Lotka-Volterra Parameter Estimation Benchmarks

Parameter estimation of Lotka Volterra model using optimisation methods

using ParameterizedFunctions, OrdinaryDiffEq, DiffEqParamEstim, Optimization, ForwardDiff
using OptimizationBBO, OptimizationNLopt, Plots, RecursiveArrayTools, BenchmarkTools
gr(fmt=:png)

Plots.GRBackend()

loc_bounds = Tuple{Float64, Float64}[(0, 5), (0, 5), (0, 5), (0, 5)]
glo_bounds = Tuple{Float64, Float64}[(0, 10), (0, 10), (0, 10), (0, 10)]
loc_init = [1,0.5,3.5,1.5]
glo_init = [5,5,5,5]

4-element Vector{Int64}:
 5
 5
 5
 5

f = @ode_def LotkaVolterraTest begin
    dx = a*x - b*x*y
    dy = -c*y + d*x*y
end a b c d

(::Main.var"##WeaveSandBox#292".LotkaVolterraTest{Main.var"##WeaveSandBox#2
92".var"###ParameterizedDiffEqFunction#294", Main.var"##WeaveSandBox#292".v
ar"###ParameterizedTGradFunction#295", Main.var"##WeaveSandBox#292".var"###
ParameterizedJacobianFunction#296", Nothing, Nothing, ModelingToolkit.ODESy
stem}) (generic function with 1 method)

u0 = [1.0,1.0]                          #initial values
tspan = (0.0,10.0)
p = [1.5,1.0,3.0,1,0]                   #parameters used, these need to be estimated from the data
tspan = (0.0, 30.0)                     # sample of 3000 observations over the (0,30) timespan
prob = ODEProblem(f, u0, tspan,p)
tspan2 = (0.0, 3.0)                     # sample of 3000 observations over the (0,30) timespan
prob_short = ODEProblem(f, u0, tspan2,p)

ODEProblem with uType Vector{Float64} and tType Float64. In-place: true
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
t  = 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,Tsit5(),saveat=t_short,reltol=1e-9,abstol=1e-9)
data_short = convert(Array, data_sol_short)
data_sol = solve(prob,Tsit5(),saveat=t,reltol=1e-9,abstol=1e-9)
data = convert(Array, data_sol)

2×3001 Matrix{Float64}:
 1.0  1.00511   1.01045   1.01601   1.02179   …  1.07814   1.08595   1.0939
8
 1.0  0.980224  0.960888  0.941986  0.923508     0.785597  0.770673  0.7560
92

Plot of the solution

Short Solution

p1 = plot(data_sol_short)

Longer Solution

p2 = 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, loc_init, lb = first.(loc_bounds), ub = last.(loc_bounds))
@btime res1 = solve(optprob, BBO_adaptive_de_rand_1_bin(); maxiters = 7e3)
# Lower tolerance could lead to smaller fitness (more accuracy)

991.087 ms (2761416 allocations: 390.08 MiB)
u: 4-element Vector{Float64}:
 1.5012937396750103
 1.0008196734772647
 2.994489835690994
 0.9983310801237163

obj_short = build_loss_objective(prob_short,Tsit5(),L2Loss(t_short,data_short),tstops=t_short,reltol=1e-9)
optprob = OptimizationProblem(obj_short, loc_init, lb = first.(loc_bounds), ub = last.(loc_bounds))
@btime res1 = solve(optprob, BBO_adaptive_de_rand_1_bin(); maxiters = 7e3)
# Change in tolerance makes it worse

994.989 ms (2767815 allocations: 391.01 MiB)
u: 4-element Vector{Float64}:
 1.4992950568315195
 0.9988746850811105
 3.0009138156704704
 1.0003543865982154

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, loc_init, lb = first.(loc_bounds), ub = last.(loc_bounds))
@btime res1 = solve(optprob, BBO_adaptive_de_rand_1_bin(); maxiters = 7e3)
# using the moe accurate Vern9() reduces the fitness marginally and leads to some increase in time taken

1.251 s (2804718 allocations: 399.09 MiB)
u: 4-element Vector{Float64}:
 1.4991827108002216
 0.9994570870562814
 3.003103120393439
 1.001046164781995

Using NLopt

Global Optimisation first

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, glo_init, lb = first.(glo_bounds), ub = last.(glo_bounds))

OptimizationProblem. In-place: true
u0: 4-element Vector{Int64}:
 5
 5
 5
 5

opt = Opt(:GN_ORIG_DIRECT_L, 4)
@btime res1 = solve(optprob, opt, maxiters = 10000, xtol_rel = 1e-12)

659.507 ms (1433251 allocations: 242.18 MiB)
u: 4-element Vector{Float64}:
 1.7283950617224937
 2.22222222222419
 3.580246913586148
 1.1172077427280471

opt = Opt(:GN_CRS2_LM, 4)
@btime res1 = solve(optprob, opt, maxiters = 10000, xtol_rel = 1e-12)

1.177 s (2537118 allocations: 428.66 MiB)
u: 4-element Vector{Float64}:
 1.5000000000642564
 1.000000000087474
 2.999999999545464
 0.9999999999383153

opt = Opt(:GN_ISRES, 4)
@btime res1 = solve(optprob, opt, maxiters = 10000, xtol_rel = 1e-12)

1.705 s (3670116 allocations: 620.05 MiB)
u: 4-element Vector{Float64}:
 1.4848235043460403
 1.0369671856971896
 3.0821313353267885
 1.0426458112174553

opt = Opt(:GN_ESCH, 4)
@btime res1 = solve(optprob, opt, maxiters = 10000, xtol_rel = 1e-12)

1.686 s (3670116 allocations: 620.05 MiB)
u: 4-element Vector{Float64}:
 0.8498129983794842
 0.7096873174755658
 8.385745763750789
 3.6571951106190697

Now local optimization algorithms are used to check the global ones, these use the local constraints, different initial values and time step

optprob = OptimizationProblem(obj_short, loc_init, lb = first.(loc_bounds), ub = last.(loc_bounds))

OptimizationProblem. In-place: true
u0: 4-element Vector{Float64}:
 1.0
 0.5
 3.5
 1.5

opt = Opt(:LN_BOBYQA, 4)
@btime res1 = solve(optprob, opt, maxiters = 10000, xtol_rel = 1e-12)

49.606 ms (111317 allocations: 18.87 MiB)
u: 4-element Vector{Float64}:
 1.5000000000702955
 1.0000000000848333
 2.9999999995076982
 0.9999999999252087

opt = Opt(:LN_NELDERMEAD, 4)
@btime res1 = solve(optprob, opt, maxiters = 10000, xtol_rel = 1e-12)

79.822 ms (181047 allocations: 30.65 MiB)
u: 4-element Vector{Float64}:
 1.5000000000705307
 1.000000000085224
 2.999999999507768
 0.9999999999249004

opt = Opt(:LD_SLSQP, 4)
@btime res1 = solve(optprob, opt, maxiters = 10000, xtol_rel = 1e-12)

16.369 ms (60772 allocations: 5.34 MiB)
u: 4-element Vector{Float64}:
 1.5000000000702354
 1.000000000084916
 2.999999999508495
 0.9999999999254099

opt = Opt(:LN_COBYLA, 4)
@btime res1 = solve(optprob, opt, maxiters = 10000, xtol_rel = 1e-12)

1.707 s (3670116 allocations: 620.05 MiB)
u: 4-element Vector{Float64}:
 1.499998585072833
 0.9999995756417143
 3.0000072871946215
 1.0000023045858315

opt = Opt(:LN_NEWUOA_BOUND, 4)
@btime res1 = solve(optprob, opt, maxiters = 10000, xtol_rel = 1e-12)

621.716 ms (333352 allocations: 56.38 MiB)
u: 4-element Vector{Float64}:
 1.500000738607671
 1.0000013474277258
 2.9999923998862905
 0.9999981102014334

opt = Opt(:LN_PRAXIS, 4)
@btime res1 = solve(optprob, opt, maxiters = 10000, xtol_rel = 1e-12)

34.878 ms (79021 allocations: 13.41 MiB)
u: 4-element Vector{Float64}:
 1.5000000000805267
 1.0000000000899547
 2.99999999945556
 0.9999999999095093

opt = Opt(:LN_SBPLX, 4)
@btime res1 = solve(optprob, opt, maxiters = 10000, xtol_rel = 1e-12)

1.699 s (3670116 allocations: 620.05 MiB)
u: 4-element Vector{Float64}:
 1.4999999301104459
 0.9999999814386067
 3.000000353466034
 1.0000001103210938

opt = Opt(:LD_MMA, 4)
@btime res1 = solve(optprob, opt, maxiters = 10000, xtol_rel = 1e-12)

1.333 s (5036679 allocations: 404.35 MiB)
u: 4-element Vector{Float64}:
 1.4999999999592728
 1.0000000000448461
 3.0000000000407674
 1.000000000097796

opt = Opt(:LD_TNEWTON_PRECOND_RESTART, 4)
@btime res1 = solve(optprob, opt, maxiters = 10000, xtol_rel = 1e-12)

19.962 ms (78467 allocations: 6.37 MiB)
u: 4-element Vector{Float64}:
 1.5000000000702258
 1.0000000000849023
 2.99999999950852
 0.9999999999254172

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(t,data),tstops=t,reltol=1e-9,abstol=1e-9)
optprob = OptimizationProblem(obj, glo_init, lb = first.(glo_bounds), ub = last.(glo_bounds))

OptimizationProblem. In-place: true
u0: 4-element Vector{Int64}:
 5
 5
 5
 5

@btime res1 = solve(optprob, BBO_adaptive_de_rand_1_bin(), maxiters = 4e3)

Error: MethodError: no method matching iterate(::BlackBoxOptim.ContinuousRe
ctSearchSpace)

Closest candidates are:
  iterate(!Matched::Union{LinRange, StepRangeLen})
   @ Base range.jl:880
  iterate(!Matched::Union{LinRange, StepRangeLen}, !Matched::Integer)
   @ Base range.jl:880
  iterate(!Matched::T) where T<:Union{Base.KeySet{<:Any, <:Dict}, Base.Valu
eIterator{<:Dict}}
   @ Base dict.jl:698
  ...

opt = Opt(:GN_ORIG_DIRECT_L, 4)
@btime res1 = solve(optprob, opt, maxiters = 10000, xtol_rel = 1e-12)

3.494 s (6427692 allocations: 858.47 MiB)
u: 4-element Vector{Float64}:
 8.271604938277504
 7.42112482850273
 7.402834933693231
 3.7037037037056706

opt = Opt(:GN_CRS2_LM, 4)
@btime res1 = solve(optprob, opt, maxiters = 20000, xtol_rel = 1e-12)

33.467 s (61410833 allocations: 8.01 GiB)
u: 4-element Vector{Float64}:
 9.999999999999996
 9.11102030658218
 6.094629634596672
 2.9508146581297554

opt = Opt(:GN_ISRES, 4)
@btime res1 = solve(optprob, opt, maxiters = 50000, xtol_rel = 1e-12)

83.394 s (153550089 allocations: 20.03 GiB)
u: 4-element Vector{Float64}:
 5.106670359969432
 3.6282898375721886
 3.2104141423763277
 1.4029835502880337

opt = Opt(:GN_ESCH, 4)
@btime res1 = solve(optprob, opt, maxiters = 20000, xtol_rel = 1e-12)

33.490 s (61420089 allocations: 8.01 GiB)
u: 4-element Vector{Float64}:
 5.952290063872788
 5.843675880922962
 0.643393545041886
 0.21933385445297787

Local problem

obj = build_loss_objective(prob,Vern9(),L2Loss(t,data),Optimization.AutoForwardDiff(),tstops=t,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}:
 1.0
 0.5
 3.5
 1.5

opt = Opt(:LN_BOBYQA, 4)
@btime res1 = solve(optprob, opt, maxiters = 10000, xtol_rel = 1e-12)

49.696 ms (111317 allocations: 18.87 MiB)
u: 4-element Vector{Float64}:
 1.5000000000702955
 1.0000000000848333
 2.9999999995076982
 0.9999999999252087

opt = Opt(:LN_NELDERMEAD, 4)
@btime res1 = solve(optprob, opt, maxiters = 10000, xtol_rel = 1e-12)

80.127 ms (181047 allocations: 30.65 MiB)
u: 4-element Vector{Float64}:
 1.5000000000705307
 1.000000000085224
 2.999999999507768
 0.9999999999249004

opt = Opt(:LD_SLSQP, 4)
@btime res1 = solve(optprob, opt, maxiters = 10000, xtol_rel = 1e-12)

16.401 ms (60772 allocations: 5.34 MiB)
u: 4-element Vector{Float64}:
 1.5000000000702354
 1.000000000084916
 2.999999999508495
 0.9999999999254099

Parameter estimation on the longer sample proves to be extremely challenging for some of the global optimizers. A few give the accurate values, BlacBoxOptim also performs quite well while others seem to struggle with accuracy a lot.

Conclusion

In general we observe that lower tolerance lead to higher accuracy but too low tolerance could affect the convergence time drastically. Also fitting a shorter timespan seems to be easier in comparison (quite intuitively). NLOpt methods seem to give great accuracy in the shorter problem with a lot of the algorithms giving 0 fitness, BBO performs very well on it with marginal change with tol values. In case of global optimization of the longer problem there is some difference in the performance amongst the algorithms with LD_SLSQPGN_ESCHGN_ISRESGN_ORIG_DIRECT_L performing among the worse, BBO also gives a bit high fitness in comparison. QuadDIRECT gives accurate results in the case of the shorter problem but doesn't perform very well in the longer problem case.

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","LotkaVolterraParameterEstimation.jmd")

Computer Information:

Julia Version 1.9.4
Commit 8e5136fa297 (2023-11-14 08:46 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
  LIBM: libopenlibm
  LLVM: libLLVM-14.0.6 (ORCJIT, znver2)
  Threads: 1 on 128 virtual cores
Environment:
  JULIA_CPU_THREADS = 128
  JULIA_DEPOT_PATH = /cache/julia-buildkite-plugin/depots/5b300254-1738-4989-ae0a-f4d2d937f953

Package Information:

Status `/cache/build/exclusive-amdci1-0/julialang/scimlbenchmarks-dot-jl/benchmarks/ParameterEstimation/Project.toml`
⌃ [6e4b80f9] BenchmarkTools v1.3.2
⌃ [a134a8b2] BlackBoxOptim v0.6.2
⌃ [1130ab10] DiffEqParamEstim v2.0.1
⌃ [31c24e10] Distributions v0.25.100
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⌅ [76087f3c] NLopt v0.6.5
⌃ [7f7a1694] Optimization v3.16.0
⌃ [3e6eede4] OptimizationBBO v0.1.5
⌃ [4e6fcdb7] OptimizationNLopt v0.1.8
⌅ [1dea7af3] OrdinaryDiffEq v6.55.0
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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`
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.

And the full manifest:

Status `/cache/build/exclusive-amdci1-0/julialang/scimlbenchmarks-dot-jl/benchmarks/ParameterEstimation/Manifest.toml`
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⌃ [739be429] MbedTLS v1.1.7
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  [e1d29d7a] Missings v1.1.0
⌃ [961ee093] ModelingToolkit v8.66.0
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⌃ [102ac46a] MultivariatePolynomials v0.5.1
⌃ [ffc61752] Mustache v1.0.17
⌃ [d8a4904e] MutableArithmetics v1.3.1
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⌅ [8913a72c] NonlinearSolve v1.10.0
⌃ [6fe1bfb0] OffsetArrays v1.12.10
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⌃ [7f7a1694] Optimization v3.16.0
⌃ [3e6eede4] OptimizationBBO v0.1.5
⌃ [4e6fcdb7] OptimizationNLopt v0.1.8
⌃ [bac558e1] OrderedCollections v1.6.2
⌅ [1dea7af3] OrdinaryDiffEq v6.55.0
⌃ [90014a1f] PDMats v0.11.17
⌃ [65ce6f38] PackageExtensionCompat v1.0.1
⌃ [65888b18] ParameterizedFunctions v5.15.0
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⌃ [69de0a69] Parsers v2.7.2
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⌃ [995b91a9] PlotUtils v1.3.5
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⌃ [f517fe37] Polyester v0.7.5
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⌅ [d236fae5] PreallocationTools v0.4.12
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⌃ [21216c6a] Preferences v1.4.0
⌃ [27ebfcd6] Primes v0.5.4
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⌃ [92933f4c] ProgressMeter v1.8.0
⌃ [1fd47b50] QuadGK v2.8.2
⌃ [fb686558] RandomExtensions v0.4.3
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⌅ [731186ca] RecursiveArrayTools v2.38.7
⌃ [f2c3362d] RecursiveFactorization v0.2.20
  [189a3867] Reexport v1.2.2
⌃ [05181044] RelocatableFolders v1.0.0
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  [7e49a35a] RuntimeGeneratedFunctions v0.5.12
⌃ [fdea26ae] SIMD v3.4.5
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⌃ [476501e8] SLEEFPirates v0.6.39
⌅ [0bca4576] SciMLBase v1.95.0
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⌃ [e9a6253c] SciMLNLSolve v0.1.8
⌃ [c0aeaf25] SciMLOperators v0.3.6
⌃ [6c6a2e73] Scratch v1.2.0
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⌅ [727e6d20] SimpleNonlinearSolve v0.1.19
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⌃ [a2af1166] SortingAlgorithms v1.1.1
⌃ [47a9eef4] SparseDiffTools v2.5.1
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⌃ [d4ead438] SpatialIndexing v0.1.5
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⌃ [0d7ed370] StaticArrayInterface v1.4.1
⌃ [90137ffa] StaticArrays v1.6.2
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⌃ [82ae8749] StatsAPI v1.6.0
⌅ [2913bbd2] StatsBase v0.33.21
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⌅ [7792a7ef] StrideArraysCore v0.4.17
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⌅ [2efcf032] SymbolicIndexingInterface v0.2.2
⌃ [d1185830] SymbolicUtils v1.2.0
⌅ [0c5d862f] Symbolics v5.5.1
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⌃ [bd369af6] Tables v1.10.1
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⌃ [0796e94c] Tokenize v0.5.25
⌅ [3bb67fe8] TranscodingStreams v0.9.13
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⌃ [d5829a12] TriangularSolve v0.1.19
⌃ [410a4b4d] Tricks v0.1.7
  [781d530d] TruncatedStacktraces v1.4.0
⌃ [5c2747f8] URIs v1.5.0
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⌃ [1986cc42] Unitful v1.17.0
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⌃ [a7c27f48] Unityper v0.1.5
  [41fe7b60] Unzip v0.2.0
⌃ [3d5dd08c] VectorizationBase v0.21.64
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⌃ [700de1a5] ZygoteRules v0.2.3
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⌃ [b22a6f82] FFMPEG_jll v4.4.2+2
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⌃ [0656b61e] GLFW_jll v3.3.8+0
⌅ [d2c73de3] GR_jll v0.72.9+1
  [78b55507] Gettext_jll v0.21.0+0
⌃ [f8c6e375] Git_jll v2.36.1+2
⌃ [7746bdde] Glib_jll v2.74.0+2
  [3b182d85] Graphite2_jll v1.3.14+0
  [2e76f6c2] HarfBuzz_jll v2.8.1+1
⌃ [aacddb02] JpegTurbo_jll v2.1.91+0
  [c1c5ebd0] LAME_jll v3.100.1+0
  [88015f11] LERC_jll v3.0.0+1
⌃ [1d63c593] LLVMOpenMP_jll v15.0.4+0
  [dd4b983a] LZO_jll v2.10.1+0
⌅ [e9f186c6] Libffi_jll v3.2.2+1
  [d4300ac3] Libgcrypt_jll v1.8.7+0
  [7e76a0d4] Libglvnd_jll v1.6.0+0
  [7add5ba3] Libgpg_error_jll v1.42.0+0
  [94ce4f54] Libiconv_jll v1.17.0+0
  [4b2f31a3] Libmount_jll v2.35.0+0
⌅ [89763e89] Libtiff_jll v4.5.1+1
  [38a345b3] Libuuid_jll v2.36.0+0
  [079eb43e] NLopt_jll v2.7.1+0
  [e7412a2a] Ogg_jll v1.3.5+1
⌅ [458c3c95] OpenSSL_jll v1.1.22+0
  [efe28fd5] OpenSpecFun_jll v0.5.5+0
  [91d4177d] Opus_jll v1.3.2+0
  [30392449] Pixman_jll v0.42.2+0
⌅ [c0090381] Qt6Base_jll v6.4.2+3
  [f50d1b31] Rmath_jll v0.4.0+0
⌃ [a2964d1f] Wayland_jll v1.21.0+0
⌃ [2381bf8a] Wayland_protocols_jll v1.25.0+0
⌃ [02c8fc9c] XML2_jll v2.10.4+0
  [aed1982a] XSLT_jll v1.1.34+0
⌃ [ffd25f8a] XZ_jll v5.4.4+0
  [4f6342f7] Xorg_libX11_jll v1.8.6+0
  [0c0b7dd1] Xorg_libXau_jll v1.0.11+0
  [935fb764] Xorg_libXcursor_jll v1.2.0+4
  [a3789734] Xorg_libXdmcp_jll v1.1.4+0
  [1082639a] Xorg_libXext_jll v1.3.4+4
  [d091e8ba] Xorg_libXfixes_jll v5.0.3+4
  [a51aa0fd] Xorg_libXi_jll v1.7.10+4
  [d1454406] Xorg_libXinerama_jll v1.1.4+4
  [ec84b674] Xorg_libXrandr_jll v1.5.2+4
  [ea2f1a96] Xorg_libXrender_jll v0.9.10+4
  [14d82f49] Xorg_libpthread_stubs_jll v0.1.1+0
  [c7cfdc94] Xorg_libxcb_jll v1.15.0+0
  [cc61e674] Xorg_libxkbfile_jll v1.1.2+0
  [12413925] Xorg_xcb_util_image_jll v0.4.0+1
  [2def613f] Xorg_xcb_util_jll v0.4.0+1
  [975044d2] Xorg_xcb_util_keysyms_jll v0.4.0+1
  [0d47668e] Xorg_xcb_util_renderutil_jll v0.3.9+1
  [c22f9ab0] Xorg_xcb_util_wm_jll v0.4.1+1
  [35661453] Xorg_xkbcomp_jll v1.4.6+0
  [33bec58e] Xorg_xkeyboard_config_jll v2.39.0+0
  [c5fb5394] Xorg_xtrans_jll v1.5.0+0
  [8f1865be] ZeroMQ_jll v4.3.4+0
  [3161d3a3] Zstd_jll v1.5.5+0
⌅ [214eeab7] fzf_jll v0.29.0+0
  [a4ae2306] libaom_jll v3.4.0+0
  [0ac62f75] libass_jll v0.15.1+0
  [f638f0a6] libfdk_aac_jll v2.0.2+0
⌃ [b53b4c65] libpng_jll v1.6.38+0
  [a9144af2] libsodium_jll v1.0.20+0
  [f27f6e37] libvorbis_jll v1.3.7+1
  [1270edf5] x264_jll v2021.5.5+0
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⌃ [d8fb68d0] xkbcommon_jll v1.4.1+0
  [0dad84c5] ArgTools v1.1.1
  [56f22d72] Artifacts
  [2a0f44e3] Base64
  [ade2ca70] Dates
  [8ba89e20] Distributed
  [f43a241f] Downloads v1.6.0
  [7b1f6079] FileWatching
  [9fa8497b] Future
  [b77e0a4c] InteractiveUtils
  [b27032c2] LibCURL v0.6.3
  [76f85450] LibGit2
  [8f399da3] Libdl
  [37e2e46d] LinearAlgebra
  [56ddb016] Logging
  [d6f4376e] Markdown
  [a63ad114] Mmap
  [ca575930] NetworkOptions v1.2.0
  [44cfe95a] Pkg v1.9.0
  [de0858da] Printf
  [9abbd945] Profile
  [3fa0cd96] REPL
  [9a3f8284] Random
  [ea8e919c] SHA v0.7.0
  [9e88b42a] Serialization
  [1a1011a3] SharedArrays
  [6462fe0b] Sockets
  [2f01184e] SparseArrays
  [10745b16] Statistics v1.9.0
  [4607b0f0] SuiteSparse
  [fa267f1f] TOML v1.0.3
  [a4e569a6] Tar v1.10.0
  [8dfed614] Test
  [cf7118a7] UUIDs
  [4ec0a83e] Unicode
  [e66e0078] CompilerSupportLibraries_jll v1.0.2+0
  [deac9b47] LibCURL_jll v7.84.0+0
  [29816b5a] LibSSH2_jll v1.10.2+0
  [c8ffd9c3] MbedTLS_jll v2.28.2+0
  [14a3606d] MozillaCACerts_jll v2022.10.11
  [4536629a] OpenBLAS_jll v0.3.21+4
  [05823500] OpenLibm_jll v0.8.1+0
  [efcefdf7] PCRE2_jll v10.42.0+0
  [bea87d4a] SuiteSparse_jll v5.10.1+6
  [83775a58] Zlib_jll v1.2.13+0
  [8e850b90] libblastrampoline_jll v5.8.0+0
  [8e850ede] nghttp2_jll v1.48.0+0
  [3f19e933] p7zip_jll v17.4.0+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.