FitzHugh-Nagumo Bayesian Parameter Estimation Benchmarks
using DiffEqBayes, BenchmarkToolsusing OrdinaryDiffEq, RecursiveArrayTools, Distributions, ParameterizedFunctions,
StanSample, DynamicHMC
using Plots, StaticArrays, Turing, LinearAlgebra"""Print elapsed sampling time and the Turing chain."""
function display_ess_per_sec(chain, elapsed)
println("Elapsed time: $(round(elapsed; digits=2)) seconds")
display(chain)
end
# Distributions requires a vector mean; sol[:, i] can be a scalar after ODE 7.
_mvn(u, σ) = MvNormal(
let n = length(σ)
μ = u isa AbstractVector ? collect(float.(u)) : [float(u)]
length(μ) == n ? μ : fill(μ[1], n)
end,
Diagonal(σ .^ 2),
)
"""Extract and display Stan's internal timing from its CSV output files."""
function display_stan_timing(stan_result)
sample_files = stan_result.model.sample_file
for (chain_idx, f) in enumerate(sample_files)
isfile(f) || continue
lines = readlines(f)
println("Chain $chain_idx timing (from Stan CSV):")
for line in lines
if startswith(line, "#") && occursin("Elapsed Time", line)
println(" ", strip(line[2:end]))
elseif startswith(line, "#") && occursin("seconds", line)
println(" ", strip(line[2:end]))
end
end
end
endMain.var"##WeaveSandBox#277".display_stan_timinggr(fmt = :png)Plots.GRBackend()Defining the problem.
The FitzHugh-Nagumo model is a simplified version of Hodgkin-Huxley model and is used to describe an excitable system (e.g. neuron).
fitz = @ode_def FitzhughNagumo begin
dv = v - 0.33*v^3 - w + l
dw = τinv*(v + a - b*w)
end a b τinv lMain.var"##WeaveSandBox#277".FitzhughNagumo{Main.var"##WeaveSandBox#277".va
r"###ParameterizedDiffEqFunction#279", Main.var"##WeaveSandBox#277".var"###
ParameterizedTGradFunction#280", Main.var"##WeaveSandBox#277".var"###Parame
terizedJacobianFunction#281", Nothing, Nothing, ModelingToolkitBase.System}
(Main.var"##WeaveSandBox#277".var"##ParameterizedDiffEqFunction#279", Linea
rAlgebra.UniformScaling{Bool}(true), nothing, Main.var"##WeaveSandBox#277".
var"##ParameterizedTGradFunction#280", Main.var"##WeaveSandBox#277".var"##P
arameterizedJacobianFunction#281", nothing, nothing, nothing, nothing, noth
ing, nothing, nothing, [:v, :w], :t, nothing, Model ##Parameterized#278:
Equations (2):
2 standard: see equations(##Parameterized#278)
Unknowns (2): see unknowns(##Parameterized#278)
v(t)
w(t)
Parameters (4): see parameters(##Parameterized#278)
a
b
τinv
l, nothing, nothing)prob_ode_fitzhughnagumo = ODEProblem(fitz, [1.0, 1.0], (0.0, 10.0), [0.7, 0.8, 1/12.5, 0.5])
sol = solve(prob_ode_fitzhughnagumo, Tsit5())retcode: Success
Interpolation: specialized 4th order "free" interpolation
t: 13-element Vector{Float64}:
0.0
0.1502916178003539
0.6611860158920579
1.4391493908273403
2.589451591547814
3.7602377960785525
5.101014337183989
6.709997524274457
7.604553475030161
8.336547696252527
9.031279335406245
9.556400185811816
10.0
u: 13-element Vector{Vector{Float64}}:
[1.0, 1.0]
[1.0247192356111163, 1.0109189409610948]
[1.0944137341238236, 1.049239334584406]
[1.1525604472298032, 1.1092965960073389]
[1.1446577625483758, 1.1952738138449215]
[1.0557695077719014, 1.2718985818139574]
[0.8659598744812583, 1.3388184800875969]
[0.3675854021172527, 1.3735376018319738]
[-0.3594427955481846, 1.3493319650351674]
[-1.3772889489189293, 1.2781711184359077]
[-1.905699839713037, 1.1680023987534751]
[-1.9707492736430974, 1.0777291565175875]
[-1.9650453438870346, 1.0031251492628281]sprob_ode_fitzhughnagumo = ODEProblem{false, SciMLBase.FullSpecialize}(
fitz, SA[1.0, 1.0], (0.0, 10.0), SA[0.7, 0.8, 1 / 12.5, 0.5])
sol = solve(sprob_ode_fitzhughnagumo, Tsit5())retcode: Success
Interpolation: specialized 4th order "free" interpolation
t: 13-element Vector{Float64}:
0.0
0.1502916178003539
0.6611860158920579
1.4391493908273403
2.589451591547814
3.7602377960785525
5.101014337183989
6.709997524274457
7.604553475030161
8.336547696252527
9.031279335406245
9.556400185811816
10.0
u: 13-element Vector{StaticArraysCore.SVector{2, Float64}}:
[1.0, 1.0]
[1.0247192356111163, 1.0109189409610948]
[1.0944137341238236, 1.049239334584406]
[1.1525604472298032, 1.1092965960073389]
[1.1446577625483758, 1.1952738138449215]
[1.0557695077719014, 1.2718985818139574]
[0.8659598744812583, 1.3388184800875969]
[0.3675854021172527, 1.3735376018319738]
[-0.3594427955481846, 1.3493319650351674]
[-1.3772889489189293, 1.2781711184359077]
[-1.905699839713037, 1.1680023987534751]
[-1.9707492736430974, 1.0777291565175875]
[-1.9650453438870346, 1.0031251492628281]Data is generated by adding noise to the solution obtained above.
t = collect(range(1, stop = 10, length = 10))
sig = 0.20
data = convert(Array, VectorOfArray([(sol(t[i]) + sig*randn(2)) for i in 1:length(t)]))2×10 Matrix{Float64}:
1.16987 1.40747 1.26058 0.894201 … -0.959972 -1.93754 -2.18396
1.08825 0.903743 1.05461 1.33582 1.63308 1.57208 0.944571Plot of the data and the solution.
scatter(t, data[1, :])
scatter!(t, data[2, :])
plot!(sol)
Priors for the parameters which will be passed for the Bayesian Inference
priors = [truncated(Normal(1.0, 0.5), 0, 1.5), truncated(Normal(1.0, 0.5), 0, 1.5),
truncated(Normal(0.0, 0.5), 0.0, 0.5), truncated(Normal(0.5, 0.5), 0, 1)]4-element Vector{Distributions.Truncated{Distributions.Normal{Float64}, Dis
tributions.Continuous, Float64, Float64, Float64}}:
Truncated(Distributions.Normal{Float64}(μ=1.0, σ=0.5); lower=0.0, upper=1.
5)
Truncated(Distributions.Normal{Float64}(μ=1.0, σ=0.5); lower=0.0, upper=1.
5)
Truncated(Distributions.Normal{Float64}(μ=0.0, σ=0.5); lower=0.0, upper=0.
5)
Truncated(Distributions.Normal{Float64}(μ=0.5, σ=0.5); lower=0.0, upper=1.
0)Benchmarks
Stan.jl backend
We use adapt_delta = 0.85 (slightly above Stan's default of 0.8) consistently across all backends for a fair comparison.
bayesian_result_stan = @time stan_inference(
prob_ode_fitzhughnagumo, :rk45, t, data, priors;
print_summary = false,
sample_kwargs = Dict(:delta => 0.85, :num_samples => 10_000),
vars = (DiffEqBayes.StanODEData(), InverseGamma(2, 3)))74.948333 seconds (4.89 M allocations: 239.278 MiB, 0.06% gc time, 4.77% c
ompilation time)
110.242551 seconds (34.69 M allocations: 1.712 GiB, 0.50% gc time, 14.98% c
ompilation time: 2% of which was recompilation)
10000×6 DataFrame
Row │ sigma1.1 sigma1.2 theta_1 theta_2 theta_3 theta_4
│ Float64 Float64 Float64 Float64 Float64 Float64
───────┼─────────────────────────────────────────────────────────────
1 │ 0.538924 0.486855 0.665356 0.731248 0.113366 0.643114
2 │ 0.287166 0.289731 0.887325 0.849738 0.110488 0.686292
3 │ 0.363141 0.270312 1.20935 0.851519 0.0509696 0.511569
4 │ 0.365832 0.27087 1.21418 0.821874 0.0521738 0.504169
5 │ 0.268448 0.435022 1.02763 0.660896 0.0543505 0.513199
6 │ 0.457346 0.290831 1.25219 1.02089 0.128139 0.79044
7 │ 0.443983 0.304567 1.04909 0.702483 0.104283 0.741879
8 │ 0.31223 0.469798 1.11062 0.799664 0.0958186 0.747356
⋮ │ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮
9994 │ 0.376107 0.839251 1.21309 1.03615 0.184691 0.876535
9995 │ 0.529876 0.475893 0.944174 0.878566 0.0997367 0.598545
9996 │ 0.404731 0.355408 0.777641 0.770103 0.154451 0.805294
9997 │ 0.267656 0.341508 0.943524 0.838256 0.105937 0.676728
9998 │ 0.323194 0.410861 0.629878 0.653391 0.0931657 0.56371
9999 │ 0.250219 0.422044 0.368236 0.788575 0.106304 0.443531
10000 │ 0.349895 0.415266 0.709478 0.786765 0.0721703 0.49049
9985 rows omittedStan's internal timing (excluding data serialization and CSV parsing):
display_stan_timing(bayesian_result_stan)Chain 1 timing (from Stan CSV):
Elapsed Time: 5.404 seconds (Warm-up)
65.956 seconds (Sampling)
71.36 seconds (Total)Direct Turing.jl
We use per-dimension noise parameters (matching Stan) with InverseGamma(2, 3) priors on each σ.
@model function fitfhn(data, prob)
# Prior distributions.
σ ~ filldist(InverseGamma(2, 3), 2)
a ~ truncated(Normal(1.0, 0.5), 0, 1.5)
b ~ truncated(Normal(1.0, 0.5), 0, 1.5)
τinv ~ truncated(Normal(0.0, 0.5), 0.0, 0.5)
l ~ truncated(Normal(0.5, 0.5), 0, 1)
# Simulate FitzHugh-Nagumo model.
p = SA[a, b, τinv, l]
_prob = remake(prob, p = p)
predicted = solve(_prob, Tsit5(); saveat = t)
# Observations.
for i in axes(data, 2)
data[:, i] ~ _mvn(predicted(t[i]), σ)
end
return nothing
end
model = fitfhn(data, sprob_ode_fitzhughnagumo)
# Warmup run to compile all code paths before timing
sample(model, Turing.NUTS(0.85), 10; progress = false)
elapsed_turing_direct = @elapsed chain = sample(model, Turing.NUTS(0.85), 10_000; progress = false)
chain╭─FlexiChain (10000 iterations, 1 chain) ──────────────────────────────────
────╮
│ ↓ iter = 1001:11000
│
│ → chain = 1:1
│
│
│
│ Parameters (5) ── AbstractPPL.VarName
│
│ Vector{Float64} σ (2,)
│
│ Float64 a, b, τinv, l
│
│
│
│ Extras (14)
│
│ Int64 n_steps, tree_depth
│
│ Bool is_accept, numerical_error
│
│ Float64 acceptance_rate, log_density, hamiltonian_energy,
│
│ hamiltonian_energy_error, max_hamiltonian_energy_error, step_si
ze, │
│ nom_step_size, logprior, loglikelihood, logjoint
│
╰──────────────────────────────────────────────────────────────────────────
────╯display_ess_per_sec(chain, elapsed_turing_direct)Elapsed time: 95.62 seconds
╭─FlexiChain (10000 iterations, 1 chain) ──────────────────────────────────
────╮
│ ↓ iter = 1001:11000
│
│ → chain = 1:1
│
│
│
│ Parameters (5) ── AbstractPPL.VarName
│
│ Vector{Float64} σ (2,)
│
│ Float64 a, b, τinv, l
│
│
│
│ Extras (14)
│
│ Int64 n_steps, tree_depth
│
│ Bool is_accept, numerical_error
│
│ Float64 acceptance_rate, log_density, hamiltonian_energy,
│
│ hamiltonian_energy_error, max_hamiltonian_energy_error, step_si
ze, │
│ nom_step_size, logprior, loglikelihood, logjoint
│
╰──────────────────────────────────────────────────────────────────────────
────╯Turing.jl backend
@btime bayesian_result_turing = turing_inference(
prob_ode_fitzhughnagumo, Tsit5(), t, data, priors;
sample_args = (sampler = Turing.NUTS(0.85), num_samples = 10_000),
likelihood = (u, p, t, σ) -> _mvn(u, σ),
likelihood_dist_priors = [InverseGamma(2, 3), InverseGamma(2, 3)])129.168 s (692184465 allocations: 40.37 GiB)
╭─FlexiChain (10000 iterations, 1 chain) ──────────────────────────────────
────╮
│ ↓ iter = 1001:11000
│
│ → chain = 1:1
│
│
│
│ Parameters (5) ── AbstractPPL.VarName
│
│ Float64 theta[1], theta[2], theta[3], theta[4]
│
│ Vector{Float64} σ (2,)
│
│
│
│ Extras (14)
│
│ Int64 n_steps, tree_depth
│
│ Bool is_accept, numerical_error
│
│ Float64 acceptance_rate, log_density, hamiltonian_energy,
│
│ hamiltonian_energy_error, max_hamiltonian_energy_error, step_si
ze, │
│ nom_step_size, logprior, loglikelihood, logjoint
│
╰──────────────────────────────────────────────────────────────────────────
────╯Conclusion
FitzHugh-Nagumo is a standard problem for parameter estimation studies. In the FitzHugh-Nagumo model the parameters to be estimated were [0.7,0.8,0.08,0.5]. dynamichmc_inference has issues with the model and hence was excluded from this benchmark.
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/BayesianInference","DiffEqBayesFitzHughNagumo.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:
Status `/julia/github-runners/amdci1-1/_work/SciMLBenchmarks.jl/SciMLBenchmarks.jl/benchmarks/BayesianInference/Project.toml`
[6e4b80f9] BenchmarkTools v1.8.0
[ebbdde9d] DiffEqBayes v3.16.2
⌃ [459566f4] DiffEqCallbacks v4.19.4
[31c24e10] Distributions v0.25.131
[bbc10e6e] DynamicHMC v3.6.1
[1dea7af3] OrdinaryDiffEq v7.8.1
[65888b18] ParameterizedFunctions v5.27.0
[91a5bcdd] Plots v1.41.7
⌃ [731186ca] RecursiveArrayTools v4.5.1
[31c91b34] SciMLBenchmarks v0.2.1 [loaded: `/julia/github-runners/amdci1-1/_work/SciMLBenchmarks.jl/SciMLBenchmarks.jl/src/SciMLBenchmarks.jl` (v0.2.1) expected `/home/crackauc/.julia/packages/SciMLBenchmarks/ceJyd/src/SciMLBenchmarks.jl` (v0.2.1)]
[c1514b29] StanSample v7.10.3
⌃ [90137ffa] StaticArrays v1.9.20
⌃ [fce5fe82] Turing v0.46.1
[37e2e46d] LinearAlgebra v1.12.0
Info Packages marked with ⌃ have new versions available and may be upgradable.And the full manifest:
Status `/julia/github-runners/amdci1-1/_work/SciMLBenchmarks.jl/SciMLBenchmarks.jl/benchmarks/BayesianInference/Manifest.toml`
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⌅ [2e0e35c7] Moshi v0.3.9
[46d2c3a1] MuladdMacro v0.2.7
⌃ [102ac46a] MultivariatePolynomials v0.5.19
⌃ [ffc61752] Mustache v1.0.21 [loaded: v1.1.0]
⌃ [d8a4904e] MutableArithmetics v1.8.0
[d41bc354] NLSolversBase v8.0.1
[77ba4419] NaNMath v1.1.4
[d9ec5142] NamedTupleTools v0.14.3
⌃ [8913a72c] NonlinearSolve v4.30.0
⌃ [be0214bd] NonlinearSolveBase v2.49.5
⌃ [5959db7a] NonlinearSolveFirstOrder v2.6.1
[9a2c21bd] NonlinearSolveQuasiNewton v1.15.3
[26075421] NonlinearSolveSpectralMethods v1.8.3
[6fe1bfb0] OffsetArrays v1.17.0
⌃ [429524aa] Optim v2.3.1
[3bd65402] Optimisers v0.4.9
[7f7a1694] Optimization v5.9.1
⌃ [bca83a33] OptimizationBase v5.6.1
[36348300] OptimizationOptimJL v0.4.21
⌅ [bac558e1] OrderedCollections v1.8.2 [loaded: v2.0.3]
[1dea7af3] OrdinaryDiffEq v7.8.1
⌃ [6ad6398a] OrdinaryDiffEqBDF v2.4.9
⌃ [bbf590c4] OrdinaryDiffEqCore v4.17.2
[50262376] OrdinaryDiffEqDefault v2.6.2
⌃ [4302a76b] OrdinaryDiffEqDifferentiation v3.12.0
⌃ [127b3ac7] OrdinaryDiffEqNonlinearSolve v2.9.8
⌃ [43230ef6] OrdinaryDiffEqRosenbrock v2.7.3
[b4bd8bb3] OrdinaryDiffEqRosenbrockTableaus v2.4.2
⌃ [2d112036] OrdinaryDiffEqSDIRK v2.9.4
⌃ [b1df2697] OrdinaryDiffEqTsit5 v2.1.4
⌃ [79d7bb75] OrdinaryDiffEqVerner v2.4.1
[90014a1f] PDMats v0.11.41
[65888b18] ParameterizedFunctions v5.27.0
⌅ [d96e819e] Parameters v0.12.3
⌅ [69de0a69] Parsers v2.8.8
⌃ [569bd051] PartitionedDistributions v0.1.0
[ccf2f8ad] PlotThemes v3.3.0
⌃ [995b91a9] PlotUtils v1.4.4
[91a5bcdd] Plots v1.41.7
[e409e4f3] PoissonRandom v0.4.13
[2dfb63ee] PooledArrays v1.4.3
[85a6dd25] PositiveFactorizations v0.2.4
[d236fae5] PreallocationTools v1.7.1
[aea7be01] PrecompileTools v1.3.4
[21216c6a] Preferences v1.6.0
⌃ [08abe8d2] PrettyTables v3.4.8
[27ebfcd6] Primes v0.5.7
[33c8b6b6] ProgressLogging v0.1.6
[92933f4c] ProgressMeter v1.11.0
[43287f4e] PtrArrays v1.4.0
⌃ [0c0d3e7f] PureKLU v1.5.0
[1fd47b50] QuadGK v2.11.3
[74087812] Random123 v1.7.1
[e6cf234a] RandomNumbers v1.6.0
[988b38a3] ReadOnlyArrays v0.2.0
[795d4caa] ReadOnlyDicts v1.0.1
⌃ [3cdcf5f2] RecipesBase v1.3.4
[01d81517] RecipesPipeline v0.6.12
⌃ [731186ca] RecursiveArrayTools v4.5.1
[189a3867] Reexport v1.2.2
[05181044] RelocatableFolders v1.0.1
[ae029012] Requires v1.3.1
[9fe22ead] RespecializeParams v1.3.0
[79098fc4] Rmath v0.9.0
⌃ [f2b01f46] Roots v3.0.8
⌃ [7e49a35a] RuntimeGeneratedFunctions v0.5.26
⌃ [9dfe8606] SCCNonlinearSolve v1.15.3
⌅ [26aad666] SSMProblems v0.6.1
⌃ [0bca4576] SciMLBase v3.54.0
[31c91b34] SciMLBenchmarks v0.2.1 [loaded: `/julia/github-runners/amdci1-1/_work/SciMLBenchmarks.jl/SciMLBenchmarks.jl/src/SciMLBenchmarks.jl` (v0.2.1) expected `/home/crackauc/.julia/packages/SciMLBenchmarks/ceJyd/src/SciMLBenchmarks.jl` (v0.2.1)]
⌃ [19f34311] SciMLJacobianOperators v0.1.19
[a6db7da4] SciMLLogging v2.1.0
⌃ [c0aeaf25] SciMLOperators v1.30.0
[431bcebd] SciMLPublic v1.3.0
⌃ [53ae85a6] SciMLStructures v1.10.5
[30f210dd] ScientificTypesBase v3.1.0
[6c6a2e73] Scratch v1.3.0
[91c51154] SentinelArrays v1.4.10
[efcf1570] Setfield v1.1.2
[992d4aef] Showoff v1.1.1
⌃ [727e6d20] SimpleNonlinearSolve v2.14.5
[699a6c99] SimpleTraits v0.9.6
[a2af1166] SortingAlgorithms v1.2.3
[a57abbd0] SparseColumnPivotedQR v2.1.8
⌃ [9f842d2f] SparseConnectivityTracer v1.2.3
⌃ [0a514795] SparseMatrixColorings v0.4.28
[276daf66] SpecialFunctions v2.9.0
⌃ [860ef19b] StableRNGs v1.0.4
[d0ee94f6] StanBase v4.12.4
[c1514b29] StanSample v7.10.3
[0c0c59c1] StarAlgebras v0.3.0
[64909d44] StateSelection v1.11.1
⌃ [90137ffa] StaticArrays v1.9.20
[1e83bf80] StaticArraysCore v1.4.4
⌃ [64bff920] StatisticalTraits v3.5.0
[10745b16] Statistics v1.11.5
[82ae8749] StatsAPI v1.8.0
[2913bbd2] StatsBase v0.34.13
⌅ [4c63d2b9] StatsFuns v1.5.3
⌃ [5e0ebb24] Strided v2.6.4
⌃ [4db3bf67] StridedViews v0.5.2
[69024149] StringEncodings v0.3.7
⌅ [892a3eda] StringManipulation v0.5.0
[2efcf032] SymbolicIndexingInterface v0.3.55
⌃ [19f23fe9] SymbolicLimits v1.2.1
⌃ [d1185830] SymbolicUtils v4.46.6
⌃ [0c5d862f] Symbolics v7.39.2
[ab02a1b2] TableOperations v1.2.0
[3783bdb8] TableTraits v1.0.1
[bd369af6] Tables v1.14.0
[ed4db957] TaskLocalValues v0.1.3
[02d47bb6] TensorCast v0.4.9
[62fd8b95] TensorCore v0.1.1
[8ea1fca8] TermInterface v2.0.0
[5d786b92] TerminalLoggers v0.1.8
⌃ [a759f4b9] TimerOutputs v1.2.1
[3bb67fe8] TranscodingStreams v0.11.3
[84d833dd] TransformVariables v0.8.26
[f9bc47f6] TransformedLogDensities v1.1.1
[24ddb15e] TransmuteDims v0.1.17
[781d530d] TruncatedStacktraces v1.4.0
⌃ [9d95972d] TupleTools v1.6.0
⌃ [fce5fe82] Turing v0.46.1
[3a884ed6] UnPack v1.0.2
[1cfade01] UnicodeFun v0.4.1
[41fe7b60] Unzip v0.2.0
[d30d5f5c] WeakCacheSets v0.1.0
⌅ [ea10d353] WeakRefStrings v1.4.3
[44d3d7a6] Weave v0.10.12
[76eceee3] WorkerUtilities v1.6.1
⌃ [ddb6d928] YAML v0.4.16 [loaded: v0.4.17]
[6e34b625] Bzip2_jll v1.0.9+0
⌃ [83423d85] Cairo_jll v1.18.7+0
[ee1fde0b] Dbus_jll v1.16.2+0
[2702e6a9] EpollShim_jll v0.0.20230411+1
[2e619515] Expat_jll v2.8.4+0
⌅ [b22a6f82] FFMPEG_jll v8.1.2+0
[a3f928ae] Fontconfig_jll v2.17.1+0
[d7e528f0] FreeType2_jll v2.14.3+1
[559328eb] FriBidi_jll v1.0.17+0
[0656b61e] GLFW_jll v3.5.1+0
[d2c73de3] GR_jll v0.73.27+0
⌅ [b0724c58] GettextRuntime_jll v0.22.4+0
[61579ee1] Ghostscript_jll v9.55.1+0
[7746bdde] Glib_jll v2.88.3+0
[3b182d85] Graphite2_jll v1.3.16+0
[2e76f6c2] HarfBuzz_jll v100.14004.0+0
[1d5cc7b8] IntelOpenMP_jll v2025.2.0+0
[aacddb02] JpegTurbo_jll v3.2.0+1
[c1c5ebd0] LAME_jll v3.100.3+0
[88015f11] LERC_jll v4.2.0+0
[1d63c593] LLVMOpenMP_jll v23.1.1+0
⌅ [e9f186c6] Libffi_jll v3.4.7+0
[7e76a0d4] Libglvnd_jll v1.7.1+1
[94ce4f54] Libiconv_jll v1.18.0+0
⌃ [4b2f31a3] Libmount_jll v2.42.0+0
[89763e89] Libtiff_jll v4.7.3+0
[38a345b3] Libuuid_jll v2.42.0+0
[856f044c] MKL_jll v2025.2.0+0
[e7412a2a] Ogg_jll v1.3.6+0
[efe28fd5] OpenSpecFun_jll v0.5.6+0
[91d4177d] Opus_jll v1.6.1+0
[36c8627f] Pango_jll v1.58.2+0
[30392449] Pixman_jll v0.46.4+0
[c0090381] Qt6Base_jll v6.10.2+2
[629bc702] Qt6Declarative_jll v6.10.2+2
[ce943373] Qt6ShaderTools_jll v6.10.2+1
[6de9746b] Qt6Svg_jll v6.10.2+0
[e99dba38] Qt6Wayland_jll v6.10.2+1
[f50d1b31] Rmath_jll v0.5.2+0
[a44049a8] Vulkan_Loader_jll v1.3.243+0
[a2964d1f] Wayland_jll v1.24.0+0
[ffd25f8a] XZ_jll v5.8.4+0
[f67eecfb] Xorg_libICE_jll v1.1.2+0
[c834827a] Xorg_libSM_jll v1.2.6+0
[4f6342f7] Xorg_libX11_jll v1.8.13+0
[0c0b7dd1] Xorg_libXau_jll v1.0.13+0
[935fb764] Xorg_libXcursor_jll v1.2.4+0
[a3789734] Xorg_libXdmcp_jll v1.1.6+0
[1082639a] Xorg_libXext_jll v1.3.8+0
[d091e8ba] Xorg_libXfixes_jll v6.0.2+0
[a51aa0fd] Xorg_libXi_jll v1.8.4+0
[d1454406] Xorg_libXinerama_jll v1.1.7+0
[ec84b674] Xorg_libXrandr_jll v1.5.6+0
[ea2f1a96] Xorg_libXrender_jll v0.9.12+0
[a65dc6b1] Xorg_libpciaccess_jll v0.19.0+0
[c7cfdc94] Xorg_libxcb_jll v1.17.1+0
[cc61e674] Xorg_libxkbfile_jll v1.2.0+0
[e920d4aa] Xorg_xcb_util_cursor_jll v0.1.6+0
[12413925] Xorg_xcb_util_image_jll v0.4.1+0
[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`