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FitzHugh-Nagumo Parameter Estimation Benchmarks

Parameter estimation of FitzHugh-Nagumo model using optimisation methods

using ParameterizedFunctions, OrdinaryDiffEq, DiffEqParamEstim, Optimization
using OptimizationBBO, OptimizationNLopt, ForwardDiff, Plots, BenchmarkTools
using ModelingToolkit
using ModelingToolkitBase
using SciCompDSL
using ModelingToolkit: @mtkbuild, D_nounits as D, t_nounits as t
gr(fmt = :png)
Plots.GRBackend()
loc_bounds = Tuple{Float64, Float64}[(0, 1), (0, 1), (
    0, 1), (0, 1)]
glo_bounds = Tuple{Float64, Float64}[(0, 5), (0, 5), (
    0, 5), (0, 5)]
loc_init = [0.5, 0.5, 0.5, 0.5]
glo_init = [2.5, 2.5, 2.5, 2.5]
4-element Vector{Float64}:
 2.5
 2.5
 2.5
 2.5
@mtkmodel FitzHughNagumo begin
    @parameters begin
        a = 0.7      # Parameter for excitability
        b = 0.8      # Recovery rate parameter
        τinv = 0.08  # Inverse of the time constant
        l = 0.5      # External stimulus
    end
    @variables begin
        v(t) = 1.0  # Membrane potential with initial condition
        w(t) = 1.0  # Recovery variable with initial condition
    end
    @equations begin
        D(v) ~ v - v^3 / 3 - w + l
        D(w) ~ τinv * (v + a - b * w)
    end
end

@mtkbuild fitz = FitzHughNagumo()
Model fitz:
Equations (2):
  2 standard: see equations(fitz)
Unknowns (2): see unknowns(fitz)
  w(t)
  v(t)
Parameters (4): see parameters(fitz)
  a
  b
  τinv
  l
p = [0.7, 0.8, 0.08, 0.5]              # Parameters used to construct the dataset
r0 = [1.0; 1.0]                     # initial value
tspan = (0.0, 30.0)                 # sample of 3000 observations over the (0,30) timespan
prob = ODEProblem(fitz, r0, tspan, p)
tspan2 = (0.0, 3.0)                 # sample of 300 observations with a timestep of 0.01
prob_short = ODEProblem(fitz, r0, tspan2, p)
ODEProblem with uType Vector{Float64} and tType Float64. In-place: true
Initialization status: FULLY_DETERMINED
Non-trivial mass matrix: false
timespan: (0.0, 3.0)
u0: 2-element Vector{Float64}:
 1.0
 1.0
dt = 30.0/3000
tf = 30.0
tinterval = 0:dt:tf
time_points = collect(tinterval)
3001-element Vector{Float64}:
  0.0
  0.01
  0.02
  0.03
  0.04
  0.05
  0.06
  0.07
  0.08
  0.09
  ⋮
 29.92
 29.93
 29.94
 29.95
 29.96
 29.97
 29.98
 29.99
 30.0
h = 0.01
M = 300
tstart = 0.0
tstop = tstart + M * h
tinterval_short = 0:h:tstop
t_short = collect(tinterval_short)
301-element Vector{Float64}:
 0.0
 0.01
 0.02
 0.03
 0.04
 0.05
 0.06
 0.07
 0.08
 0.09
 ⋮
 2.92
 2.93
 2.94
 2.95
 2.96
 2.97
 2.98
 2.99
 3.0
#Generate Data
data_sol_short = solve(prob_short, Vern9(), saveat = t_short, reltol = 1e-9, abstol = 1e-9)
data_short = convert(Array, data_sol_short) # This operation produces column major dataset obs as columns, equations as rows
data_sol = solve(prob, Vern9(), saveat = time_points, reltol = 1e-9, abstol = 1e-9)
data = convert(Array, data_sol)
2×3001 Matrix{Float64}:
 1.0  1.00072  1.00144  1.00216  1.00289  …  -0.229157  -0.228976  -0.22879
3
 1.0  1.00166  1.00332  1.00497  1.00661     -0.65759   -0.655923  -0.65424
8
Plot of the solution
Short Solution
plot(data_sol_short)

Longer Solution
plot(data_sol)

Local Solution from the short data set

obj_short = build_loss_objective(prob_short, Tsit5(), L2Loss(t_short, data_short), tstops = t_short)
optprob = OptimizationProblem(obj_short, glo_init, lb = first.(glo_bounds), ub = last.(glo_bounds))
@btime res1 = solve(optprob, BBO_adaptive_de_rand_1_bin(), maxiters = 7e3)
# Lower tolerance could lead to smaller fitness (more accuracy)
2.969 s (21069448 allocations: 803.43 MiB)
retcode: MaxIters
u: 4-element Vector{Float64}:
 0.5046351447591682
 0.7489055602923876
 0.09397097351892401
 0.4985245554212076
obj_short = build_loss_objective(
    prob_short, Tsit5(), L2Loss(t_short, data_short), tstops = t_short, reltol = 1e-9)
optprob = OptimizationProblem(obj_short, glo_init, lb = first.(glo_bounds), ub = last.(glo_bounds))
@btime res1 = solve(optprob, BBO_adaptive_de_rand_1_bin(), maxiters = 7e3)
# Change in tolerance makes it worse
2.912 s (21140157 allocations: 805.19 MiB)
retcode: MaxIters
u: 4-element Vector{Float64}:
 0.8312909361389815
 0.9776197016782198
 0.08554290570106331
 0.5007265188988015
obj_short = build_loss_objective(prob_short, Vern9(), L2Loss(t_short, data_short),
    tstops = t_short, reltol = 1e-9, abstol = 1e-9)
optprob = OptimizationProblem(obj_short, glo_init, lb = first.(glo_bounds), ub = last.(glo_bounds))
@btime res1 = solve(optprob, BBO_adaptive_de_rand_1_bin(), maxiters = 7e3)
# using the more accurate Vern9() reduces the fitness marginally and leads to some increase in time taken
4.779 s (42507206 allocations: 1.11 GiB)
retcode: MaxIters
u: 4-element Vector{Float64}:
 0.48349668135455476
 0.7016509896807889
 0.08965121126120089
 0.4996385714698015

Using NLopt

Global Optimisation
obj_short = build_loss_objective(prob_short, Vern9(), L2Loss(t_short, data_short),
    tstops = t_short, reltol = 1e-9, abstol = 1e-9)
SciMLBase.OptimizationFunction{true, SciMLBase.NoAD, DiffEqParamEstim.var"#
37#38"{Nothing, typeof(DiffEqParamEstim.STANDARD_PROB_GENERATOR), Base.Pair
s{Symbol, Any, Nothing, @NamedTuple{tstops::Vector{Float64}, reltol::Float6
4, abstol::Float64}}, SciMLBase.ODEProblem{Vector{Float64}, Tuple{Float64, 
Float64}, true, ModelingToolkitBase.MTKParameters{Vector{Float64}, Vector{F
loat64}, Tuple{}, Tuple{}, Tuple{}, Tuple{}}, SciMLBase.ODEFunction{true, S
ciMLBase.AutoDespecialize, ModelingToolkitBase.GeneratedFunctionWrapper{Tup
le{2, 3, true}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:___mtk
unknowns___, :___mtkparameters___, :__argₛᵧₘ12968198168038750593), Modeling
ToolkitBase.var"#_RGF_ModTag", ModelingToolkitBase.var"#_RGF_ModTag", (0xb4
dec7fc, 0x0eef51a9, 0xe6d646f8, 0xd5b37c85, 0x7ae33bfd), Nothing}, RuntimeG
eneratedFunctions.RuntimeGeneratedFunction{(:__argₛᵧₘ1401282876548370056, :
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 (0xcc4caf47, 0xa22b65af, 0xd2ae4f08, 0x45b5d405, 0xd97af149), Nothing}}, L
inearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Noth
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gToolkitBase.ObservedFunctionCache{ModelingToolkitBase.System, Nothing}, No
thing, ModelingToolkitBase.System, Union{Nothing, SciMLBase.OverrideInitDat
a}, Union{Nothing, SciMLBase.ODENLStepData}}, Base.Pairs{Symbol, Union{}, N
othing, @NamedTuple{}}, SciMLBase.StandardODEProblem}, OrdinaryDiffEqVerner
.Vern9{typeof(OrdinaryDiffEqCore.trivial_limiter!), typeof(OrdinaryDiffEqCo
re.trivial_limiter!), FastBroadcast.Serial, Val{true}}, DiffEqParamEstim.L2
Loss{Vector{Float64}, Matrix{Float64}, Nothing, Nothing, Nothing, Nothing},
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othing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLB
ase.DEFAULT_OBSERVED_NO_TIME), Nothing, Nothing, Nothing, Nothing, Nothing,
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Nothing, typeof(DiffEqParamEstim.STANDARD_PROB_GENERATOR), Base.Pairs{Symbo
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caf47, 0xa22b65af, 0xd2ae4f08, 0x45b5d405, 0xd97af149), Nothing}}, LinearAl
gebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, No
thing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, ModelingToolki
tBase.ObservedFunctionCache{ModelingToolkitBase.System, Nothing}, Nothing, 
ModelingToolkitBase.System, Union{Nothing, SciMLBase.OverrideInitData}, Uni
on{Nothing, SciMLBase.ODENLStepData}}, Base.Pairs{Symbol, Union{}, Nothing,
 @NamedTuple{}}, SciMLBase.StandardODEProblem}, OrdinaryDiffEqVerner.Vern9{
typeof(OrdinaryDiffEqCore.trivial_limiter!), typeof(OrdinaryDiffEqCore.triv
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ctor{Float64}, Matrix{Float64}, Nothing, Nothing, Nothing, Nothing}, Nothin
g, Tuple{}}(nothing, DiffEqParamEstim.STANDARD_PROB_GENERATOR, Base.Pairs{S
ymbol, Any, Nothing, @NamedTuple{tstops::Vector{Float64}, reltol::Float64, 
abstol::Float64}}(:tstops => [0.0, 0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.07
, 0.08, 0.09  …  2.91, 2.92, 2.93, 2.94, 2.95, 2.96, 2.97, 2.98, 2.99, 3.0]
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edFunction{(:___mtkunknowns___, :___mtkparameters___, :__argₛᵧₘ129681981680
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1282876548370056, :___mtkunknowns___, :___mtkparameters___, :__argₛᵧₘ129681
98168038750593), ModelingToolkitBase.var"#_RGF_ModTag", ModelingToolkitBase
.var"#_RGF_ModTag", (0xcc4caf47, 0xa22b65af, 0xd2ae4f08, 0x45b5d405, 0xd97a
f149), Nothing}}, LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Not
hing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothin
g, Nothing, ModelingToolkitBase.ObservedFunctionCache{ModelingToolkitBase.S
ystem, Nothing}, Nothing, ModelingToolkitBase.System, Union{Nothing, SciMLB
ase.OverrideInitData}, Union{Nothing, SciMLBase.ODENLStepData}}, Base.Pairs
{Symbol, Union{}, Nothing, @NamedTuple{}}, SciMLBase.StandardODEProblem}(Sc
iMLBase.ODEFunction{true, SciMLBase.AutoDespecialize, ModelingToolkitBase.G
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delingToolkitBase.var"#_RGF_ModTag", (0xcc4caf47, 0xa22b65af, 0xd2ae4f08, 0
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ol}(true), nothing, nothing, nothing, nothing, nothing, nothing, nothing, n
othing, nothing, nothing, nothing, nothing, ModelingToolkitBase.ObservedFun
ctionCache{ModelingToolkitBase.System, Nothing}(Model fitz:
Equations (2):
  2 standard: see equations(fitz)
Unknowns (2): see unknowns(fitz)
  w(t)
  v(t)
Parameters (4): see parameters(fitz)
  a
  b
  τinv
  l, Dict{Any, Any}(), false, false, ModelingToolkitBase, false, nothing), 
nothing, Model fitz:
Equations (2):
  2 standard: see equations(fitz)
Unknowns (2): see unknowns(fitz)
  w(t)
  v(t)
Parameters (4): see parameters(fitz)
  a
  b
  τinv
  l, SciMLBase.OverrideInitData{SciMLBase.NonlinearProblem{Nothing, true, M
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ing}(nothing), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:__argₛᵧ
ₘ1401282876548370056, :___mtkunknowns___, :___mtkparameters___), ModelingTo
olkitBase.var"#_RGF_ModTag", ModelingToolkitBase.var"#_RGF_ModTag", (0xac9d
d6f8, 0xf3d8414c, 0x01f2cade, 0x451b4ee8, 0x29c649f2), Nothing}(nothing)), 
LinearAlgebra.UniformScaling{Bool}(true), nothing, nothing, nothing, nothin
g, nothing, nothing, nothing, nothing, nothing, nothing, ModelingToolkitBas
e.ObservedFunctionCache{ModelingToolkitBase.System, Nothing}(Model fitz:
Parameters (9): see parameters(fitz)
  t
  a
  b
  τinv
  ⋮
Observed (4): see observed(fitz), Dict{Any, Any}(), false, false, ModelingT
oolkitBase, false, nothing), nothing, Model fitz:
Parameters (9): see parameters(fitz)
  t
  a
  b
  τinv
  ⋮
Observed (4): see observed(fitz), nothing, nothing), nothing, ModelingToolk
itBase.MTKParameters{Vector{Float64}, StaticArraysCore.SVector{0, Float64},
 Tuple{}, Tuple{}, Tuple{}, Tuple{}}([0.0, 0.7, 0.8, 0.08, 0.5, 1.0, 0.0, 0
.0, 1.0], Float64[], (), (), (), ()), SciMLBase.StandardNonlinearProblem(),
 nothing, nothing, Base.Pairs{Symbol, Union{}, Nothing, @NamedTuple{}}()), 
ModelingToolkitBase.update_initializeprob!, ModelingToolkitBase.Initializat
ionMap{true, typeof(identity), ModelingToolkitBase.PromoteToTunableEltype{M
odelingToolkitBase.CopyParamsByTemplate{true, Tuple{ModelingToolkitBase.Par
ameterIndex{SciMLStructures.Tunable, UnitRange{Int64}}, ModelingToolkitBase
.ParameterIndex{SciMLStructures.Tunable, UnitRange{Int64}}}, 1, Nothing}, F
loat64}}(identity, ModelingToolkitBase.PromoteToTunableEltype{ModelingToolk
itBase.CopyParamsByTemplate{true, Tuple{ModelingToolkitBase.ParameterIndex{
SciMLStructures.Tunable, UnitRange{Int64}}, ModelingToolkitBase.ParameterIn
dex{SciMLStructures.Tunable, UnitRange{Int64}}}, 1, Nothing}, Float64}(Mode
lingToolkitBase.CopyParamsByTemplate{true, Tuple{ModelingToolkitBase.Parame
terIndex{SciMLStructures.Tunable, UnitRange{Int64}}, ModelingToolkitBase.Pa
rameterIndex{SciMLStructures.Tunable, UnitRange{Int64}}}, 1, Nothing}((Mode
lingToolkitBase.ParameterIndex{SciMLStructures.Tunable, UnitRange{Int64}}(S
ciMLStructures.Tunable(), 9:9, false), ModelingToolkitBase.ParameterIndex{S
ciMLStructures.Tunable, UnitRange{Int64}}(SciMLStructures.Tunable(), 6:6, f
alse)), (2,), nothing))), ModelingToolkitBase.var"#initprobpmap_split#770"{
ModelingToolkitBase.MTKParametersReconstructor{ComposedFunction{ModelingToo
lkitBase.PConstructorApplicator{typeof(identity)}, ModelingToolkitBase.Copy
ParamsByTemplate{true, Tuple{ModelingToolkitBase.ParameterIndex{SciMLStruct
ures.Tunable, UnitRange{Int64}}}, 1, Nothing}}, ComposedFunction{ModelingTo
olkitBase.PConstructorApplicator{typeof(identity)}, ModelingToolkitBase.Cop
yParamsByTemplate{true, Tuple{ModelingToolkitBase.ParameterIndex{SciMLStruc
tures.Tunable, UnitRange{Int64}}}, 1, Nothing}}, Returns{Tuple{}}, Returns{
Tuple{}}, Returns{Tuple{}}}}(ModelingToolkitBase.MTKParametersReconstructor
{ComposedFunction{ModelingToolkitBase.PConstructorApplicator{typeof(identit
y)}, ModelingToolkitBase.CopyParamsByTemplate{true, Tuple{ModelingToolkitBa
se.ParameterIndex{SciMLStructures.Tunable, UnitRange{Int64}}}, 1, Nothing}}
, ComposedFunction{ModelingToolkitBase.PConstructorApplicator{typeof(identi
ty)}, ModelingToolkitBase.CopyParamsByTemplate{true, Tuple{ModelingToolkitB
ase.ParameterIndex{SciMLStructures.Tunable, UnitRange{Int64}}}, 1, Nothing}
}, Returns{Tuple{}}, Returns{Tuple{}}, Returns{Tuple{}}}(ModelingToolkitBas
e.PConstructorApplicator{typeof(identity)}(identity) ∘ ModelingToolkitBase.
CopyParamsByTemplate{true, Tuple{ModelingToolkitBase.ParameterIndex{SciMLSt
ructures.Tunable, UnitRange{Int64}}}, 1, Nothing}((ModelingToolkitBase.Para
meterIndex{SciMLStructures.Tunable, UnitRange{Int64}}(SciMLStructures.Tunab
le(), 2:5, false),), (4,), nothing), ModelingToolkitBase.PConstructorApplic
ator{typeof(identity)}(identity) ∘ ModelingToolkitBase.CopyParamsByTemplate
{true, Tuple{ModelingToolkitBase.ParameterIndex{SciMLStructures.Tunable, Un
itRange{Int64}}}, 1, Nothing}((ModelingToolkitBase.ParameterIndex{SciMLStru
ctures.Tunable, UnitRange{Int64}}(SciMLStructures.Tunable(), 6:9, false),),
 (4,), nothing), Returns{Tuple{}}(()), Returns{Tuple{}}(()), Returns{Tuple{
}}(()), 0)), ModelingToolkitBase.InitializationMetadata{ModelingToolkitBase
.ReconstructInitializeprob{ModelingToolkitBase.MTKParametersReconstructor{C
omposedFunction{ModelingToolkitBase.PConstructorApplicator{typeof(identity)
}, ModelingToolkitBase.CopyParamsByTemplate{true, Tuple{ModelingToolkitBase
.IndepVarTemplate, ModelingToolkitBase.ParameterIndex{SciMLStructures.Tunab
le, UnitRange{Int64}}, ModelingToolkitBase.ParameterIndex{SciMLStructures.I
nitials, UnitRange{Int64}}}, 1, Nothing}}, Returns{StaticArraysCore.SVector
{0, Float64}}, Returns{Tuple{}}, Returns{Tuple{}}, Returns{Tuple{}}}, Compo
sedFunction{typeof(identity), ModelingToolkitBase.ObservedWrapper{true, Mod
elingToolkitBase.GeneratedFunctionWrapper{Tuple{2, 3, true}, RuntimeGenerat
edFunctions.RuntimeGeneratedFunction{(:__mtk_arg_1, :___mtkparameters___, :
__argₛᵧₘ12968198168038750593), ModelingToolkitBase.var"#_RGF_ModTag", Model
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nction{(:x1, :x2, :x3, :x4), ModelingToolkitBase.var"#_RGF_ModTag", Modelin
gToolkitBase.var"#_RGF_ModTag", (0xb896e553, 0xa118fcf5, 0xbfeb9719, 0xa096
e58a, 0x357542a4), Nothing}}}}}, ModelingToolkitBase.GetUpdatedU0{Nothing, 
SymbolicIndexingInterface.MultipleParametersGetter{SymbolicIndexingInterfac
e.IndexerNotTimeseries, Vector{SymbolicIndexingInterface.GetParameterIndex{
ModelingToolkitBase.ParameterIndex{SciMLStructures.Initials, Int64}}}, Noth
ing}}, ModelingToolkitBase.SetInitialUnknowns{SymbolicIndexingInterface.Mul
tipleSetters{Vector{SymbolicIndexingInterface.ParameterHookWrapper{Symbolic
IndexingInterface.SetParameterIndex{ModelingToolkitBase.ParameterIndex{SciM
LStructures.Initials, Int64}}, SymbolicUtils.BasicSymbolicImpl.var"typeof(B
asicSymbolicImpl)"{SymbolicUtils.SymReal}}}}}}(ModelingToolkitBase.AtomicAr
rayDict{SymbolicUtils.BasicSymbolicImpl.var"typeof(BasicSymbolicImpl)"{Symb
olicUtils.SymReal}, Dict{SymbolicUtils.BasicSymbolicImpl.var"typeof(BasicSy
mbolicImpl)"{SymbolicUtils.SymReal}, SymbolicUtils.BasicSymbolicImpl.var"ty
peof(BasicSymbolicImpl)"{SymbolicUtils.SymReal}}}(v(t) => 1.0, Initial(w(t)
) => false, b => 0.8, a => 0.7, τinv => 0.08, l => 0.5, Initial(vˍt(t)) => 
false, Initial(wˍt(t)) => false, w(t) => 1.0, Initial(v(t)) => false…), Mod
elingToolkitBase.AtomicArrayDict{SymbolicUtils.BasicSymbolicImpl.var"typeof
(BasicSymbolicImpl)"{SymbolicUtils.SymReal}, Dict{SymbolicUtils.BasicSymbol
icImpl.var"typeof(BasicSymbolicImpl)"{SymbolicUtils.SymReal}, SymbolicUtils
.BasicSymbolicImpl.var"typeof(BasicSymbolicImpl)"{SymbolicUtils.SymReal}}}(
), Symbolics.Equation[], true, true, ModelingToolkitBase.ReconstructInitial
izeprob{ModelingToolkitBase.MTKParametersReconstructor{ComposedFunction{Mod
elingToolkitBase.PConstructorApplicator{typeof(identity)}, ModelingToolkitB
ase.CopyParamsByTemplate{true, Tuple{ModelingToolkitBase.IndepVarTemplate, 
ModelingToolkitBase.ParameterIndex{SciMLStructures.Tunable, UnitRange{Int64
}}, ModelingToolkitBase.ParameterIndex{SciMLStructures.Initials, UnitRange{
Int64}}}, 1, Nothing}}, Returns{StaticArraysCore.SVector{0, Float64}}, Retu
rns{Tuple{}}, Returns{Tuple{}}, Returns{Tuple{}}}, ComposedFunction{typeof(
identity), ModelingToolkitBase.ObservedWrapper{true, ModelingToolkitBase.Ge
neratedFunctionWrapper{Tuple{2, 3, true}, RuntimeGeneratedFunctions.Runtime
GeneratedFunction{(:__mtk_arg_1, :___mtkparameters___, :__argₛᵧₘ12968198168
038750593), ModelingToolkitBase.var"#_RGF_ModTag", ModelingToolkitBase.var"
#_RGF_ModTag", (0x05e7e591, 0x9a09c886, 0x0267af3f, 0x585cfe8b, 0x75f79d7b)
, Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:x1, :x2, :
x3, :x4), ModelingToolkitBase.var"#_RGF_ModTag", ModelingToolkitBase.var"#_
RGF_ModTag", (0xb896e553, 0xa118fcf5, 0xbfeb9719, 0xa096e58a, 0x357542a4), 
Nothing}}}}}(ModelingToolkitBase.MTKParametersReconstructor{ComposedFunctio
n{ModelingToolkitBase.PConstructorApplicator{typeof(identity)}, ModelingToo
lkitBase.CopyParamsByTemplate{true, Tuple{ModelingToolkitBase.IndepVarTempl
ate, ModelingToolkitBase.ParameterIndex{SciMLStructures.Tunable, UnitRange{
Int64}}, ModelingToolkitBase.ParameterIndex{SciMLStructures.Initials, UnitR
ange{Int64}}}, 1, Nothing}}, Returns{StaticArraysCore.SVector{0, Float64}},
 Returns{Tuple{}}, Returns{Tuple{}}, Returns{Tuple{}}}(ModelingToolkitBase.
PConstructorApplicator{typeof(identity)}(identity) ∘ ModelingToolkitBase.Co
pyParamsByTemplate{true, Tuple{ModelingToolkitBase.IndepVarTemplate, Modeli
ngToolkitBase.ParameterIndex{SciMLStructures.Tunable, UnitRange{Int64}}, Mo
delingToolkitBase.ParameterIndex{SciMLStructures.Initials, UnitRange{Int64}
}}, 1, Nothing}((ModelingToolkitBase.IndepVarTemplate(), ModelingToolkitBas
e.ParameterIndex{SciMLStructures.Tunable, UnitRange{Int64}}(SciMLStructures
.Tunable(), 1:4, false), ModelingToolkitBase.ParameterIndex{SciMLStructures
.Initials, UnitRange{Int64}}(SciMLStructures.Initials(), 1:4, false)), (9,)
, nothing), Returns{StaticArraysCore.SVector{0, Float64}}(Float64[]), Retur
ns{Tuple{}}(()), Returns{Tuple{}}(()), Returns{Tuple{}}(()), 0), identity ∘
 ModelingToolkitBase.ObservedWrapper{true, ModelingToolkitBase.GeneratedFun
ctionWrapper{Tuple{2, 3, true}, RuntimeGeneratedFunctions.RuntimeGeneratedF
unction{(:__mtk_arg_1, :___mtkparameters___, :__argₛᵧₘ12968198168038750593)
, ModelingToolkitBase.var"#_RGF_ModTag", ModelingToolkitBase.var"#_RGF_ModT
ag", (0x05e7e591, 0x9a09c886, 0x0267af3f, 0x585cfe8b, 0x75f79d7b), Nothing}
, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:x1, :x2, :x3, :x4), 
ModelingToolkitBase.var"#_RGF_ModTag", ModelingToolkitBase.var"#_RGF_ModTag
", (0xb896e553, 0xa118fcf5, 0xbfeb9719, 0xa096e58a, 0x357542a4), Nothing}}}
(ModelingToolkitBase.GeneratedFunctionWrapper{Tuple{2, 3, true}, RuntimeGen
eratedFunctions.RuntimeGeneratedFunction{(:__mtk_arg_1, :___mtkparameters__
_, :__argₛᵧₘ12968198168038750593), ModelingToolkitBase.var"#_RGF_ModTag", M
odelingToolkitBase.var"#_RGF_ModTag", (0x05e7e591, 0x9a09c886, 0x0267af3f, 
0x585cfe8b, 0x75f79d7b), Nothing}, RuntimeGeneratedFunctions.RuntimeGenerat
edFunction{(:x1, :x2, :x3, :x4), ModelingToolkitBase.var"#_RGF_ModTag", Mod
elingToolkitBase.var"#_RGF_ModTag", (0xb896e553, 0xa118fcf5, 0xbfeb9719, 0x
a096e58a, 0x357542a4), Nothing}}(RuntimeGeneratedFunctions.RuntimeGenerated
Function{(:__mtk_arg_1, :___mtkparameters___, :__argₛᵧₘ12968198168038750593
), ModelingToolkitBase.var"#_RGF_ModTag", ModelingToolkitBase.var"#_RGF_Mod
Tag", (0x05e7e591, 0x9a09c886, 0x0267af3f, 0x585cfe8b, 0x75f79d7b), Nothing
}(nothing), RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:x1, :x2, :
x3, :x4), ModelingToolkitBase.var"#_RGF_ModTag", ModelingToolkitBase.var"#_
RGF_ModTag", (0xb896e553, 0xa118fcf5, 0xbfeb9719, 0xa096e58a, 0x357542a4), 
Nothing}(nothing)))), ModelingToolkitBase.GetUpdatedU0{Nothing, SymbolicInd
exingInterface.MultipleParametersGetter{SymbolicIndexingInterface.IndexerNo
tTimeseries, Vector{SymbolicIndexingInterface.GetParameterIndex{ModelingToo
lkitBase.ParameterIndex{SciMLStructures.Initials, Int64}}}, Nothing}}(Bool[
0, 0], nothing, SymbolicIndexingInterface.MultipleParametersGetter{Symbolic
IndexingInterface.IndexerNotTimeseries, Vector{SymbolicIndexingInterface.Ge
tParameterIndex{ModelingToolkitBase.ParameterIndex{SciMLStructures.Initials
, Int64}}}, Nothing}(SymbolicIndexingInterface.GetParameterIndex{ModelingTo
olkitBase.ParameterIndex{SciMLStructures.Initials, Int64}}[SymbolicIndexing
Interface.GetParameterIndex{ModelingToolkitBase.ParameterIndex{SciMLStructu
res.Initials, Int64}}(ModelingToolkitBase.ParameterIndex{SciMLStructures.In
itials, Int64}(SciMLStructures.Initials(), 4, false)), SymbolicIndexingInte
rface.GetParameterIndex{ModelingToolkitBase.ParameterIndex{SciMLStructures.
Initials, Int64}}(ModelingToolkitBase.ParameterIndex{SciMLStructures.Initia
ls, Int64}(SciMLStructures.Initials(), 1, false))], nothing)), ModelingTool
kitBase.SetInitialUnknowns{SymbolicIndexingInterface.MultipleSetters{Vector
{SymbolicIndexingInterface.ParameterHookWrapper{SymbolicIndexingInterface.S
etParameterIndex{ModelingToolkitBase.ParameterIndex{SciMLStructures.Initial
s, Int64}}, SymbolicUtils.BasicSymbolicImpl.var"typeof(BasicSymbolicImpl)"{
SymbolicUtils.SymReal}}}}}(SymbolicIndexingInterface.MultipleSetters{Vector
{SymbolicIndexingInterface.ParameterHookWrapper{SymbolicIndexingInterface.S
etParameterIndex{ModelingToolkitBase.ParameterIndex{SciMLStructures.Initial
s, Int64}}, SymbolicUtils.BasicSymbolicImpl.var"typeof(BasicSymbolicImpl)"{
SymbolicUtils.SymReal}}}}(SymbolicIndexingInterface.ParameterHookWrapper{Sy
mbolicIndexingInterface.SetParameterIndex{ModelingToolkitBase.ParameterInde
x{SciMLStructures.Initials, Int64}}, SymbolicUtils.BasicSymbolicImpl.var"ty
peof(BasicSymbolicImpl)"{SymbolicUtils.SymReal}}[SymbolicIndexingInterface.
ParameterHookWrapper{SymbolicIndexingInterface.SetParameterIndex{ModelingTo
olkitBase.ParameterIndex{SciMLStructures.Initials, Int64}}, SymbolicUtils.B
asicSymbolicImpl.var"typeof(BasicSymbolicImpl)"{SymbolicUtils.SymReal}}(Sym
bolicIndexingInterface.SetParameterIndex{ModelingToolkitBase.ParameterIndex
{SciMLStructures.Initials, Int64}}(ModelingToolkitBase.ParameterIndex{SciML
Structures.Initials, Int64}(SciMLStructures.Initials(), 4, false)), Initial
(w(t))), SymbolicIndexingInterface.ParameterHookWrapper{SymbolicIndexingInt
erface.SetParameterIndex{ModelingToolkitBase.ParameterIndex{SciMLStructures
.Initials, Int64}}, SymbolicUtils.BasicSymbolicImpl.var"typeof(BasicSymboli
cImpl)"{SymbolicUtils.SymReal}}(SymbolicIndexingInterface.SetParameterIndex
{ModelingToolkitBase.ParameterIndex{SciMLStructures.Initials, Int64}}(Model
ingToolkitBase.ParameterIndex{SciMLStructures.Initials, Int64}(SciMLStructu
res.Initials(), 1, false)), Initial(v(t)))]), [4, 1]), ModelingToolkitBase.
MissingGuessValue.var"typeof(MissingGuessValue)"(ModelingToolkitBase.Missin
gGuessValue.var"##Storage#HashedRandom"())), Val{true}()), nothing), [1.0, 
1.0], (0.0, 3.0), ModelingToolkitBase.MTKParameters{Vector{Float64}, Vector
{Float64}, Tuple{}, Tuple{}, Tuple{}, Tuple{}}([0.7, 0.8, 0.08, 0.5], [1.0,
 0.0, 0.0, 1.0], (), (), (), ()), Base.Pairs{Symbol, Union{}, Nothing, @Nam
edTuple{}}(), SciMLBase.StandardODEProblem()), OrdinaryDiffEqVerner.Vern9{t
ypeof(OrdinaryDiffEqCore.trivial_limiter!), typeof(OrdinaryDiffEqCore.trivi
al_limiter!), FastBroadcast.Serial, Val{true}}(OrdinaryDiffEqCore.trivial_l
imiter!, OrdinaryDiffEqCore.trivial_limiter!, FastBroadcast.Serial(), Val{t
rue}()), DiffEqParamEstim.L2Loss{Vector{Float64}, Matrix{Float64}, Nothing,
 Nothing, Nothing, Nothing}([0.0, 0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.07,
 0.08, 0.09  …  2.91, 2.92, 2.93, 2.94, 2.95, 2.96, 2.97, 2.98, 2.99, 3.0],
 [1.0 1.000720435211627 … 1.22193331177933 1.222601511669354; 1.0 1.0016630
55982029 … 1.1134077677576417 1.11271910687873], nothing, nothing, nothing,
 nothing, nothing), nothing, ()), SciMLBase.NoAD(), nothing, nothing, nothi
ng, nothing, nothing, nothing, nothing, nothing, nothing, nothing, nothing,
 nothing, nothing, SciMLBase.DEFAULT_OBSERVED_NO_TIME, nothing, nothing, no
thing, nothing, nothing, nothing, nothing, nothing, nothing, nothing)
opt = Opt(:GN_ORIG_DIRECT_L, 4)
optprob = OptimizationProblem(obj_short, glo_init, lb = first.(glo_bounds), ub = last.(glo_bounds))
@btime res1 = solve(optprob, opt, maxiters = 10000, xtol_rel = 1e-12)
6.798 s (59865528 allocations: 1.56 GiB)
retcode: MaxIters
u: 4-element Vector{Float64}:
 0.1920438957477088
 1.1316872427984634
 1.1111111111112206
 0.509577685189625
opt = Opt(:GN_CRS2_LM, 4)
@btime res1 = solve(optprob, opt, maxiters = 10000, xtol_rel = 1e-12)
6.882 s (59746198 allocations: 1.56 GiB)
retcode: MaxIters
u: 4-element Vector{Float64}:
 0.7000001054289524
 0.8000000245355546
 0.07999999329973194
 0.49999999995230004
opt = Opt(:GN_ISRES, 4)
@btime res1 = solve(optprob, opt, maxiters = 10000, xtol_rel = 1e-12)
6.891 s (59770053 allocations: 1.56 GiB)
retcode: MaxIters
u: 4-element Vector{Float64}:
 4.072530850031646
 4.081573004816701
 0.09810169203282876
 0.5131216584764253
opt = Opt(:GN_ESCH, 4)
@btime res1 = solve(optprob, opt, maxiters = 10000, xtol_rel = 1e-12)
6.869 s (59770053 allocations: 1.56 GiB)
retcode: MaxIters
u: 4-element Vector{Float64}:
 2.5776978151220717
 2.9698384556488815
 0.1717557282991468
 0.5094505446268731

Now local optimization algorithms are used to check the global ones. These use the local bounds (loc_bounds) and initial values (loc_init).

obj_short = build_loss_objective(prob_short, Vern9(), L2Loss(t_short, data_short),
    Optimization.AutoForwardDiff(), tstops = t_short, reltol = 1e-9, abstol = 1e-9)
optprob = OptimizationProblem(obj_short, loc_init, lb = first.(loc_bounds), ub = last.(loc_bounds))
OptimizationProblem. In-place: true
u0: 4-element Vector{Float64}:
 0.5
 0.5
 0.5
 0.5
opt = Opt(:LN_BOBYQA, 4)
@btime res1 = solve(optprob, opt, maxiters = 10000, xtol_rel = 1e-12)
1.269 s (11028088 allocations: 294.58 MiB)
retcode: Success
u: 4-element Vector{Float64}:
 0.7000000000188623
 0.8000000000060236
 0.07999999999893552
 0.5000000000000322
opt = Opt(:LN_NELDERMEAD, 4)
@btime res1 = solve(optprob, opt, maxiters = 10000, xtol_rel = 1e-12)
652.073 ms (5748224 allocations: 153.55 MiB)
retcode: Success
u: 4-element Vector{Float64}:
 1.0
 1.0
 0.07355092571547887
 0.5004047023109518
opt = Opt(:LD_SLSQP, 4)
@btime res1 = solve(optprob, opt, maxiters = 10000, xtol_rel = 1e-12)
8.660 s (71095530 allocations: 1.90 GiB)
retcode: MaxIters
u: 4-element Vector{Float64}:
 0.700000000015133
 0.8000000000055394
 0.07999999999920873
 0.5000000000000321
opt = Opt(:LN_COBYLA, 4)
@btime res1 = solve(optprob, opt, maxiters = 10000, xtol_rel = 1e-12)
6.923 s (59740084 allocations: 1.56 GiB)
retcode: MaxIters
u: 4-element Vector{Float64}:
 0.1829436856114406
 0.8339606715478033
 0.19453032306019252
 0.5003613601073567
opt = Opt(:LN_NEWUOA_BOUND, 4)
@btime res1 = solve(optprob, opt, maxiters = 10000, xtol_rel = 1e-12)
627.666 ms (4325260 allocations: 115.54 MiB)
retcode: Success
u: 4-element Vector{Float64}:
 0.24815174877228105
 0.4389927966494055
 0.08539344966317435
 0.49911205692389365
opt = Opt(:LN_PRAXIS, 4)
@btime res1 = solve(optprob, opt, maxiters = 10000, xtol_rel = 1e-12)
559.904 ms (4959275 allocations: 132.47 MiB)
retcode: Success
u: 4-element Vector{Float64}:
 0.7000000000078808
 0.8000000000075309
 0.08000000000000884
 0.5000000000000498
opt = Opt(:LN_SBPLX, 4)
@btime res1 = solve(optprob, opt, maxiters = 10000, xtol_rel = 1e-12)
6.909 s (59740066 allocations: 1.56 GiB)
retcode: MaxIters
u: 4-element Vector{Float64}:
 0.7000016809870933
 0.8000002415243684
 0.07999987937160621
 0.5000000003805862
opt = Opt(:LD_MMA, 4)
@btime res1 = solve(optprob, opt, maxiters = 10000, xtol_rel = 1e-12)
16.221 s (119380443 allocations: 3.39 GiB)
retcode: MaxIters
u: 4-element Vector{Float64}:
 0.2194953414908776
 0.7035126977082891
 0.13312823531746235
 0.499708318694746

Now the longer problem is solved for a global solution

Vern9 solver with reltol=1e-9 and abstol=1e-9 is used and the dataset is increased to 3000 observations per variable with the same integration time step of 0.01.

obj = build_loss_objective(
    prob, Vern9(), L2Loss(time_points, data), Optimization.AutoForwardDiff(),
    tstops = time_points, reltol = 1e-9, abstol = 1e-9)
optprob = OptimizationProblem(obj, glo_init, lb = first.(glo_bounds), ub = last.(glo_bounds))
@btime res1 = solve(optprob, BBO_adaptive_de_rand_1_bin(), maxiters = 4e3)
23.431 s (224364010 allocations: 4.64 GiB)
retcode: MaxIters
u: 4-element Vector{Float64}:
 0.38711692700102035
 0.6954201963531315
 0.060000819766535256
 0.40501129015572684
opt = Opt(:GN_ORIG_DIRECT_L, 4)
@btime res1 = solve(optprob, opt, maxiters = 10000, xtol_rel = 1e-12)
57.190 s (546202158 allocations: 11.28 GiB)
retcode: MaxIters
u: 4-element Vector{Float64}:
 1.1111111111111116
 1.1111111111111107
 0.10059442158207468
 0.5761316872427985
opt = Opt(:GN_CRS2_LM, 4)
@btime res1 = solve(optprob, opt, maxiters = 20000, xtol_rel = 1e-12)
114.803 s (1091640234 allocations: 22.55 GiB)
retcode: MaxIters
u: 4-element Vector{Float64}:
 0.6999999999966802
 0.8000000000028483
 0.08000000000032173
 0.49999999999845446
opt = Opt(:GN_ISRES, 4)
@btime res1 = solve(optprob, opt, maxiters = 50000, xtol_rel = 1e-12)
286.339 s (2729250063 allocations: 56.38 GiB)
retcode: MaxIters
u: 4-element Vector{Float64}:
 0.7000000014419183
 0.8000000017353587
 0.08000000007590248
 0.5000000001004294
opt = Opt(:GN_ESCH, 4)
@btime res1 = solve(optprob, opt, maxiters = 20000, xtol_rel = 1e-12)
114.795 s (1091700060 allocations: 22.55 GiB)
retcode: MaxIters
u: 4-element Vector{Float64}:
 0.0007885361774983767
 0.5836388822043367
 0.04172521411051209
 0.3267094319284882
optprob = OptimizationProblem(obj_short, loc_init, lb = first.(loc_bounds), ub = last.(loc_bounds))
OptimizationProblem. In-place: true
u0: 4-element Vector{Float64}:
 0.5
 0.5
 0.5
 0.5
opt = Opt(:LN_BOBYQA, 4)
@btime res1 = solve(optprob, opt, maxiters = 10000, xtol_rel = 1e-12)
1.215 s (11028088 allocations: 294.58 MiB)
retcode: Success
u: 4-element Vector{Float64}:
 0.7000000000188623
 0.8000000000060236
 0.07999999999893552
 0.5000000000000322
opt = Opt(:LN_NELDERMEAD, 4)
@btime res1 = solve(optprob, opt, maxiters = 10000, xtol_rel = 1e-9)
632.844 ms (5748224 allocations: 153.55 MiB)
retcode: Success
u: 4-element Vector{Float64}:
 1.0
 1.0
 0.07355092571547887
 0.5004047023109518
opt = Opt(:LD_SLSQP, 4)
@btime res1 = solve(optprob, opt, maxiters = 10000, xtol_rel = 1e-12)
8.634 s (71095530 allocations: 1.90 GiB)
retcode: MaxIters
u: 4-element Vector{Float64}:
 0.700000000015133
 0.8000000000055394
 0.07999999999920873
 0.5000000000000321

Conclusion

The parameters used to generate the data are [0.7, 0.8, 0.08, 0.5]. In the latest run:

  • On the short (300-observation) problem, GN_CRS2_LM and the local methods LN_BOBYQA, LN_NELDERMEAD, LD_SLSQP and LN_PRAXIS recover these values to within about 1e-9, and LN_NEWUOA_BOUND and LD_MMA get close. GN_ORIG_DIRECT_L, GN_ISRES, GN_ESCH, LN_COBYLA and LN_SBPLX do not.
  • BBO gets close on the short problem with the default Tsit5 tolerances, but tightening the ODE solver tolerances (reltol = 1e-9, then Vern9 at 1e-9) moved its estimate further from the true values and made the run slower.
  • On the longer (3000-observation) problem, GN_CRS2_LM and GN_ISRES recover the true values, BBO only gets close, and GN_ORIG_DIRECT_L and GN_ESCH do not. Every global run takes considerably longer than on the short problem.
  • The local optimizers in the longer-problem section are run on the short objective obj_short, so they repeat the short-problem results rather than testing the longer problem.

Appendix

These benchmarks are a part of the SciMLBenchmarks.jl repository, found at: https://github.com/SciML/SciMLBenchmarks.jl. For more information on high-performance scientific machine learning, check out the SciML Open Source Software Organization https://sciml.ai.

To locally run this benchmark, do the following commands:

using SciMLBenchmarks
SciMLBenchmarks.weave_file("benchmarks/ParameterEstimation","FitzHughNagumoParameterEstimation.jmd")

Computer Information:

Julia Version 1.12.7
Commit 6d172b025e4 (2026-08-15 08:05 UTC)
Build Info:
  Official https://julialang.org release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 128 × AMD EPYC 7502 32-Core Processor
  WORD_SIZE: 64
  LLVM: libLLVM-18.1.7 (ORCJIT, znver2)
  GC: Built with stock GC
Threads: 128 default, 1 interactive, 128 GC (on 128 virtual cores)
Environment:
  JULIA_NUM_THREADS = auto

Package Information:

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Info Packages marked with ⌃ have new versions available and may be upgradable.
Warning The project dependencies or compat requirements have changed since the manifest was last resolved. It is recommended to `Pkg.resolve()` or consider `Pkg.update()` if necessary.

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  [2def613f] Xorg_xcb_util_jll v0.4.1+0
  [975044d2] Xorg_xcb_util_keysyms_jll v0.4.1+0
  [0d47668e] Xorg_xcb_util_renderutil_jll v0.3.10+0
  [c22f9ab0] Xorg_xcb_util_wm_jll v0.4.2+0
  [35661453] Xorg_xkbcomp_jll v1.4.7+0
  [33bec58e] Xorg_xkeyboard_config_jll v2.47.0+2
  [c5fb5394] Xorg_xtrans_jll v1.6.0+0
  [3161d3a3] Zstd_jll v1.5.7+1
  [35ca27e7] eudev_jll v3.2.14+0
⌅ [214eeab7] fzf_jll v0.61.1+0
⌃ [a4ae2306] libaom_jll v3.14.1+0
  [0ac62f75] libass_jll v0.17.5+0
  [1183f4f0] libdecor_jll v0.2.2+0
  [8e53e030] libdrm_jll v2.4.134+0
  [2db6ffa8] libevdev_jll v1.13.4+0
  [f638f0a6] libfdk_aac_jll v2.0.4+0
  [36db933b] libinput_jll v1.28.1+0
  [b53b4c65] libpng_jll v1.6.58+0
  [9a156e7d] libva_jll v2.23.0+0
  [f27f6e37] libvorbis_jll v1.3.8+0
  [009596ad] mtdev_jll v1.1.7+0
  [1317d2d5] oneTBB_jll v2022.3.0+0
⌅ [1270edf5] x264_jll v10164.0.1+0
  [dfaa095f] x265_jll v4.1.0+0
  [d8fb68d0] xkbcommon_jll v1.13.0+0
  [0dad84c5] ArgTools v1.1.2
  [56f22d72] Artifacts v1.11.0
  [2a0f44e3] Base64 v1.11.0
  [ade2ca70] Dates v1.11.0
  [8ba89e20] Distributed v1.11.0
  [f43a241f] Downloads v1.7.0
  [7b1f6079] FileWatching v1.11.0
  [9fa8497b] Future v1.11.0
  [b77e0a4c] InteractiveUtils v1.11.0
  [ac6e5ff7] JuliaSyntaxHighlighting v1.12.0
  [4af54fe1] LazyArtifacts v1.11.0
  [b27032c2] LibCURL v0.6.4
  [76f85450] LibGit2 v1.11.0
  [8f399da3] Libdl v1.11.0
  [37e2e46d] LinearAlgebra v1.12.0
  [56ddb016] Logging v1.11.0
  [d6f4376e] Markdown v1.11.0
  [a63ad114] Mmap v1.11.0
  [ca575930] NetworkOptions v1.3.0
  [44cfe95a] Pkg v1.12.1
  [de0858da] Printf v1.11.0
  [9abbd945] Profile v1.11.0
  [3fa0cd96] REPL v1.11.0
  [9a3f8284] Random v1.11.0
  [ea8e919c] SHA v0.7.0
  [9e88b42a] Serialization v1.11.0
  [6462fe0b] Sockets v1.11.0
  [2f01184e] SparseArrays v1.12.0
  [f489334b] StyledStrings v1.11.0
  [4607b0f0] SuiteSparse
  [fa267f1f] TOML v1.0.3
  [a4e569a6] Tar v1.10.0
  [8dfed614] Test v1.11.0
  [cf7118a7] UUIDs v1.11.0
  [4ec0a83e] Unicode v1.11.0
  [e66e0078] CompilerSupportLibraries_jll v1.3.1+2
  [deac9b47] LibCURL_jll v8.15.0+0
  [e37daf67] LibGit2_jll v1.9.0+0
  [29816b5a] LibSSH2_jll v1.11.3+1
  [14a3606d] MozillaCACerts_jll v2025.11.4
  [4536629a] OpenBLAS_jll v0.3.29+0
  [05823500] OpenLibm_jll v0.8.7+0
  [458c3c95] OpenSSL_jll v3.5.6+0
  [efcefdf7] PCRE2_jll v10.44.0+1
  [bea87d4a] SuiteSparse_jll v7.8.3+2
  [83775a58] Zlib_jll v1.3.1+2
  [8e850b90] libblastrampoline_jll v5.15.0+0
  [8e850ede] nghttp2_jll v1.64.0+1
  [3f19e933] p7zip_jll v17.7.0+0
Info Packages marked with ⌃ and ⌅ have new versions available. Those with ⌃ may be upgradable, but those with ⌅ are restricted by compatibility constraints from upgrading. To see why use `status --outdated -m`
Warning The project dependencies or compat requirements have changed since the manifest was last resolved. It is recommended to `Pkg.resolve()` or consider `Pkg.update()` if necessary.