Lorenz Bayesian Parameter Estimation Benchmarks
Parameter estimation of Lorenz Equation using DiffEqBayes.jl
using DiffEqBayes
using DiffEqCallbacks, StaticArrays
using Distributions, StanSample, DynamicHMC, Turing
using OrdinaryDiffEq, RecursiveArrayTools, ParameterizedFunctions, DiffEqCallbacks
using Plots, LinearAlgebragr(fmt=:png)Plots.GRBackend()Initializing the problem
g1 = @ode_def LorenzExample begin
dx = σ*(y-x)
dy = x*(ρ-z) - y
dz = x*y - β*z
end σ ρ β(::Main.var"##WeaveSandBox#225".LorenzExample{Main.var"##WeaveSandBox#225".
var"###ParameterizedDiffEqFunction#227", Main.var"##WeaveSandBox#225".var"#
##ParameterizedTGradFunction#228", Main.var"##WeaveSandBox#225".var"###Para
meterizedJacobianFunction#229", Nothing, Nothing, ModelingToolkit.ODESystem
}) (generic function with 1 method)r0 = [1.0; 0.0; 0.0]
tspan = (0.0, 30.0)
p = [10.0,28.0,2.66]3-element Vector{Float64}:
10.0
28.0
2.66prob = ODEProblem(g1, r0, tspan, p)
sol = solve(prob,Tsit5())retcode: Success
Interpolation: specialized 4th order "free" interpolation
t: 362-element Vector{Float64}:
0.0
3.5678604836301404e-5
0.0003924646531993154
0.003262343160292866
0.00905768915231668
0.016955558260817218
0.027688386680734336
0.04185394923402222
0.060237081190933954
0.08368091876192292
⋮
29.454408593999744
29.535835262016416
29.605800898814937
29.680544237315484
29.76351894459027
29.830453975921273
29.895187958428064
29.951353159401716
30.0
u: 362-element Vector{Vector{Float64}}:
[1.0, 0.0, 0.0]
[0.9996434557625105, 0.0009988049817849054, 1.7814349300524274e-8]
[0.9961045497425811, 0.010965399721242273, 2.1469572398550344e-6]
[0.969359731583511, 0.08976885926574524, 0.00014379728741456088]
[0.9242069970136711, 0.24227921748230874, 0.0010460982665403552]
[0.8800496059816251, 0.4387144111226294, 0.003424048327994956]
[0.8483334490657588, 0.6915266898669253, 0.008487275727945722]
[0.8494997033541278, 1.014487977850381, 0.018211867322766993]
[0.9138893443162335, 1.4424796048698445, 0.03669462235325829]
[1.088820494006628, 2.0521989010862804, 0.07402932469846656]
⋮
[12.961137512020898, 18.279918361318895, 26.25897074938116]
[14.392465492943021, 11.508987143103287, 37.65923554892938]
[10.152335863282124, 2.269979011509871, 36.547101446703415]
[4.808585699119702, -0.8952979613542543, 30.11368867713037]
[1.6024263579730906, -0.6846122220278174, 23.951371949023542]
[0.6084324252084657, -0.25780977194812565, 20.01475398456359]
[0.2684879085098022, -0.002836416861666546, 16.8456113650265]
[0.18738369956893544, 0.14299558298777929, 14.508658451450762]
[0.19493344255581885, 0.2638385897822422, 12.749361976073427]sr0 = SA[1.0; 0.0; 0.0]
tspan = (0.0, 30.0)
sp = SA[10.0,28.0,2.66]
sprob = ODEProblem{false,SciMLBase.FullSpecialize}(g1, sr0, tspan, sp)
sol = solve(sprob,Tsit5())retcode: Success
Interpolation: specialized 4th order "free" interpolation
t: 362-element Vector{Float64}:
0.0
3.5678604836301404e-5
0.0003924646531993154
0.003262343160292866
0.00905768915231668
0.016955558260817218
0.027688386680734336
0.04185394923402222
0.060237081190933954
0.08368091876192292
⋮
29.45440860820997
29.535835277148024
29.605800914738243
29.680544254084552
29.76351899890051
29.830454031907585
29.89518801188915
29.95135321067184
30.0
u: 362-element Vector{StaticArraysCore.SVector{3, Float64}}:
[1.0, 0.0, 0.0]
[0.9996434557625105, 0.0009988049817849054, 1.7814349300524274e-8]
[0.9961045497425811, 0.010965399721242273, 2.1469572398550344e-6]
[0.969359731583511, 0.08976885926574524, 0.00014379728741456088]
[0.9242069970136711, 0.24227921748230874, 0.0010460982665403552]
[0.8800496059816251, 0.4387144111226294, 0.003424048327994956]
[0.8483334490657588, 0.6915266898669252, 0.008487275727945722]
[0.8494997033541277, 1.014487977850381, 0.018211867322766986]
[0.9138893443162334, 1.4424796048698445, 0.03669462235325828]
[1.088820494006628, 2.05219890108628, 0.07402932469846653]
⋮
[12.961138489125066, 18.279918309485804, 26.258974000912552]
[14.392464847216962, 11.508984146832098, 37.65923672513932]
[10.152334234091272, 2.2699772912331264, 36.5470998219813]
[4.808584535722784, -0.8952980440122978, 30.11368685429087]
[1.6024250955199508, -0.6846116829208884, 23.95136813347255]
[0.6084320079771826, -0.2578093152137886, 20.014750756773317]
[0.2684878928983248, -0.002836030553965167, 16.845608772737304]
[0.18738386874531499, 0.14299602936335054, 14.508656308449002]
[0.19493371295291068, 0.2638390569115199, 12.749361835984178]Generating data for bayesian estimation of parameters from the obtained solutions using the Tsit5 algorithm by adding random noise to it.
t = collect(range(1, stop=30, length=30))
sig = 0.49
data = convert(Array, VectorOfArray([(sol(t[i]) + sig*randn(3)) for i in 1:length(t)]))3×30 Matrix{Float64}:
-10.6601 -7.54385 -7.83015 -9.87397 … 12.0027 3.25321 0.136849
-9.38595 -9.20388 -6.50847 -10.6299 16.1373 1.04234 0.0756352
28.7707 25.7196 28.599 26.9251 24.8948 26.1235 12.4032Plots of the generated data and the actual data.
Plots.scatter(t, data[1,:],markersize=4,color=:purple)
Plots.scatter!(t, data[2,:],markersize=4,color=:yellow)
Plots.scatter!(t, data[3,:],markersize=4,color=:black)
plot!(sol)
Uncertainty Quantification plot is used to decide the tolerance for the differential equation.
cb = AdaptiveProbIntsUncertainty(5)
monte_prob = EnsembleProblem(prob)
sim = solve(monte_prob,Tsit5(),trajectories=100,callback=cb,reltol=1e-5,abstol=1e-5)
plot(sim,vars=(0,1),linealpha=0.4)
cb = AdaptiveProbIntsUncertainty(5)
monte_prob = EnsembleProblem(prob)
sim = solve(monte_prob,Tsit5(),trajectories=100,callback=cb,reltol=1e-6,abstol=1e-6)
plot(sim,vars=(0,1),linealpha=0.4)
cb = AdaptiveProbIntsUncertainty(5)
monte_prob = EnsembleProblem(prob)
sim = solve(monte_prob,Tsit5(),trajectories=100,callback=cb,reltol=1e-8,abstol=1e-8)
plot(sim,vars=(0,1),linealpha=0.4)
priors = [truncated(Normal(10,2),1,15),truncated(Normal(30,5),1,45),truncated(Normal(2.5,0.5),1,4)]3-element Vector{Distributions.Truncated{Distributions.Normal{Float64}, Dis
tributions.Continuous, Float64, Float64, Float64}}:
Truncated(Distributions.Normal{Float64}(μ=10.0, σ=2.0); lower=1.0, upper=1
5.0)
Truncated(Distributions.Normal{Float64}(μ=30.0, σ=5.0); lower=1.0, upper=4
5.0)
Truncated(Distributions.Normal{Float64}(μ=2.5, σ=0.5); lower=1.0, upper=4.
0)Using Stan.jl backend
Lorenz equation is a chaotic system hence requires very low tolerance to be estimated in a reasonable way, we use 1e-8 obtained from the uncertainty plots. Use of truncated priors is necessary to prevent Stan from stepping into negative and other improbable areas.
@time bayesian_result_stan = stan_inference(prob,t,data,priors; delta = 0.65, reltol=1e-8,abstol=1e-8, vars=(DiffEqBayes.StanODEData(), InverseGamma(2, 3)))1093.111150 seconds (2.13 M allocations: 144.995 MiB, 0.14% compilation tim
e)
1114.449960 seconds (6.49 M allocations: 439.356 MiB, 0.01% gc time, 0.39%
compilation time: <1% of which was recompilation)
Chains MCMC chain (1000×6×1 Array{Float64, 3}):
Iterations = 1:1:1000
Number of chains = 1
Samples per chain = 1000
parameters = sigma1.1, sigma1.2, sigma1.3, theta_1, theta_2, theta_3
internals =
Summary Statistics
parameters mean std mcse ess_bulk ess_tail rhat
e ⋯
Symbol Float64 Float64 Float64 Float64 Float64 Float64
⋯
sigma1.1 6.1551 0.8508 0.0819 105.4194 210.6085 1.0042
⋯
sigma1.2 7.9956 1.0096 0.0733 197.1286 348.4017 0.9998
⋯
sigma1.3 6.8392 0.9287 0.0730 182.4107 313.3166 1.0228
⋯
theta_1 8.9803 1.0706 0.1771 38.8040 51.5322 1.0219
⋯
theta_2 22.6191 0.2137 0.0314 50.7946 41.4548 1.0094
⋯
theta_3 2.2141 0.0522 0.0077 40.2201 44.0878 1.0082
⋯
1 column om
itted
Quantiles
parameters 2.5% 25.0% 50.0% 75.0% 97.5%
Symbol Float64 Float64 Float64 Float64 Float64
sigma1.1 4.7065 5.5682 6.1206 6.5845 8.0399
sigma1.2 6.2641 7.2486 7.9738 8.6878 10.0300
sigma1.3 5.3269 6.1705 6.7684 7.4394 8.8077
theta_1 7.0475 8.2906 8.8480 9.5756 11.3679
theta_2 22.3532 22.4632 22.5817 22.7040 23.2649
theta_3 2.1435 2.1807 2.1996 2.2316 2.3574Direct Turing.jl
@model function fitlv(data, prob)
# Prior distributions.
α ~ InverseGamma(2, 3)
σ ~ truncated(Normal(10, 2), 1, 15)
ρ ~ truncated(Normal(30, 5), 1, 45)
β ~ truncated(Normal(2.5, 0.5), 1, 4)
# Simulate Lotka-Volterra model.
p = SA[σ, ρ, β]
_prob = remake(prob, p = p)
predicted = solve(_prob, Vern9(); saveat=t)
# Observations.
for i in 1:length(predicted)
data[:, i] ~ MvNormal(predicted[i], α^2 * I)
end
return nothing
end
model = fitlv(data, sprob)
@time chain = sample(model, Turing.NUTS(0.65), 10000; progress=false)2085.584748 seconds (3.80 G allocations: 761.065 GiB, 3.72% gc time, 1.04%
compilation time)
Chains MCMC chain (10000×16×1 Array{Float64, 3}):
Iterations = 1001:1:11000
Number of chains = 1
Samples per chain = 10000
Wall duration = 2077.72 seconds
Compute duration = 2077.72 seconds
parameters = α, σ, ρ, β
internals = lp, n_steps, is_accept, acceptance_rate, log_density, h
amiltonian_energy, hamiltonian_energy_error, max_hamiltonian_energy_error,
tree_depth, numerical_error, step_size, nom_step_size
Summary Statistics
parameters mean std mcse ess_bulk ess_tail rhat
e ⋯
Symbol Float64 Float64 Float64 Float64 Float64 Float64
⋯
α 0.3147 0.0000 0.0000 21.7102 38.1369 1.7173
⋯
σ 13.0925 0.0000 0.0000 NaN NaN NaN
⋯
ρ 29.1572 0.0000 0.0000 NaN NaN NaN
⋯
β 1.8379 0.0000 0.0000 307.4406 336.1443 1.0002
⋯
1 column om
itted
Quantiles
parameters 2.5% 25.0% 50.0% 75.0% 97.5%
Symbol Float64 Float64 Float64 Float64 Float64
α 0.3147 0.3147 0.3147 0.3147 0.3147
σ 13.0925 13.0925 13.0925 13.0925 13.0925
ρ 29.1572 29.1572 29.1572 29.1572 29.1572
β 1.8379 1.8379 1.8379 1.8379 1.8379Using Turing.jl backend
@time bayesian_result_turing = turing_inference(prob, Vern9(), t, data, priors; reltol=1e-8, abstol=1e-8, likelihood=(u, p, t, σ) -> MvNormal(u, Diagonal((σ) .^ 2 .* ones(length(u)))), likelihood_dist_priors=[InverseGamma(2, 3), InverseGamma(2, 3), InverseGamma(2, 3)])368.818015 seconds (1.63 G allocations: 84.286 GiB, 2.58% gc time, 4.80% co
mpilation time)
Chains MCMC chain (1000×18×1 Array{Float64, 3}):
Iterations = 501:1:1500
Number of chains = 1
Samples per chain = 1000
Wall duration = 366.27 seconds
Compute duration = 366.27 seconds
parameters = theta[1], theta[2], theta[3], σ[1], σ[2], σ[3]
internals = lp, n_steps, is_accept, acceptance_rate, log_density, h
amiltonian_energy, hamiltonian_energy_error, max_hamiltonian_energy_error,
tree_depth, numerical_error, step_size, nom_step_size
Summary Statistics
parameters mean std mcse ess_bulk ess_tail rhat
e ⋯
Symbol Float64 Float64 Float64 Float64 Float64 Float64
⋯
theta[1] 11.7361 0.9001 0.1593 33.2634 88.6128 1.0592
⋯
theta[2] 25.1943 0.0933 0.0391 5.9667 38.3165 1.2245
⋯
theta[3] 2.6593 0.0514 0.0086 36.3936 95.6147 1.0442
⋯
σ[1] 6.5917 0.7180 0.1536 21.7595 62.4331 1.0159
⋯
σ[2] 8.5671 1.2913 0.2568 25.5158 36.4270 1.0080
⋯
σ[3] 7.3115 1.0896 0.2273 30.7537 26.9866 1.0059
⋯
1 column om
itted
Quantiles
parameters 2.5% 25.0% 50.0% 75.0% 97.5%
Symbol Float64 Float64 Float64 Float64 Float64
theta[1] 10.2393 10.9923 11.6469 12.5727 13.2497
theta[2] 25.0458 25.1223 25.1843 25.2662 25.4015
theta[3] 2.5865 2.6114 2.6541 2.6972 2.7629
σ[1] 5.4081 6.0630 6.5654 7.0090 7.9817
σ[2] 6.1665 7.6454 8.5773 9.4328 10.9029
σ[3] 5.8644 6.4202 7.0854 8.0180 9.8265Using DynamicHMC.jl backend
@time bayesian_result_dynamichmc = dynamichmc_inference(prob,Tsit5(),t,data,priors;solve_kwargs = (reltol=1e-8,abstol=1e-8,))724.259517 seconds (136.99 M allocations: 26.957 GiB, 0.51% gc time, 0.86%
compilation time)
(posterior = @NamedTuple{parameters::Vector{Float64}, σ::Vector{Float64}}[(
parameters = [7.694801171482742, 22.893818968086762, 2.2976578521757185], σ
= [6.2167536964683645, 7.5413837881846195, 6.868909454859528]), (parameter
s = [8.153555317462024, 22.69727675682712, 2.2445230607600357], σ = [5.8757
91510510043, 7.1334974432702225, 7.156284300675723]), (parameters = [8.4937
56136014097, 22.59554009087766, 2.2114403153310516], σ = [5.742043050239264
, 7.0764716928604345, 7.943822036552526]), (parameters = [8.249675901152653
, 22.698945800427715, 2.229346752388919], σ = [5.814410339873596, 6.9678237
44250997, 7.804823565633406]), (parameters = [9.363353564439103, 22.5377108
38909764, 2.1877961553112546], σ = [5.707802252328887, 7.179872156131361, 7
.847122262367753]), (parameters = [9.082403363772633, 22.511833510114037, 2
.1876575361401747], σ = [5.996062649980872, 7.405976475291018, 7.3696530558
04812]), (parameters = [9.021181810908196, 22.51769906918402, 2.19219507836
17046], σ = [6.01949951664016, 7.3928894057213554, 7.383938167151761]), (pa
rameters = [8.963310030361393, 22.452547997099884, 2.19759660171501], σ = [
6.023716462096951, 7.3629588783110425, 7.460442015183531]), (parameters = [
8.909560909882261, 22.586392198004905, 2.199227530101629], σ = [6.017715685
880321, 7.359429013997393, 7.451684448832139]), (parameters = [9.0001263854
83759, 22.587411093870752, 2.1963553815563746], σ = [5.949664474532547, 7.3
5659018067715, 7.158340840201999]) … (parameters = [7.71832152983362, 22.
8323110721328, 2.2855344115943987], σ = [6.032425770743965, 8.6931001510124
2, 6.0655610255245795]), (parameters = [7.778961466933968, 22.8060724912803
75, 2.291662713572156], σ = [6.058793667502328, 8.705500145281798, 6.082672
110714241]), (parameters = [7.796188544728113, 22.843575323343014, 2.291847
467219827], σ = [6.056768412999365, 8.707613037121552, 6.071269968214637]),
(parameters = [7.686667751202682, 22.87968512695112, 2.2951126413085134],
σ = [6.1040681798803575, 8.719079415655479, 6.039301089192822]), (parameter
s = [7.045937750000604, 23.298500913338746, 2.3597834557040396], σ = [6.272
3787517816545, 8.688059053119792, 5.924824947640448]), (parameters = [7.557
592187711866, 22.968971395035812, 2.313393349000611], σ = [6.56989308030619
1, 8.777372151791468, 5.886149445652496]), (parameters = [8.829175649557438
, 22.5976901501517, 2.1949294119015392], σ = [5.964026178142975, 9.21264821
929834, 6.141610420052226]), (parameters = [8.159827561145491, 22.744310401
780044, 2.2415237611723096], σ = [6.141047695414409, 8.79174405672379, 6.73
3857805092642]), (parameters = [9.914220491934637, 22.439678344489995, 2.17
74527259001943], σ = [6.131338110236664, 8.447693188950316, 5.8282215113543
28]), (parameters = [10.879654852259806, 22.4148164242974, 2.15909735340049
74], σ = [6.322439779113763, 8.255519574816802, 5.59017028873388])], poster
ior_matrix = [2.0405449282933072 2.098454067401242 … 2.2939701398124988 2.3
86894517786722; 3.130866960069492 3.1222449506311833 … 3.1108307465272524 3
.1097221877142807; … ; 2.0204056914654087 1.9648016391609797 … 2.1338934087
085626 2.1108820160112565; 1.92700535343858 1.9679908938505508 … 1.76271189
57359815 1.7210097498038899], tree_statistics = DynamicHMC.TreeStatisticsNU
TS[DynamicHMC.TreeStatisticsNUTS(-313.85054519422147, 10, reached maximum d
epth without divergence or turning, 0.9998634941642631, 1023, DynamicHMC.Di
rections(0xfc481725)), DynamicHMC.TreeStatisticsNUTS(-307.9253967799472, 10
, reached maximum depth without divergence or turning, 0.9967038324935233,
1023, DynamicHMC.Directions(0xaf040856)), DynamicHMC.TreeStatisticsNUTS(-30
8.7189196055699, 9, turning at positions 820:827, 0.9629416780862775, 863,
DynamicHMC.Directions(0xd5bdafdb)), DynamicHMC.TreeStatisticsNUTS(-311.3157
8057774607, 8, turning at positions -251:-282, 0.9131306297862282, 511, Dyn
amicHMC.Directions(0x50f96ce5)), DynamicHMC.TreeStatisticsNUTS(-307.7591299
070481, 10, reached maximum depth without divergence or turning, 0.99777092
61481045, 1023, DynamicHMC.Directions(0x8895f417)), DynamicHMC.TreeStatisti
csNUTS(-307.4693372853194, 10, reached maximum depth without divergence or
turning, 0.9980062767443947, 1023, DynamicHMC.Directions(0x4dd73a93)), Dyna
micHMC.TreeStatisticsNUTS(-308.24780230613595, 7, turning at positions -67:
-68, 0.8799452019205208, 163, DynamicHMC.Directions(0xbe4e735f)), DynamicHM
C.TreeStatisticsNUTS(-311.76221847360387, 6, turning at positions -46:-49,
0.6127654465464937, 67, DynamicHMC.Directions(0x3e71af92)), DynamicHMC.Tree
StatisticsNUTS(-311.66838373885, 4, turning at positions -11:-14, 0.9259258
294289162, 27, DynamicHMC.Directions(0xa5a0ef8d)), DynamicHMC.TreeStatistic
sNUTS(-307.5823472012412, 10, reached maximum depth without divergence or t
urning, 0.9996562243292789, 1023, DynamicHMC.Directions(0x1cb7e59a)) … Dy
namicHMC.TreeStatisticsNUTS(-310.1265294838295, 9, turning at positions -49
0:-505, 0.8060015321905788, 639, DynamicHMC.Directions(0x7a521886)), Dynami
cHMC.TreeStatisticsNUTS(-310.1822301102478, 7, turning at positions 126:129
, 0.5975038460927558, 215, DynamicHMC.Directions(0x7275b0a9)), DynamicHMC.T
reeStatisticsNUTS(-311.4915892664929, 5, turning at positions 31:34, 0.4113
17086637644, 39, DynamicHMC.Directions(0xde2e367a)), DynamicHMC.TreeStatist
icsNUTS(-309.16806256004406, 7, turning at positions 244:247, 0.95919270046
78042, 247, DynamicHMC.Directions(0x1f847eff)), DynamicHMC.TreeStatisticsNU
TS(-309.4718684672975, 9, turning at positions 665:666, 0.9955484954247962,
917, DynamicHMC.Directions(0xaeab3f04)), DynamicHMC.TreeStatisticsNUTS(-30
8.151758683113, 10, reached maximum depth without divergence or turning, 0.
9927802505726506, 1023, DynamicHMC.Directions(0xfd443fd6)), DynamicHMC.Tree
StatisticsNUTS(-310.0717027624037, 10, reached maximum depth without diverg
ence or turning, 0.9907029152155133, 1023, DynamicHMC.Directions(0x30c5df49
)), DynamicHMC.TreeStatisticsNUTS(-308.6979951391607, 10, reached maximum d
epth without divergence or turning, 0.9960066970390885, 1023, DynamicHMC.Di
rections(0x8db9dc77)), DynamicHMC.TreeStatisticsNUTS(-307.9184472424107, 10
, reached maximum depth without divergence or turning, 0.9998323272964955,
1023, DynamicHMC.Directions(0x1547d71d)), DynamicHMC.TreeStatisticsNUTS(-31
0.09970528966534, 9, turning at positions -322:-323, 0.9764746207943619, 51
7, DynamicHMC.Directions(0x742788c2))], κ = Gaussian kinetic energy (Diagon
al), √diag(M⁻¹): [0.818696409766844, 1.3913870567567268, 0.2808566504257373
, 0.27501982605234715, 0.23452958084565675, 0.5379005339742007], ϵ = 0.0003
208163681735802)Conclusion
Due to the chaotic nature of Lorenz Equation, it is a very hard problem to estimate as it has the property of exponentially increasing errors. Its uncertainty plot points to its chaotic behaviour and goes awry for different values of tolerance, we use 1e-8 as the tolerance as it makes its uncertainty small enough to be trusted in (0,30) time span.
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","DiffEqBayesLorenz.jmd")Computer Information:
Julia Version 1.10.5
Commit 6f3fdf7b362 (2024-08-27 14:19 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-15.0.7 (ORCJIT, znver2)
Threads: 1 default, 0 interactive, 1 GC (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/BayesianInference/Project.toml`
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⌅ [459566f4] DiffEqCallbacks v2.29.1
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[37e2e46d] LinearAlgebra
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:
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[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
⌅ [dfaa095f] x265_jll v3.5.0+0
⌃ [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
[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 v1.9.0
[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.