState{ODESystem}, Dict{Any, Any}, BitVector, Vector{Any}, Tuple{Vector{Int64}, Vector{BitSet}}, SymbolicUtils.Code.LazyState, Dict{Any, Int64}}, Nothing}, Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}, alg::Tsit5{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!), Static.False}, timeseries_init::Tuple{}, ts_init::Tuple{}, ks_init::Tuple{}, recompile::Type{Val{true}}) (repeats 5 times)
    @ OrdinaryDiffEq ~/.julia/packages/OrdinaryDiffEq/irVAX/src/solve.jl:9
  [4] __solve(::ODEProblem{Nothing, Tuple{Float64, Float64}, true, Nothing, ODEFunction{true, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(Symbol("##out#335"), Symbol("##arg#8441539597060760774"), Symbol("##arg#8441539597060760774"), :t), ModelingToolkit.StructuralTransformations.var"#_RGF_ModTag", ModelingToolkit.StructuralTransformations.var"#_RGF_ModTag", (0x6b5e1fad, 0x6ae8718d, 0xb753908c, 0x3897280c, 0xad418a6d)}, LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, SparseArrays.SparseMatrixCSC{Bool, Int64}, Nothing, Nothing, Nothing, Vector{Symbol}, Nothing, ModelingToolkit.StructuralTransformations.var"#generated_observed#226"{Bool, ModelingToolkit.BipartiteGraphs.Matching{ModelingToolkit.BipartiteGraphs.Unassigned, Vector{Union{ModelingToolkit.BipartiteGraphs.Unassigned, Int64}}}, TearingState{ODESystem}, Dict{Any, Any}, BitVector, Vector{Any}, Tuple{Vector{Int64}, Vector{BitSet}}, SymbolicUtils.Code.LazyState, Dict{Any, Int64}}, Nothing}, Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}, ::Tsit5{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!), Static.False}; kwargs::Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}})
    @ OrdinaryDiffEq ~/.julia/packages/OrdinaryDiffEq/irVAX/src/solve.jl:4
  [5] __solve(::ODEProblem{Nothing, Tuple{Float64, Float64}, true, Nothing, ODEFunction{true, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(Symbol("##out#335"), Symbol("##arg#8441539597060760774"), Symbol("##arg#8441539597060760774"), :t), ModelingToolkit.StructuralTransformations.var"#_RGF_ModTag", ModelingToolkit.StructuralTransformations.var"#_RGF_ModTag", (0x6b5e1fad, 0x6ae8718d, 0xb753908c, 0x3897280c, 0xad418a6d)}, LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, SparseArrays.SparseMatrixCSC{Bool, Int64}, Nothing, Nothing, Nothing, Vector{Symbol}, Nothing, ModelingToolkit.StructuralTransformations.var"#generated_observed#226"{Bool, ModelingToolkit.BipartiteGraphs.Matching{ModelingToolkit.BipartiteGraphs.Unassigned, Vector{Union{ModelingToolkit.BipartiteGraphs.Unassigned, Int64}}}, TearingState{ODESystem}, Dict{Any, Any}, BitVector, Vector{Any}, Tuple{Vector{Int64}, Vector{BitSet}}, SymbolicUtils.Code.LazyState, Dict{Any, Int64}}, Nothing}, Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}, ::Tsit5{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!), Static.False})
    @ OrdinaryDiffEq ~/.julia/packages/OrdinaryDiffEq/irVAX/src/solve.jl:1
  [6] solve_call(_prob::ODEProblem{Nothing, Tuple{Float64, Float64}, true, Nothing, ODEFunction{true, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(Symbol("##out#335"), Symbol("##arg#8441539597060760774"), Symbol("##arg#8441539597060760774"), :t), ModelingToolkit.StructuralTransformations.var"#_RGF_ModTag", ModelingToolkit.StructuralTransformations.var"#_RGF_ModTag", (0x6b5e1fad, 0x6ae8718d, 0xb753908c, 0x3897280c, 0xad418a6d)}, LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, SparseArrays.SparseMatrixCSC{Bool, Int64}, Nothing, Nothing, Nothing, Vector{Symbol}, Nothing, ModelingToolkit.StructuralTransformations.var"#generated_observed#226"{Bool, ModelingToolkit.BipartiteGraphs.Matching{ModelingToolkit.BipartiteGraphs.Unassigned, Vector{Union{ModelingToolkit.BipartiteGraphs.Unassigned, Int64}}}, TearingState{ODESystem}, Dict{Any, Any}, BitVector, Vector{Any}, Tuple{Vector{Int64}, Vector{BitSet}}, SymbolicUtils.Code.LazyState, Dict{Any, Int64}}, Nothing}, Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}, args::Tsit5{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!), Static.False}; merge_callbacks::Bool, kwargshandle::KeywordArgError, kwargs::Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/lY3yl/src/solve.jl:426
  [7] solve_call(_prob::ODEProblem{Nothing, Tuple{Float64, Float64}, true, Nothing, ODEFunction{true, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(Symbol("##out#335"), Symbol("##arg#8441539597060760774"), Symbol("##arg#8441539597060760774"), :t), ModelingToolkit.StructuralTransformations.var"#_RGF_ModTag", ModelingToolkit.StructuralTransformations.var"#_RGF_ModTag", (0x6b5e1fad, 0x6ae8718d, 0xb753908c, 0x3897280c, 0xad418a6d)}, LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, SparseArrays.SparseMatrixCSC{Bool, Int64}, Nothing, Nothing, Nothing, Vector{Symbol}, Nothing, ModelingToolkit.StructuralTransformations.var"#generated_observed#226"{Bool, ModelingToolkit.BipartiteGraphs.Matching{ModelingToolkit.BipartiteGraphs.Unassigned, Vector{Union{ModelingToolkit.BipartiteGraphs.Unassigned, Int64}}}, TearingState{ODESystem}, Dict{Any, Any}, BitVector, Vector{Any}, Tuple{Vector{Int64}, Vector{BitSet}}, SymbolicUtils.Code.LazyState, Dict{Any, Int64}}, Nothing}, Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}, args::Tsit5{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!), Static.False})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/lY3yl/src/solve.jl:407
  [8] solve_up(prob::ODEProblem{Nothing, Tuple{Float64, Float64}, true, Nothing, ODEFunction{true, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(Symbol("##out#335"), Symbol("##arg#8441539597060760774"), Symbol("##arg#8441539597060760774"), :t), ModelingToolkit.StructuralTransformations.var"#_RGF_ModTag", ModelingToolkit.StructuralTransformations.var"#_RGF_ModTag", (0x6b5e1fad, 0x6ae8718d, 0xb753908c, 0x3897280c, 0xad418a6d)}, LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, SparseArrays.SparseMatrixCSC{Bool, Int64}, Nothing, Nothing, Nothing, Vector{Symbol}, Nothing, ModelingToolkit.StructuralTransformations.var"#generated_observed#226"{Bool, ModelingToolkit.BipartiteGraphs.Matching{ModelingToolkit.BipartiteGraphs.Unassigned, Vector{Union{ModelingToolkit.BipartiteGraphs.Unassigned, Int64}}}, TearingState{ODESystem}, Dict{Any, Any}, BitVector, Vector{Any}, Tuple{Vector{Int64}, Vector{BitSet}}, SymbolicUtils.Code.LazyState, Dict{Any, Int64}}, Nothing}, Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}, sensealg::Nothing, u0::Nothing, p::Nothing, args::Tsit5{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!), Static.False}; kwargs::Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/lY3yl/src/solve.jl:724
  [9] solve_up(prob::ODEProblem{Nothing, Tuple{Float64, Float64}, true, Nothing, ODEFunction{true, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(Symbol("##out#335"), Symbol("##arg#8441539597060760774"), Symbol("##arg#8441539597060760774"), :t), ModelingToolkit.StructuralTransformations.var"#_RGF_ModTag", ModelingToolkit.StructuralTransformations.var"#_RGF_ModTag", (0x6b5e1fad, 0x6ae8718d, 0xb753908c, 0x3897280c, 0xad418a6d)}, LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, SparseArrays.SparseMatrixCSC{Bool, Int64}, Nothing, Nothing, Nothing, Vector{Symbol}, Nothing, ModelingToolkit.StructuralTransformations.var"#generated_observed#226"{Bool, ModelingToolkit.BipartiteGraphs.Matching{ModelingToolkit.BipartiteGraphs.Unassigned, Vector{Union{ModelingToolkit.BipartiteGraphs.Unassigned, Int64}}}, TearingState{ODESystem}, Dict{Any, Any}, BitVector, Vector{Any}, Tuple{Vector{Int64}, Vector{BitSet}}, SymbolicUtils.Code.LazyState, Dict{Any, Int64}}, Nothing}, Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}, sensealg::Nothing, u0::Nothing, p::Nothing, args::Tsit5{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!), Static.False})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/lY3yl/src/solve.jl:711
 [10] solve(prob::ODEProblem{Nothing, Tuple{Float64, Float64}, true, Nothing, ODEFunction{true, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(Symbol("##out#335"), Symbol("##arg#8441539597060760774"), Symbol("##arg#8441539597060760774"), :t), ModelingToolkit.StructuralTransformations.var"#_RGF_ModTag", ModelingToolkit.StructuralTransformations.var"#_RGF_ModTag", (0x6b5e1fad, 0x6ae8718d, 0xb753908c, 0x3897280c, 0xad418a6d)}, LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, SparseArrays.SparseMatrixCSC{Bool, Int64}, Nothing, Nothing, Nothing, Vector{Symbol}, Nothing, ModelingToolkit.StructuralTransformations.var"#generated_observed#226"{Bool, ModelingToolkit.BipartiteGraphs.Matching{ModelingToolkit.BipartiteGraphs.Unassigned, Vector{Union{ModelingToolkit.BipartiteGraphs.Unassigned, Int64}}}, TearingState{ODESystem}, Dict{Any, Any}, BitVector, Vector{Any}, Tuple{Vector{Int64}, Vector{BitSet}}, SymbolicUtils.Code.LazyState, Dict{Any, Int64}}, Nothing}, Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}, args::Tsit5{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!), Static.False}; sensealg::Nothing, u0::Nothing, p::Nothing, kwargs::Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/lY3yl/src/solve.jl:708
 [11] solve(prob::ODEProblem{Nothing, Tuple{Float64, Float64}, true, Nothing, ODEFunction{true, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(Symbol("##out#335"), Symbol("##arg#8441539597060760774"), Symbol("##arg#8441539597060760774"), :t), ModelingToolkit.StructuralTransformations.var"#_RGF_ModTag", ModelingToolkit.StructuralTransformations.var"#_RGF_ModTag", (0x6b5e1fad, 0x6ae8718d, 0xb753908c, 0x3897280c, 0xad418a6d)}, LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, SparseArrays.SparseMatrixCSC{Bool, Int64}, Nothing, Nothing, Nothing, Vector{Symbol}, Nothing, ModelingToolkit.StructuralTransformations.var"#generated_observed#226"{Bool, ModelingToolkit.BipartiteGraphs.Matching{ModelingToolkit.BipartiteGraphs.Unassigned, Vector{Union{ModelingToolkit.BipartiteGraphs.Unassigned, Int64}}}, TearingState{ODESystem}, Dict{Any, Any}, BitVector, Vector{Any}, Tuple{Vector{Int64}, Vector{BitSet}}, SymbolicUtils.Code.LazyState, Dict{Any, Int64}}, Nothing}, Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}, args::Tsit5{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!), Static.False})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/lY3yl/src/solve.jl:701
 [12] top-level scope

ODAEProblem() should check its inputs and not pass the buck all the way down to missing.jl

[ChrisRackauckas]

Thanks! I'm not sure this is an MTK issue at all, but something solve at the DiffEqBase level. I'll look into this one.

[YingboMa]

This is resolved in DiffEqBase v8.15.1.