Diffusion Equation Physics-Informed Neural Network (PINN) Optimizer Benchmarks

Adapted from NeuralPDE: Automating Physics-Informed Neural Networks (PINNs) with Error Approximations. Uses the NeuralPDE.jl library from the SciML Scientific Machine Learning Open Source Organization for the implementation of physics-informed neural networks (PINNs) and other science-guided AI techniques.

Setup

using NeuralPDE, OptimizationFlux, ModelingToolkit, Optimization, OptimizationOptimJL
using Lux, Plots
import ModelingToolkit: Interval, infimum, supremum

function solve(opt)
    strategy = QuadratureTraining()

    @parameters x t
    @variables u(..)
    Dt = Differential(t)
    Dxx = Differential(x)^2

    eq = Dt(u(x,t)) - Dxx(u(x,t)) ~ -exp(-t) * (sin(pi * x) - pi^2 * sin(pi * x))

    bcs = [u(x,0) ~ sin(pi*x),
           u(-1,t) ~ 0.,
           u(1,t) ~ 0.]

    domains = [x ∈ Interval(-1.0,1.0),
               t ∈ Interval(0.0,1.0)]

    chain = Lux.Chain(Lux.Dense(2,18,tanh),Lux.Dense(18,18,tanh),Lux.Dense(18,1))

    discretization = PhysicsInformedNN(chain,strategy)

    indvars = [x, t]   #phisically independent variables
    depvars = [u(x,t)]       #dependent (target) variable

    loss = []
    initial_time = nothing

    times = []

    cb_ = function (p,l)
        if initial_time == nothing
            initial_time = time()
        end
        push!(times, time() - initial_time)
        #println("Current loss for $opt is: $l")
        push!(loss, l)
      #  println(l )
      #  println(time() - initial_time)
        return false
    end

    @named pde_system = PDESystem(eq, bcs, domains, indvars, depvars)
    prob = discretize(pde_system, discretization)

    if opt == "both"
        res = Optimization.solve(prob, ADAM(); callback = cb_, maxiters=50)
        prob = remake(prob,u0=res.minimizer)
        res = Optimization.solve(prob, BFGS(); callback = cb_, maxiters=150)
    else
        res = Optimization.solve(prob, opt; callback = cb_, maxiters=200)
    end

    times[1] = 0.01

    return loss, times #add numeric solution
end

solve (generic function with 1 method)

opt1 = ADAM()
opt2 = ADAM(0.005)
opt3 = ADAM(0.05)
opt4 = RMSProp()
opt5 = RMSProp(0.005)
opt6 = RMSProp(0.05)
opt7 = OptimizationOptimJL.BFGS()
opt8 = OptimizationOptimJL.LBFGS()

Optim.LBFGS{Nothing, LineSearches.InitialStatic{Float64}, LineSearches.Hage
rZhang{Float64, Base.RefValue{Bool}}, Optim.var"#19#21"}(10, LineSearches.I
nitialStatic{Float64}
  alpha: Float64 1.0
  scaled: Bool false
, LineSearches.HagerZhang{Float64, Base.RefValue{Bool}}
  delta: Float64 0.1
  sigma: Float64 0.9
  alphamax: Float64 Inf
  rho: Float64 5.0
  epsilon: Float64 1.0e-6
  gamma: Float64 0.66
  linesearchmax: Int64 50
  psi3: Float64 0.1
  display: Int64 0
  mayterminate: Base.RefValue{Bool}
, nothing, Optim.var"#19#21"(), Optim.Flat(), true)

Solve

loss_1, times_1 = solve(opt1)
loss_2, times_2 = solve(opt2)
loss_3, times_3 = solve(opt3)
loss_4, times_4 = solve(opt4)
loss_5, times_5 = solve(opt5)
loss_6, times_6 = solve(opt6)
loss_7, times_7 = solve(opt7)
loss_8, times_8 = solve(opt8)
loss_9, times_9 = solve("both")

(Any[238.21335902701475, 233.15150981770586, 228.2759814545742, 223.5864068
3724764, 219.08278596850778, 214.76317176839612, 210.62656708898461, 206.67
141844249306, 202.89550289206377, 199.29761802461766  …  0.0001936341440421
4462, 0.00018948955625926338, 0.00018578581458421353, 0.0001806412684902067
, 0.00017731365657409258, 0.00017565859286636375, 0.00017238029428692176, 0
.0001642512179898975, 0.00016149209935286015, 0.00015612380672063613], Any[
0.01, 0.012009859085083008, 0.023529052734375, 0.03496289253234863, 0.04635
190963745117, 0.05791902542114258, 0.06946301460266113, 0.08103203773498535
, 0.09284090995788574, 0.10445594787597656  …  11.564873933792114, 11.58957
3860168457, 11.614413022994995, 11.639391899108887, 11.664484024047852, 11.
689626932144165, 11.714773893356323, 11.739902019500732, 11.765043020248413
, 11.790174961090088])

Results

p = plot([times_1, times_2, times_3, times_4, times_5, times_6, times_7, times_8, times_9], [loss_1, loss_2, loss_3, loss_4, loss_5, loss_6, loss_7, loss_8, loss_9],xlabel="time (s)", ylabel="loss", xscale=:log10, yscale=:log10, labels=["ADAM(0.001)" "ADAM(0.005)" "ADAM(0.05)" "RMSProp(0.001)" "RMSProp(0.005)" "RMSProp(0.05)" "BFGS()" "LBFGS()" "ADAM + BFGS"], legend=:bottomleft, linecolor=["#2660A4" "#4CD0F4" "#FEC32F" "#F763CD" "#44BD79" "#831894" "#A6ED18" "#980000" "#FF912B"])

p = plot([loss_1, loss_2, loss_3, loss_4, loss_5, loss_6, loss_7, loss_8, loss_9], xlabel="iterations", ylabel="loss", yscale=:log10, labels=["ADAM(0.001)" "ADAM(0.005)" "ADAM(0.05)" "RMSProp(0.001)" "RMSProp(0.005)" "RMSProp(0.05)" "BFGS()" "LBFGS()" "ADAM + BFGS"], legend=:bottomleft, linecolor=["#2660A4" "#4CD0F4" "#FEC32F" "#F763CD" "#44BD79" "#831894" "#A6ED18" "#980000" "#FF912B"])

@show loss_1[end], loss_2[end], loss_3[end], loss_4[end], loss_5[end], loss_6[end], loss_7[end], loss_8[end], loss_9[end]

(loss_1[end], loss_2[end], loss_3[end], loss_4[end], loss_5[end], loss_6[en
d], loss_7[end], loss_8[end], loss_9[end]) = (32.02590503889115, 0.51000893
33286841, 0.16831991580578395, 23.22538735494057, 5.253505406940997, 10.886
119247552827, 3.572109904700025e-5, 0.04940374724215937, 0.0001561238067206
3613)
(32.02590503889115, 0.5100089333286841, 0.16831991580578395, 23.22538735494
057, 5.253505406940997, 10.886119247552827, 3.572109904700025e-5, 0.0494037
4724215937, 0.00015612380672063613)

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/PINNOptimizers","1d_diffusion.jmd")

Computer Information:

Julia Version 1.8.5
Commit 17cfb8e65ea (2023-01-08 06:45 UTC)
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 128 × AMD EPYC 7502 32-Core Processor
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-13.0.1 (ORCJIT, znver2)
  Threads: 128 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-amdci3-0/julialang/scimlbenchmarks-dot-jl/benchmarks/PINNOptimizers/Project.toml`
⌅ [b2108857] Lux v0.4.11
⌃ [961ee093] ModelingToolkit v8.18.1
⌃ [315f7962] NeuralPDE v5.0.0
⌃ [7f7a1694] Optimization v3.8.1
⌃ [253f991c] OptimizationFlux v0.1.0
⌃ [36348300] OptimizationOptimJL v0.1.2
⌃ [91a5bcdd] Plots v1.31.4
⌃ [31c91b34] SciMLBenchmarks v0.1.0
Info Packages marked with ⌃ and ⌅ have new versions available, 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-amdci3-0/julialang/scimlbenchmarks-dot-jl/benchmarks/PINNOptimizers/Manifest.toml`
⌅ [c3fe647b] AbstractAlgebra v0.27.1
⌃ [621f4979] AbstractFFTs v1.2.1
⌃ [1520ce14] AbstractTrees v0.4.2
⌃ [7d9f7c33] Accessors v0.1.18
⌃ [79e6a3ab] Adapt v3.3.3
  [dce04be8] ArgCheck v2.3.0
  [ec485272] ArnoldiMethod v0.2.0
⌅ [4fba245c] ArrayInterface v6.0.21
⌃ [30b0a656] ArrayInterfaceCore v0.1.15
⌃ [6ba088a2] ArrayInterfaceGPUArrays v0.2.1
⌃ [015c0d05] ArrayInterfaceOffsetArrays v0.1.6
⌃ [b0d46f97] ArrayInterfaceStaticArrays v0.1.4
⌃ [dd5226c6] ArrayInterfaceStaticArraysCore v0.1.0
  [15f4f7f2] AutoHashEquals v0.2.0
⌅ [ab4f0b2a] BFloat16s v0.2.0
⌃ [198e06fe] BangBang v0.3.36
  [9718e550] Baselet v0.1.1
  [e2ed5e7c] Bijections v0.1.4
⌃ [62783981] BitTwiddlingConvenienceFunctions v0.1.4
  [fa961155] CEnum v0.4.2
⌅ [2a0fbf3d] CPUSummary v0.1.25
  [00ebfdb7] CSTParser v3.3.6
⌅ [052768ef] CUDA v3.12.0
  [49dc2e85] Calculus v0.5.1
⌃ [082447d4] ChainRules v1.39.1
⌃ [d360d2e6] ChainRulesCore v1.15.3
⌃ [9e997f8a] ChangesOfVariables v0.1.4
⌃ [fb6a15b2] CloseOpenIntervals v0.1.10
⌃ [944b1d66] CodecZlib v0.7.0
⌃ [35d6a980] ColorSchemes v3.19.0
  [3da002f7] ColorTypes v0.11.4
⌅ [c3611d14] ColorVectorSpace v0.9.9
⌃ [5ae59095] Colors v0.12.8
  [861a8166] Combinatorics v1.0.2
⌃ [a80b9123] CommonMark v0.8.6
⌃ [38540f10] CommonSolve v0.2.1
  [bbf7d656] CommonSubexpressions v0.3.0
⌅ [34da2185] Compat v3.45.0
⌅ [b0b7db55] ComponentArrays v0.12.4
⌃ [b152e2b5] CompositeTypes v0.1.2
⌃ [a33af91c] CompositionsBase v0.1.1
⌃ [8f4d0f93] Conda v1.7.0
  [88cd18e8] ConsoleProgressMonitor v0.1.2
⌃ [187b0558] ConstructionBase v1.4.0
⌃ [6add18c4] ContextVariablesX v0.1.2
  [d38c429a] Contour v0.6.2
  [adafc99b] CpuId v0.3.1
  [a8cc5b0e] Crayons v4.1.1
  [667455a9] Cubature v1.5.1
⌃ [9a962f9c] DataAPI v1.10.0
⌃ [864edb3b] DataStructures v0.18.13
  [e2d170a0] DataValueInterfaces v1.0.0
  [244e2a9f] DefineSingletons v0.1.2
  [b429d917] DensityInterface v0.4.0
⌅ [2b5f629d] DiffEqBase v6.94.4
⌃ [459566f4] DiffEqCallbacks v2.23.1
⌃ [77a26b50] DiffEqNoiseProcess v5.12.0
⌃ [163ba53b] DiffResults v1.0.3
⌃ [b552c78f] DiffRules v1.11.0
⌃ [b4f34e82] Distances v0.10.7
⌃ [31c24e10] Distributions v0.25.66
⌅ [ffbed154] DocStringExtensions v0.8.6
⌅ [5b8099bc] DomainSets v0.5.11
  [fa6b7ba4] DualNumbers v0.6.8
⌅ [7c1d4256] DynamicPolynomials v0.4.5
⌃ [d4d017d3] ExponentialUtilities v1.18.0
⌃ [e2ba6199] ExprTools v0.1.8
  [c87230d0] FFMPEG v0.4.1
⌃ [cc61a311] FLoops v0.2.0
  [b9860ae5] FLoopsBase v0.1.1
⌃ [7034ab61] FastBroadcast v0.2.1
  [9aa1b823] FastClosures v0.3.2
⌅ [29a986be] FastLapackInterface v1.1.0
⌅ [1a297f60] FillArrays v0.13.2
⌃ [6a86dc24] FiniteDiff v2.13.1
  [53c48c17] FixedPointNumbers v0.8.4
⌅ [587475ba] Flux v0.13.4
⌃ [9c68100b] FoldsThreads v0.1.1
  [59287772] Formatting v0.4.2
⌃ [f6369f11] ForwardDiff v0.10.30
⌃ [069b7b12] FunctionWrappers v1.1.2
⌅ [d9f16b24] Functors v0.2.8
⌃ [0c68f7d7] GPUArrays v8.4.2
⌅ [46192b85] GPUArraysCore v0.1.1
⌅ [61eb1bfa] GPUCompiler v0.16.2
⌅ [28b8d3ca] GR v0.66.0
  [c145ed77] GenericSchur v0.5.3
⌃ [5c1252a2] GeometryBasics v0.4.2
⌃ [d7ba0133] Git v1.2.1
⌃ [86223c79] Graphs v1.7.1
  [42e2da0e] Grisu v1.0.2
⌅ [0b43b601] Groebner v0.2.8
  [d5909c97] GroupsCore v0.4.0
⌃ [19dc6840] HCubature v1.5.0
⌃ [cd3eb016] HTTP v1.2.0
⌅ [eafb193a] Highlights v0.4.5
⌃ [3e5b6fbb] HostCPUFeatures v0.1.8
⌃ [34004b35] HypergeometricFunctions v0.3.11
⌃ [7073ff75] IJulia v1.23.3
⌃ [7869d1d1] IRTools v0.4.6
  [615f187c] IfElse v0.1.1
⌃ [d25df0c9] Inflate v0.1.2
  [83e8ac13] IniFile v0.5.1
  [22cec73e] InitialValues v0.3.1
⌃ [18e54dd8] IntegerMathUtils v0.1.0
⌃ [de52edbc] Integrals v3.1.0
⌃ [c31f79ba] IntegralsCubature v0.2.0
⌃ [8197267c] IntervalSets v0.7.1
⌃ [3587e190] InverseFunctions v0.1.7
⌅ [92d709cd] IrrationalConstants v0.1.1
⌃ [c8e1da08] IterTools v1.4.0
  [42fd0dbc] IterativeSolvers v0.9.2
  [82899510] IteratorInterfaceExtensions v1.0.0
  [692b3bcd] JLLWrappers v1.4.1
⌃ [682c06a0] JSON v0.21.3
⌃ [98e50ef6] JuliaFormatter v1.0.7
  [b14d175d] JuliaVariables v0.2.4
⌃ [ccbc3e58] JumpProcesses v9.0.1
⌅ [ef3ab10e] KLU v0.3.0
⌅ [ba0b0d4f] Krylov v0.8.3
⌅ [0b1a1467] KrylovKit v0.5.4
⌅ [929cbde3] LLVM v4.14.0
  [b964fa9f] LaTeXStrings v1.3.0
⌃ [2ee39098] LabelledArrays v1.11.1
⌅ [23fbe1c1] Latexify v0.15.16
⌃ [a5e1c1ea] LatinHypercubeSampling v1.8.0
  [73f95e8e] LatticeRules v0.0.1
⌃ [10f19ff3] LayoutPointers v0.1.10
  [2d8b4e74] LevyArea v1.0.0
⌃ [d3d80556] LineSearches v7.1.1
⌅ [7ed4a6bd] LinearSolve v1.23.0
⌃ [2ab3a3ac] LogExpFunctions v0.3.16
⌅ [e6f89c97] LoggingExtras v0.4.9
⌃ [bdcacae8] LoopVectorization v0.12.120
⌅ [b2108857] Lux v0.4.11
⌃ [d8e11817] MLStyle v0.4.13
⌅ [f1d291b0] MLUtils v0.2.9
⌃ [1914dd2f] MacroTools v0.5.9
  [d125e4d3] ManualMemory v0.1.8
⌃ [739be429] MbedTLS v1.1.1
⌃ [442fdcdd] Measures v0.3.1
⌅ [e9d8d322] Metatheory v1.3.4
⌃ [128add7d] MicroCollections v0.1.2
⌃ [e1d29d7a] Missings v1.0.2
⌃ [961ee093] ModelingToolkit v8.18.1
⌅ [4886b29c] MonteCarloIntegration v0.0.3
⌃ [46d2c3a1] MuladdMacro v0.2.2
⌅ [102ac46a] MultivariatePolynomials v0.4.6
⌃ [ffc61752] Mustache v1.0.14
⌃ [d8a4904e] MutableArithmetics v1.0.4
⌃ [d41bc354] NLSolversBase v7.8.2
  [2774e3e8] NLsolve v4.5.1
⌅ [872c559c] NNlib v0.8.9
⌃ [a00861dc] NNlibCUDA v0.2.4
⌅ [77ba4419] NaNMath v0.3.7
  [71a1bf82] NameResolution v0.1.5
⌃ [315f7962] NeuralPDE v5.0.0
⌅ [8913a72c] NonlinearSolve v0.3.21
⌃ [6fe1bfb0] OffsetArrays v1.12.7
⌃ [429524aa] Optim v1.7.1
⌃ [3bd65402] Optimisers v0.2.8
⌃ [7f7a1694] Optimization v3.8.1
⌃ [253f991c] OptimizationFlux v0.1.0
⌃ [36348300] OptimizationOptimJL v0.1.2
⌃ [bac558e1] OrderedCollections v1.4.1
⌃ [1dea7af3] OrdinaryDiffEq v6.19.2
⌃ [90014a1f] PDMats v0.11.16
  [d96e819e] Parameters v0.12.3
⌃ [69de0a69] Parsers v2.3.2
⌃ [ccf2f8ad] PlotThemes v3.0.0
⌃ [995b91a9] PlotUtils v1.3.0
⌃ [91a5bcdd] Plots v1.31.4
⌃ [e409e4f3] PoissonRandom v0.4.1
⌅ [f517fe37] Polyester v0.6.14
⌅ [1d0040c9] PolyesterWeave v0.1.7
  [85a6dd25] PositiveFactorizations v0.2.4
⌃ [d236fae5] PreallocationTools v0.4.0
⌃ [21216c6a] Preferences v1.3.0
  [8162dcfd] PrettyPrint v0.2.0
⌃ [27ebfcd6] Primes v0.5.3
  [33c8b6b6] ProgressLogging v0.1.4
  [92933f4c] ProgressMeter v1.7.2
⌃ [1fd47b50] QuadGK v2.4.2
⌅ [8a4e6c94] QuasiMonteCarlo v0.2.9
⌃ [74087812] Random123 v1.5.0
  [fb686558] RandomExtensions v0.4.3
  [e6cf234a] RandomNumbers v1.5.3
  [c1ae055f] RealDot v0.1.0
⌃ [3cdcf5f2] RecipesBase v1.2.1
⌃ [01d81517] RecipesPipeline v0.6.2
⌃ [731186ca] RecursiveArrayTools v2.31.2
⌃ [f2c3362d] RecursiveFactorization v0.2.11
  [189a3867] Reexport v1.2.2
  [42d2dcc6] Referenceables v0.1.2
⌅ [05181044] RelocatableFolders v0.3.0
  [ae029012] Requires v1.3.0
  [ae5879a3] ResettableStacks v1.1.1
⌃ [37e2e3b7] ReverseDiff v1.14.1
⌃ [79098fc4] Rmath v0.7.0
⌃ [7e49a35a] RuntimeGeneratedFunctions v0.5.3
  [3cdde19b] SIMDDualNumbers v0.1.1
  [94e857df] SIMDTypes v0.1.0
⌃ [476501e8] SLEEFPirates v0.6.33
⌃ [0bca4576] SciMLBase v1.45.0
⌃ [31c91b34] SciMLBenchmarks v0.1.0
⌃ [6c6a2e73] Scratch v1.1.1
⌅ [efcf1570] Setfield v0.8.2
  [605ecd9f] ShowCases v0.1.0
  [992d4aef] Showoff v1.0.3
  [777ac1f9] SimpleBufferStream v1.1.0
  [699a6c99] SimpleTraits v0.9.4
  [ed01d8cd] Sobol v1.5.0
  [b85f4697] SoftGlobalScope v1.1.0
⌃ [a2af1166] SortingAlgorithms v1.0.1
⌅ [47a9eef4] SparseDiffTools v1.24.0
⌃ [276daf66] SpecialFunctions v2.1.7
⌃ [171d559e] SplittablesBase v0.1.14
  [860ef19b] StableRNGs v1.0.0
⌅ [aedffcd0] Static v0.7.6
⌃ [90137ffa] StaticArrays v1.5.2
⌃ [1e83bf80] StaticArraysCore v1.0.1
⌃ [82ae8749] StatsAPI v1.4.0
⌅ [2913bbd2] StatsBase v0.33.20
⌃ [4c63d2b9] StatsFuns v1.0.1
⌃ [789caeaf] StochasticDiffEq v6.51.0
⌅ [7792a7ef] StrideArraysCore v0.3.15
⌃ [69024149] StringEncodings v0.3.5
⌃ [09ab397b] StructArrays v0.6.11
⌅ [d1185830] SymbolicUtils v0.19.11
⌅ [0c5d862f] Symbolics v4.10.2
  [3783bdb8] TableTraits v1.0.1
⌃ [bd369af6] Tables v1.7.0
  [62fd8b95] TensorCore v0.1.1
⌅ [8ea1fca8] TermInterface v0.2.3
⌃ [5d786b92] TerminalLoggers v0.1.0
⌃ [8290d209] ThreadingUtilities v0.5.0
⌃ [ac1d9e8a] ThreadsX v0.1.10
⌃ [a759f4b9] TimerOutputs v0.5.20
⌃ [0796e94c] Tokenize v0.5.24
⌃ [3bb67fe8] TranscodingStreams v0.9.6
⌃ [28d57a85] Transducers v0.4.73
  [a2a6695c] TreeViews v0.3.0
⌃ [d5829a12] TriangularSolve v0.1.12
⌃ [5c2747f8] URIs v1.4.0
  [3a884ed6] UnPack v1.0.2
  [1cfade01] UnicodeFun v0.4.1
⌃ [1986cc42] Unitful v1.11.0
⌅ [41fe7b60] Unzip v0.1.2
⌃ [3d5dd08c] VectorizationBase v0.21.43
  [81def892] VersionParsing v1.3.0
  [19fa3120] VertexSafeGraphs v0.2.0
⌃ [44d3d7a6] Weave v0.10.9
⌃ [ddb6d928] YAML v0.4.7
⌃ [c2297ded] ZMQ v1.2.1
⌃ [e88e6eb3] Zygote v0.6.41
⌃ [700de1a5] ZygoteRules v0.2.2
  [6e34b625] Bzip2_jll v1.0.8+0
  [83423d85] Cairo_jll v1.16.1+1
  [7bc98958] Cubature_jll v1.0.5+0
⌃ [5ae413db] EarCut_jll v2.2.3+0
⌃ [2e619515] Expat_jll v2.4.8+0
⌃ [b22a6f82] FFMPEG_jll v4.4.2+0
  [a3f928ae] Fontconfig_jll v2.13.93+0
⌃ [d7e528f0] FreeType2_jll v2.10.4+0
  [559328eb] FriBidi_jll v1.0.10+0
⌃ [0656b61e] GLFW_jll v3.3.6+0
⌅ [d2c73de3] GR_jll v0.66.0+0
  [78b55507] Gettext_jll v0.21.0+0
⌅ [f8c6e375] Git_jll v2.34.1+0
⌃ [7746bdde] Glib_jll v2.68.3+2
  [3b182d85] Graphite2_jll v1.3.14+0
  [2e76f6c2] HarfBuzz_jll v2.8.1+1
⌃ [aacddb02] JpegTurbo_jll v2.1.2+0
  [c1c5ebd0] LAME_jll v3.100.1+0
  [88015f11] LERC_jll v3.0.0+1
⌅ [dad2f222] LLVMExtra_jll v0.0.16+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 v1.3.0+3
  [7add5ba3] Libgpg_error_jll v1.42.0+0
⌃ [94ce4f54] Libiconv_jll v1.16.1+1
  [4b2f31a3] Libmount_jll v2.35.0+0
⌅ [89763e89] Libtiff_jll v4.4.0+0
  [38a345b3] Libuuid_jll v2.36.0+0
  [e7412a2a] Ogg_jll v1.3.5+1
⌅ [458c3c95] OpenSSL_jll v1.1.17+0
  [efe28fd5] OpenSpecFun_jll v0.5.5+0
  [91d4177d] Opus_jll v1.3.2+0
  [2f80f16e] PCRE_jll v8.44.0+0
⌃ [30392449] Pixman_jll v0.40.1+0
⌃ [ea2cea3b] Qt5Base_jll v5.15.3+1
⌅ [f50d1b31] Rmath_jll v0.3.0+0
⌃ [a2964d1f] Wayland_jll v1.19.0+0
  [2381bf8a] Wayland_protocols_jll v1.25.0+0
⌃ [02c8fc9c] XML2_jll v2.9.14+0
  [aed1982a] XSLT_jll v1.1.34+0
⌃ [4f6342f7] Xorg_libX11_jll v1.6.9+4
⌃ [0c0b7dd1] Xorg_libXau_jll v1.0.9+4
  [935fb764] Xorg_libXcursor_jll v1.2.0+4
⌃ [a3789734] Xorg_libXdmcp_jll v1.1.3+4
  [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 v0.1.0+3
⌃ [c7cfdc94] Xorg_libxcb_jll v1.13.0+3
⌃ [cc61e674] Xorg_libxkbfile_jll v1.1.0+4
  [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 v1.4.2+4
⌃ [33bec58e] Xorg_xkeyboard_config_jll v2.27.0+4
⌃ [c5fb5394] Xorg_xtrans_jll v1.4.0+3
  [8f1865be] ZeroMQ_jll v4.3.4+0
⌃ [3161d3a3] Zstd_jll v1.5.2+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
  [dfaa095f] x265_jll v3.5.0+0
⌃ [d8fb68d0] xkbcommon_jll v0.9.1+5
  [0dad84c5] ArgTools v1.1.1
  [56f22d72] Artifacts
  [2a0f44e3] Base64
  [ade2ca70] Dates
  [8bb1440f] DelimitedFiles
  [8ba89e20] Distributed
  [f43a241f] Downloads v1.6.0
  [7b1f6079] FileWatching
  [9fa8497b] Future
  [b77e0a4c] InteractiveUtils
  [4af54fe1] LazyArtifacts
  [b27032c2] LibCURL v0.6.3
  [76f85450] LibGit2
  [8f399da3] Libdl
  [37e2e46d] LinearAlgebra
  [56ddb016] Logging
  [d6f4376e] Markdown
  [a63ad114] Mmap
  [ca575930] NetworkOptions v1.2.0
  [44cfe95a] Pkg v1.8.0
  [de0858da] Printf
  [3fa0cd96] REPL
  [9a3f8284] Random
  [ea8e919c] SHA v0.7.0
  [9e88b42a] Serialization
  [1a1011a3] SharedArrays
  [6462fe0b] Sockets
  [2f01184e] SparseArrays
  [10745b16] Statistics
  [4607b0f0] SuiteSparse
  [fa267f1f] TOML v1.0.0
  [a4e569a6] Tar v1.10.0
  [8dfed614] Test
  [cf7118a7] UUIDs
  [4ec0a83e] Unicode
  [e66e0078] CompilerSupportLibraries_jll v0.5.2+0
  [deac9b47] LibCURL_jll v7.81.0+0
  [29816b5a] LibSSH2_jll v1.10.2+0
  [c8ffd9c3] MbedTLS_jll v2.28.0+0
  [14a3606d] MozillaCACerts_jll v2022.2.1
  [4536629a] OpenBLAS_jll v0.3.20+0
  [05823500] OpenLibm_jll v0.8.1+0
  [efcefdf7] PCRE2_jll v10.40.0+0
  [bea87d4a] SuiteSparse_jll v5.10.1+0
  [83775a58] Zlib_jll v1.2.12+3
  [8e850b90] libblastrampoline_jll v5.1.0+0
  [8e850ede] nghttp2_jll v1.41.0+1
  [3f19e933] p7zip_jll v17.4.0+0
Info Packages marked with ⌃ and ⌅ have new versions available, 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.