SciML / OrdinaryDiffEq.jl

High performance ordinary differential equation (ODE) and differential-algebraic equation (DAE) solvers, including neural ordinary differential equations (neural ODEs) and scientific machine learning (SciML)
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Automatically chosen algorithm by `solve(prob; alg_hints=:auto)` fails to solve ODEs #2146

Closed jonasmac16 closed 4 months ago

jonasmac16 commented 4 months ago

Describe the bug 🐞

The automated solver selection of solve leads to DomainError while solving the system of ODEs and only explicitly setting a stiff solver such as Rosenbrock23() leads to successfully solving the ODE problem.

Expected behavior Speaking to @ChrisRackauckas on Slack, the solve with automated solver selection should not fail.

Minimal Reproducible Example 👇

using DifferentialEquations
using ModelingToolkit

schedule = 2
dosetimes_pk = [14, 28]
bolus_size = [10000.0,30000.0]
tspan = (0.0, dosetimes_pk[end]+10)

function pk_submodel_creator(;name, tinjection=[], bolus = 0.0)
    @variables t
    D = Differential(t)
    ps = @parameters k_12=672 k_3=959 V_c=3410 V_p=3410
    vars = @variables PK_c(t) PK_p(t)

    bolus = length(bolus) < length(tinjection) ? repeat([bolus[1]], length(tinjection)) : bolus

    injection = [[tinjection[j]] => [PK_c ~ PK_c + bolus[j]] for j in 1:length(tinjection)]

    eqs = [
        D(PK_c) ~ k_12 * PK_p/V_p - k_12 * PK_c/V_c  - k_3 * PK_c/V_c,
        D(PK_p) ~ k_12 * PK_c/V_c - k_12 * PK_p/V_p
    ]

    ODESystem(eqs, t, vars, ps; name, discrete_events = injection)
end

function tcell_submodel_creator(;name)
    @variables t
    ps = @parameters σ, δ
    vars = @variables E(t) ip(t)=0.0 [input = true] op(t)=0.0 [input = true]
    D = Differential(t)

    eqs = [
        D(E) ~ σ - δ*E + ip - op,
    ]

    ODESystem(eqs, t, vars, ps; name)
end

function tumourcell_submodel_creator(;name)
    @variables t
    ps = @parameters α
    vars = @variables T(t) op(t)=0.0 [input = true] ip(t)=0.0 [input = true] 
    D = Differential(t)

    eqs = [
        D(T) ~ α * T - op + ip
    ]

    ODESystem(eqs, t, vars, ps; name)
end

function extended_model(;name)
    @named tcell = tcell_submodel_creator()
    @named tumour = tumourcell_submodel_creator()
    @named pk = pk_submodel_creator(; tinjection=dosetimes_pk, bolus=bolus_size)

    @variables t
    D = Differential(t)

    ps = @parameters ρ, η, μ, c, ν, E_maxkill, EC_50_kill

    mm_PK_kill = ((E_maxkill * pk.PK_c)/(EC_50_kill + pk.PK_c))

    tumour_induced_tcell_proliferation = (ρ * tcell.E * (tumour.T)^c)/(η + (tumour.T)^c)

    tumour_induced_tcell_death = μ * tcell.E * (tumour.T)^c

    t_cell_induce_tumour_death = (ν + mm_PK_kill) * tcell.E * (tumour.T)^c

    connections = [
        tcell.ip ~ tumour_induced_tcell_proliferation,
        tcell.op ~ tumour_induced_tcell_death,
        tumour.op ~ t_cell_induce_tumour_death,
        ]

connected_blood_peripheral = compose(ODESystem(connections, t, [], ps; name), tcell, tumour, pk)
end

function create_ode_problem(model, tspan; kwargs...)
    @variables t
    #parameters
    @unpack tumour₊α, tcell₊σ, tcell₊δ, ρ, η, μ, c, ν, E_maxkill, EC_50_kill = model
    #state variables
    @unpack tcell₊E, tumour₊T, pk₊PK_c, pk₊PK_p = model

    u0 = [
        tcell₊E => 10e0,
        tumour₊T => 10e2,
        pk₊PK_c => 2500.0, 
        pk₊PK_p => 0.0,
    ]

    p = [tumour₊α => 0.12,
        tcell₊σ => 0.091, 
        tcell₊δ => 0.00911,
        ρ => 0.11,
        η => 2.019e5,
        μ => 3.422e-10,
        c => 0.75,
        ν => 1.101e-7,
        E_maxkill => 4.801e-1,
        EC_50_kill => 10000.0
    ]

    return ODEProblem(model, u0, tspan, p; kwargs...)
end

@named model = extended_model();
model_simp = structural_simplify(model)
ode_prob = create_ode_problem(model_simp, tspan)

solve(ode_prob, Rosenbrock23())
solve(ode_prob)
solve(ode_prob; alg_hints=[:auto])

Error & Stacktrace ⚠️ The last two solve calls lead to the following error:

ERROR: DomainError with -231.21243360645084:
Exponentiation yielding a complex result requires a complex argument.
Replace x^y with (x+0im)^y, Complex(x)^y, or similar.

Stacktrace:
  [1] throw_exp_domainerror(x::Float64)
    @ Base.Math ./math.jl:41
  [2] ^(x::Float64, y::Float64)
    @ Base.Math ./math.jl:1206
  [3] macro expansion
    @ ~/.julia/packages/SymbolicUtils/ssQsQ/src/code.jl:375 [inlined]
  [4] macro expansion
    @ ~/.julia/packages/RuntimeGeneratedFunctions/Yo8zx/src/RuntimeGeneratedFunctions.jl:163 [inlined]
  [5] macro expansion
    @ ./none:0 [inlined]
  [6] generated_callfunc
    @ ./none:0 [inlined]
  [7] (::RuntimeGeneratedFunctions.RuntimeGeneratedFunction{…})(::Vector{…}, ::Vector{…}, ::Vector{…}, ::Float64)
    @ RuntimeGeneratedFunctions ~/.julia/packages/RuntimeGeneratedFunctions/Yo8zx/src/RuntimeGeneratedFunctions.jl:150
  [8] k
    @ ModelingToolkit ~/.julia/packages/ModelingToolkit/BsHty/src/systems/diffeqs/abstractodesystem.jl:370 [inlined]
  [9] Void
    @ SciMLBase ~/.julia/packages/SciMLBase/szsYq/src/utils.jl:473 [inlined]
 [10] (::FunctionWrappers.CallWrapper{…})(f::SciMLBase.Void{…}, arg1::Vector{…}, arg2::Vector{…}, arg3::Vector{…}, arg4::Float64)
    @ FunctionWrappers ~/.julia/packages/FunctionWrappers/Q5cBx/src/FunctionWrappers.jl:65
 [11] macro expansion
    @ FunctionWrappers ~/.julia/packages/FunctionWrappers/Q5cBx/src/FunctionWrappers.jl:137 [inlined]
 [12] do_ccall
    @ FunctionWrappers ~/.julia/packages/FunctionWrappers/Q5cBx/src/FunctionWrappers.jl:125 [inlined]
 [13] FunctionWrapper
    @ FunctionWrappers ~/.julia/packages/FunctionWrappers/Q5cBx/src/FunctionWrappers.jl:144 [inlined]
 [14] _call
    @ FunctionWrappersWrappers ~/.julia/packages/FunctionWrappersWrappers/9XR0m/src/FunctionWrappersWrappers.jl:12 [inlined]
 [15] FunctionWrappersWrapper
    @ FunctionWrappersWrappers ~/.julia/packages/FunctionWrappersWrappers/9XR0m/src/FunctionWrappersWrappers.jl:10 [inlined]
 [16] Void
    @ SciMLBase ~/.julia/packages/SciMLBase/szsYq/src/utils.jl:473 [inlined]
 [17] (::FunctionWrappers.CallWrapper{…})(f::SciMLBase.Void{…}, arg1::Vector{…}, arg2::Vector{…}, arg3::Vector{…}, arg4::Float64)
    @ FunctionWrappers ~/.julia/packages/FunctionWrappers/Q5cBx/src/FunctionWrappers.jl:65
 [18] macro expansion
    @ ~/.julia/packages/FunctionWrappers/Q5cBx/src/FunctionWrappers.jl:137 [inlined]
 [19] do_ccall
    @ ~/.julia/packages/FunctionWrappers/Q5cBx/src/FunctionWrappers.jl:125 [inlined]
 [20] FunctionWrapper
    @ ~/.julia/packages/FunctionWrappers/Q5cBx/src/FunctionWrappers.jl:144 [inlined]
 [21] _call
    @ ~/.julia/packages/FunctionWrappersWrappers/9XR0m/src/FunctionWrappersWrappers.jl:12 [inlined]
 [22] FunctionWrappersWrapper
    @ ~/.julia/packages/FunctionWrappersWrappers/9XR0m/src/FunctionWrappersWrappers.jl:10 [inlined]
 [23] ODEFunction
    @ ~/.julia/packages/SciMLBase/szsYq/src/scimlfunctions.jl:2266 [inlined]
 [24] perform_step!(integrator::OrdinaryDiffEq.ODEIntegrator{…}, cache::OrdinaryDiffEq.Tsit5Cache{…}, repeat_step::Bool)
    @ OrdinaryDiffEq ~/.julia/packages/OrdinaryDiffEq/FFFcA/src/perform_step/low_order_rk_perform_step.jl:816
 [25] perform_step!
    @ ~/.julia/packages/OrdinaryDiffEq/FFFcA/src/perform_step/composite_perform_step.jl:91 [inlined]
 [26] perform_step!
    @ ~/.julia/packages/OrdinaryDiffEq/FFFcA/src/perform_step/composite_perform_step.jl:90 [inlined]
 [27] solve!(integrator::OrdinaryDiffEq.ODEIntegrator{…})
    @ OrdinaryDiffEq ~/.julia/packages/OrdinaryDiffEq/FFFcA/src/solve.jl:528
 [28] #__solve#740
    @ ~/.julia/packages/OrdinaryDiffEq/FFFcA/src/solve.jl:6 [inlined]
 [29] __solve
    @ ~/.julia/packages/OrdinaryDiffEq/FFFcA/src/solve.jl:1 [inlined]
 [30] solve_call(_prob::ODEProblem{…}, args::CompositeAlgorithm{…}; merge_callbacks::Bool, kwargshandle::KeywordArgError, kwargs::@Kwargs{…})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/s433k/src/solve.jl:559
 [31] solve_call
    @ DiffEqBase ~/.julia/packages/DiffEqBase/s433k/src/solve.jl:529 [inlined]
 [32] #solve_up#42
    @ DiffEqBase ~/.julia/packages/DiffEqBase/s433k/src/solve.jl:1020 [inlined]
 [33] solve_up
    @ DiffEqBase ~/.julia/packages/DiffEqBase/s433k/src/solve.jl:993 [inlined]
 [34] #solve#40
    @ DiffEqBase ~/.julia/packages/DiffEqBase/s433k/src/solve.jl:930 [inlined]
 [35] __solve(::ODEProblem{…}, ::Nothing; default_set::Bool, kwargs::@Kwargs{…})
    @ DifferentialEquations ~/.julia/packages/DifferentialEquations/aKmaf/src/default_solve.jl:14
 [36] __solve
    @ DifferentialEquations ~/.julia/packages/DifferentialEquations/aKmaf/src/default_solve.jl:1 [inlined]
 [37] #__solve#62
    @ DiffEqBase ~/.julia/packages/DiffEqBase/s433k/src/solve.jl:1299 [inlined]
 [38] __solve
    @ DiffEqBase ~/.julia/packages/DiffEqBase/s433k/src/solve.jl:1292 [inlined]
 [39] #solve_call#34
    @ DiffEqBase ~/.julia/packages/DiffEqBase/s433k/src/solve.jl:559 [inlined]
 [40] solve_call(::ODEProblem{Vector{…}, Tuple{…}, true, Vector{…}, ODEFunction{…}, @Kwargs{…}, SciMLBase.StandardODEProblem})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/s433k/src/solve.jl:529
 [41] solve_up(prob::SciMLBase.AbstractDEProblem, sensealg::Any, u0::Any, p::Any, args::Vararg{Any}; kwargs...)
    @ DiffEqBase ~/.julia/packages/DiffEqBase/s433k/src/solve.jl:1024 [inlined]
 [42] solve_up
    @ ~/.julia/packages/DiffEqBase/s433k/src/solve.jl:993 [inlined]
 [43] solve(::ODEProblem{…}; sensealg::Nothing, u0::Nothing, p::Nothing, wrap::Val{…}, kwargs::@Kwargs{})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/s433k/src/solve.jl:930
 [44] solve(::ODEProblem{Vector{…}, Tuple{…}, true, Vector{…}, ODEFunction{…}, @Kwargs{…}, SciMLBase.StandardODEProblem})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/s433k/src/solve.jl:920
 [45] top-level scope
    @ ~/OneDrive/shared_work/02_research_projects/01_roche_cd8_tracer_study/notebooks/001_local/003_Extended_Kuznetsov_model_Simulation_Fitting/mwe.jl:123
Some type information was truncated. Use `show(err)` to see complete types.

Environment:

  [cbdf2221] AlgebraOfGraphics v0.6.18
  [6e4b80f9] BenchmarkTools v1.4.0
  [336ed68f] CSV v0.10.12
  [13f3f980] CairoMakie v0.11.6
⌃ [2445eb08] DataDrivenDiffEq v1.1.0
  [5b588203] DataDrivenSparse v0.1.2
  [a93c6f00] DataFrames v1.6.1
⌃ [aae7a2af] DiffEqFlux v1.53.0
⌃ [0c46a032] DifferentialEquations v7.10.0
  [31c24e10] Distributions v0.25.107
  [e30172f5] Documenter v1.2.1
  [634d3b9d] DrWatson v2.13.0
  [ef4b24a4] EasyModelAnalysis v0.1.13
⌃ [af5da776] GlobalSensitivity v2.4.0
  [033835bb] JLD2 v0.4.45
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  [30fc2ffe] LossFunctions v0.11.1
  [6fafb56a] Memoization v0.2.1
⌃ [961ee093] ModelingToolkit v8.70.0
  [6f286f6a] MultivariateStats v0.10.2
⌅ [3bd65402] Optimisers v0.2.15
⌃ [7f7a1694] Optimization v3.19.3
⌅ [3e6eede4] OptimizationBBO v0.1.5
⌃ [bd407f91] OptimizationCMAEvolutionStrategy v0.1.4
⌃ [cb963754] OptimizationEvolutionary v0.1.3
⌅ [253f991c] OptimizationFlux v0.1.5
⌃ [6f0a0517] OptimizationGCMAES v0.1.6
⌃ [3aafef2f] OptimizationMetaheuristics v0.1.3
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⌅ [c3fe647b] AbstractAlgebra v0.34.7
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⌅ [764a87c0] BoundaryValueDiffEq v4.0.1
⌅ [fa961155] CEnum v0.4.2
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⌅ [052768ef] CUDA v4.4.1
  [1af6417a] CUDA_Runtime_Discovery v0.2.3
  [159f3aea] Cairo v1.0.5
  [13f3f980] CairoMakie v0.11.6
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⌅ [82cc6244] DataInterpolations v3.12.0
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⌃ [bcd4f6db] DelayDiffEq v5.44.0
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⌅ [d1acc4aa] IntervalArithmetic v0.20.9
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⌅ [d0bbae9a] LuxCUDA v0.1.2
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⌅ [82251201] LuxLib v0.2.5
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⌅ [872c559c] NNlib v0.8.21
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⌅ [86f7a689] NamedArrays v0.9.8
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⌅ [2edaba10] Nemo v0.38.3
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⌅ [8913a72c] NonlinearSolve v1.10.1
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⌃ [bd407f91] OptimizationCMAEvolutionStrategy v0.1.4
⌃ [cb963754] OptimizationEvolutionary v0.1.3
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⌅ [fd9f6733] OptimizationMOI v0.1.16
⌃ [3aafef2f] OptimizationMetaheuristics v0.1.3
⌃ [e4316d97] OptimizationMultistartOptimization v0.1.4
⌅ [4e6fcdb7] OptimizationNLopt v0.1.8
⌅ [36348300] OptimizationOptimJL v0.1.14
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⌅ [9cc047cb] Ipopt_jll v300.1400.400+0
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Julia Version 1.10.0
Commit 3120989f39b (2023-12-25 18:01 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 16 × 12th Gen Intel(R) Core(TM) i7-1270P
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-15.0.7 (ORCJIT, alderlake)
  Threads: 23 on 16 virtual cores
Environment:
  JULIA_EDITOR = code
ChrisRackauckas commented 4 months ago

Your packages are just old. On the latest version this seems fine:

using DifferentialEquations
using ModelingToolkit

schedule = 2
dosetimes_pk = [14, 28]
bolus_size = [10000.0,30000.0]
tspan = (0.0, dosetimes_pk[end]+10)

function pk_submodel_creator(;name, tinjection=[], bolus = 0.0)
    @variables t
    D = Differential(t)
    ps = @parameters k_12=672 k_3=959 V_c=3410 V_p=3410
    vars = @variables PK_c(t) PK_p(t)

    bolus = length(bolus) < length(tinjection) ? repeat([bolus[1]], length(tinjection)) : bolus

    injection = [[tinjection[j]] => [PK_c ~ PK_c + bolus[j]] for j in 1:length(tinjection)]

    eqs = [
        D(PK_c) ~ k_12 * PK_p/V_p - k_12 * PK_c/V_c  - k_3 * PK_c/V_c,
        D(PK_p) ~ k_12 * PK_c/V_c - k_12 * PK_p/V_p
    ]

    ODESystem(eqs, t, vars, ps; name, discrete_events = injection)
end

function tcell_submodel_creator(;name)
    @variables t
    ps = @parameters σ, δ
    vars = @variables E(t) ip(t)=0.0 [input = true] op(t)=0.0 [input = true]
    D = Differential(t)

    eqs = [
        D(E) ~ σ - δ*E + ip - op,
    ]

    ODESystem(eqs, t, vars, ps; name)
end

function tumourcell_submodel_creator(;name)
    @variables t
    ps = @parameters α
    vars = @variables T(t) op(t)=0.0 [input = true] ip(t)=0.0 [input = true] 
    D = Differential(t)

    eqs = [
        D(T) ~ α * T - op + ip
    ]

    ODESystem(eqs, t, vars, ps; name)
end

function extended_model(;name)
    @named tcell = tcell_submodel_creator()
    @named tumour = tumourcell_submodel_creator()
    @named pk = pk_submodel_creator(; tinjection=dosetimes_pk, bolus=bolus_size)

    @variables t
    D = Differential(t)

    ps = @parameters ρ, η, μ, c, ν, E_maxkill, EC_50_kill

    mm_PK_kill = ((E_maxkill * pk.PK_c)/(EC_50_kill + pk.PK_c))

    tumour_induced_tcell_proliferation = (ρ * tcell.E * (tumour.T)^c)/(η + (tumour.T)^c)

    tumour_induced_tcell_death = μ * tcell.E * (tumour.T)^c

    t_cell_induce_tumour_death = (ν + mm_PK_kill) * tcell.E * (tumour.T)^c

    connections = [
        tcell.ip ~ tumour_induced_tcell_proliferation,
        tcell.op ~ tumour_induced_tcell_death,
        tumour.op ~ t_cell_induce_tumour_death,
        ]

connected_blood_peripheral = compose(ODESystem(connections, t, [], ps; name), tcell, tumour, pk)
end

function create_ode_problem(model, tspan; kwargs...)
    @variables t    
    u0 = [
        model.tcell.E => 10e0,
        model.tumour.T => 10e2,
        model.pk.PK_c => 2500.0, 
        model.pk.PK_p => 0.0,
    ]

    p = [
        model.tumour.α => 0.12,
        model.tcell.σ => 0.091, 
        model.tcell.δ => 0.00911,
        model.ρ => 0.11,
        model.η => 2.019e5,
        model.μ => 3.422e-10,
        model.c => 0.75,
        model.ν => 1.101e-7,
        model.E_maxkill => 4.801e-1,
        model.EC_50_kill => 10000.0
    ]

    return ODEProblem(model, u0, tspan, p; kwargs...)
end

@named model = extended_model();
model_simp = structural_simplify(model)
ode_prob = create_ode_problem(model_simp, tspan)

solve(ode_prob, Rosenbrock23())
solve(ode_prob)
solve(ode_prob; alg_hints=[:auto])
ChrisRackauckas commented 4 months ago

Updated syntax there works, so closing.