Bruss Scaling PDE Differentaition Benchmarks
From the paper A Comparison of Automatic Differentiation and Continuous Sensitivity Analysis for Derivatives of Differential Equation Solutions
using OrdinaryDiffEq, ReverseDiff, ForwardDiff, FiniteDiff, SciMLSensitivity
using LinearAlgebra, Tracker, Plotsfunction makebrusselator(N=8)
xyd_brusselator = range(0,stop=1,length=N)
function limit(a, N)
if a == N+1
return 1
elseif a == 0
return N
else
return a
end
end
brusselator_f(x, y, t) = ifelse((((x-0.3)^2 + (y-0.6)^2) <= 0.1^2) &&
(t >= 1.1), 5., 0.)
brusselator_2d_loop = let N=N, xyd=xyd_brusselator, dx=step(xyd_brusselator)
function brusselator_2d_loop(du, u, p, t)
@inbounds begin
ii1 = N^2
ii2 = ii1+N^2
ii3 = ii2+2(N^2)
A = @view p[1:ii1]
B = @view p[ii1+1:ii2]
α = @view p[ii2+1:ii3]
II = LinearIndices((N, N, 2))
for I in CartesianIndices((N, N))
x = xyd[I[1]]
y = xyd[I[2]]
i = I[1]
j = I[2]
ip1 = limit(i+1, N); im1 = limit(i-1, N)
jp1 = limit(j+1, N); jm1 = limit(j-1, N)
du[II[i,j,1]] = α[II[i,j,1]]*(u[II[im1,j,1]] + u[II[ip1,j,1]] + u[II[i,jp1,1]] + u[II[i,jm1,1]] - 4u[II[i,j,1]])/dx^2 +
B[II[i,j,1]] + u[II[i,j,1]]^2*u[II[i,j,2]] - (A[II[i,j,1]] + 1)*u[II[i,j,1]] + brusselator_f(x, y, t)
end
for I in CartesianIndices((N, N))
i = I[1]
j = I[2]
ip1 = limit(i+1, N)
im1 = limit(i-1, N)
jp1 = limit(j+1, N)
jm1 = limit(j-1, N)
du[II[i,j,2]] = α[II[i,j,2]]*(u[II[im1,j,2]] + u[II[ip1,j,2]] + u[II[i,jp1,2]] + u[II[i,jm1,2]] - 4u[II[i,j,2]])/dx^2 +
A[II[i,j,1]]*u[II[i,j,1]] - u[II[i,j,1]]^2*u[II[i,j,2]]
end
return nothing
end
end
end
function init_brusselator_2d(xyd)
N = length(xyd)
u = zeros(N, N, 2)
for I in CartesianIndices((N, N))
x = xyd[I[1]]
y = xyd[I[2]]
u[I,1] = 22*(y*(1-y))^(3/2)
u[I,2] = 27*(x*(1-x))^(3/2)
end
vec(u)
end
dx = step(xyd_brusselator)
e1 = ones(N-1)
off = N-1
e4 = ones(N-off)
T = diagm(0=>-2ones(N), -1=>e1, 1=>e1, off=>e4, -off=>e4) ./ dx^2
Ie = Matrix{Float64}(I, N, N)
# A + df/du
Op = kron(Ie, T) + kron(T, Ie)
brusselator_jac = let N=N
(J,a,p,t) -> begin
ii1 = N^2
ii2 = ii1+N^2
ii3 = ii2+2(N^2)
A = @view p[1:ii1]
B = @view p[ii1+1:ii2]
α = @view p[ii2+1:ii3]
u = @view a[1:end÷2]
v = @view a[end÷2+1:end]
N2 = length(a)÷2
α1 = @view α[1:end÷2]
α2 = @view α[end÷2+1:end]
fill!(J, 0)
J[1:N2, 1:N2] .= α1.*Op
J[N2+1:end, N2+1:end] .= α2.*Op
J1 = @view J[1:N2, 1:N2]
J2 = @view J[N2+1:end, 1:N2]
J3 = @view J[1:N2, N2+1:end]
J4 = @view J[N2+1:end, N2+1:end]
J1[diagind(J1)] .+= @. 2u*v-(A+1)
J2[diagind(J2)] .= @. A-2u*v
J3[diagind(J3)] .= @. u^2
J4[diagind(J4)] .+= @. -u^2
nothing
end
end
Jmat = zeros(2N*N, 2N*N)
dp = zeros(2N*N, 4N*N)
brusselator_comp = let N=N, xyd=xyd_brusselator, dx=step(xyd_brusselator), Jmat=Jmat, dp=dp, brusselator_jac=brusselator_jac
function brusselator_comp(dus, us, p, t)
@inbounds begin
ii1 = N^2
ii2 = ii1+N^2
ii3 = ii2+2(N^2)
@views u, s = us[1:ii2], us[ii2+1:end]
du = @view dus[1:ii2]
ds = @view dus[ii2+1:end]
fill!(dp, 0)
A = @view p[1:ii1]
B = @view p[ii1+1:ii2]
α = @view p[ii2+1:ii3]
dfdα = @view dp[:, ii2+1:ii3]
diagind(dfdα)
for i in 1:ii1
dp[i, ii1+i] = 1
end
II = LinearIndices((N, N, 2))
uu = @view u[1:end÷2]
for i in eachindex(uu)
dp[i, i] = -uu[i]
dp[i+ii1, i] = uu[i]
end
for I in CartesianIndices((N, N))
x = xyd[I[1]]
y = xyd[I[2]]
i = I[1]
j = I[2]
ip1 = limit(i+1, N); im1 = limit(i-1, N)
jp1 = limit(j+1, N); jm1 = limit(j-1, N)
au = dfdα[II[i,j,1],II[i,j,1]] = (u[II[im1,j,1]] + u[II[ip1,j,1]] + u[II[i,jp1,1]] + u[II[i,jm1,1]] - 4u[II[i,j,1]])/dx^2
du[II[i,j,1]] = α[II[i,j,1]]*(au) + B[II[i,j,1]] + u[II[i,j,1]]^2*u[II[i,j,2]] - (A[II[i,j,1]] + 1)*u[II[i,j,1]] + brusselator_f(x, y, t)
end
for I in CartesianIndices((N, N))
i = I[1]
j = I[2]
ip1 = limit(i+1, N)
im1 = limit(i-1, N)
jp1 = limit(j+1, N)
jm1 = limit(j-1, N)
av = dfdα[II[i,j,2],II[i,j,2]] = (u[II[im1,j,2]] + u[II[ip1,j,2]] + u[II[i,jp1,2]] + u[II[i,jm1,2]] - 4u[II[i,j,2]])/dx^2
du[II[i,j,2]] = α[II[i,j,2]]*(av) + A[II[i,j,1]]*u[II[i,j,1]] - u[II[i,j,1]]^2*u[II[i,j,2]]
end
brusselator_jac(Jmat,u,p,t)
BLAS.gemm!('N', 'N', 1., Jmat, reshape(s, 2N*N, 4N*N), 1., dp)
copyto!(ds, vec(dp))
return nothing
end
end
end
u0 = init_brusselator_2d(xyd_brusselator)
p = [fill(3.4,N^2); fill(1.,N^2); fill(10.,2*N^2)]
brusselator_2d_loop, u0, p, brusselator_jac, ODEProblem(brusselator_comp, copy([u0;zeros((N^2*2)*(N^2*4))]), (0.,10.), p)
end
Base.eps(::Type{Tracker.TrackedReal{T}}) where T = eps(T)
Base.vec(v::Adjoint{<:Real, <:AbstractVector}) = vec(v') # bad bad hackSetup AutoDiff
bt = 0:0.1:1
tspan = (0.0, 1.0)
forwarddiffn = vcat(2:10,12,15)
reversediffn = 2:10
numdiffn = vcat(2:10,12)
csan = vcat(2:10,12,15,17)
#csaseedn = 2:10
tols = (abstol=1e-5, reltol=1e-7)
@isdefined(PROBS) || (const PROBS = Dict{Int,Any}())
makebrusselator!(dict, n) = get!(()->makebrusselator(n), dict, n)
_adjoint_methods = ntuple(3) do ii
Alg = (InterpolatingAdjoint, QuadratureAdjoint, BacksolveAdjoint)[ii]
(
user = Alg(autodiff=false,autojacvec=false), # user Jacobian
adjc = Alg(autodiff=true,autojacvec=false), # AD Jacobian
advj = Alg(autodiff=true,autojacvec=EnzymeVJP()), # AD vJ
)
end |> NamedTuple{(:interp, :quad, :backsol)}
@isdefined(ADJOINT_METHODS) || (const ADJOINT_METHODS = mapreduce(collect, vcat, _adjoint_methods))
function auto_sen_l2(f, u0, tspan, p, t, alg=Tsit5(); diffalg=ReverseDiff.gradient, kwargs...)
test_f(p) = begin
prob = ODEProblem{true, SciMLBase.FullSpecialize}(f,convert.(eltype(p),u0),tspan,p)
sol = solve(prob,alg,saveat=t; kwargs...)
sum(sol.u) do x
sum(z->(1-z)^2/2, x)
end
end
diffalg(test_f, p)
end
@inline function diffeq_sen_l2(df, u0, tspan, p, t, alg=Tsit5();
abstol=1e-5, reltol=1e-7, iabstol=abstol, ireltol=reltol,
sensalg=SensitivityAlg(), kwargs...)
prob = ODEProblem{true, SciMLBase.FullSpecialize}(df,u0,tspan,p)
saveat = tspan[1] != t[1] && tspan[end] != t[end] ? vcat(tspan[1],t,tspan[end]) : t
sol = solve(prob, alg, abstol=abstol, reltol=reltol, saveat=saveat; kwargs...)
dg(out,u,p,t,i) = (out.=u.-1.0)
adjoint_sensitivities(sol,alg;t,abstol=abstol,dgdu_discrete = dg,
reltol=reltol,sensealg=sensalg)
enddiffeq_sen_l2 (generic function with 2 methods)AD Choice Benchmarks
forwarddiff = map(forwarddiffn) do n
bfun, b_u0, b_p, brusselator_jac, brusselator_comp = makebrusselator!(PROBS, n)
@elapsed auto_sen_l2(bfun, b_u0, tspan, b_p, bt, (Rodas5()); diffalg=(ForwardDiff.gradient), tols...)
t = @elapsed auto_sen_l2(bfun, b_u0, tspan, b_p, bt, (Rodas5()); diffalg=(ForwardDiff.gradient), tols...)
@show n,t
t
end(n, t) = (2, 0.000593566)
(n, t) = (3, 0.014666473)
(n, t) = (4, 0.095285573)
(n, t) = (5, 0.510046743)
(n, t) = (6, 1.724554577)
(n, t) = (7, 5.594205049)
(n, t) = (8, 15.43367799)
(n, t) = (9, 36.868764125)
(n, t) = (10, 84.720352452)
(n, t) = (12, 353.685991406)
(n, t) = (15, 2138.569337856)
11-element Vector{Float64}:
0.000593566
0.014666473
0.095285573
0.510046743
1.724554577
5.594205049
15.43367799
36.868764125
84.720352452
353.685991406
2138.569337856#=
reversediff = map(reversediffn) do n
bfun, b_u0, b_p, brusselator_jac, brusselator_comp = makebrusselator!(PROBS, n)
@elapsed auto_sen_l2(bfun, b_u0, tspan, b_p, bt, (Rodas5(autodiff=false)); diffalg=(ReverseDiff.gradient), tols...)
t = @elapsed auto_sen_l2(bfun, b_u0, tspan, b_p, bt, (Rodas5(autodiff=false)); diffalg=(ReverseDiff.gradient), tols...)
@show n,t
t
end
=#numdiff = map(numdiffn) do n
bfun, b_u0, b_p, brusselator_jac, brusselator_comp = makebrusselator!(PROBS, n)
@elapsed auto_sen_l2(bfun, b_u0, tspan, b_p, bt, (Rodas5()); diffalg=(FiniteDiff.finite_difference_gradient), tols...)
t = @elapsed auto_sen_l2(bfun, b_u0, tspan, b_p, bt, (Rodas5()); diffalg=(FiniteDiff.finite_difference_gradient), tols...)
@show n,t
t
end(n, t) = (2, 0.002410863)
(n, t) = (3, 0.021323631)
(n, t) = (4, 0.07305235)
(n, t) = (5, 0.216378298)
(n, t) = (6, 0.595115271)
(n, t) = (7, 1.338426427)
(n, t) = (8, 3.073240173)
(n, t) = (9, 6.67059502)
(n, t) = (10, 12.356934268)
(n, t) = (12, 44.055875029)
10-element Vector{Float64}:
0.002410863
0.021323631
0.07305235
0.216378298
0.595115271
1.338426427
3.073240173
6.67059502
12.356934268
44.055875029csa = map(csan) do n
bfun, b_u0, b_p, brusselator_jac, brusselator_comp = makebrusselator!(PROBS, n)
@time ts = map(ADJOINT_METHODS[1:2end÷3]) do alg
@info "Running $alg"
f = SciMLSensitivity.alg_autodiff(alg) ? bfun : ODEFunction(bfun, jac=brusselator_jac)
solver = Rodas5(autodiff=false)
@time diffeq_sen_l2(bfun, b_u0, tspan, b_p, bt, solver; sensalg=alg, tols...)
t = @elapsed diffeq_sen_l2(bfun, b_u0, tspan, b_p, bt, solver; sensalg=alg, tols...)
return t
end
@show n,ts
ts
end11.485924 seconds (23.12 M allocations: 1.468 GiB, 2.65% gc time, 99.91% c
ompilation time)
7.361928 seconds (9.50 M allocations: 612.516 MiB, 2.44% gc time, 99.92%
compilation time)
15.843818 seconds (17.59 M allocations: 1.154 GiB, 1.79% gc time, 99.97% c
ompilation time)
10.190482 seconds (16.93 M allocations: 1.061 GiB, 2.48% gc time, 99.94% c
ompilation time)
5.540694 seconds (6.32 M allocations: 409.568 MiB, 1.94% gc time, 99.92%
compilation time)
6.000752 seconds (9.68 M allocations: 635.581 MiB, 1.78% gc time, 99.93%
compilation time)
57.028598 seconds (83.70 M allocations: 5.340 GiB, 2.24% gc time, 99.89% c
ompilation time)
(n, ts) = (2, [0.00574782, 0.002653532, 0.001610379, 0.002345503, 0.0011835
12, 0.001086602])
0.077633 seconds (62.26 k allocations: 5.428 MiB)
10.215891 seconds (4.90 M allocations: 313.528 MiB, 1.17% gc time, 99.87%
compilation time)
0.003002 seconds (1.33 k allocations: 335.484 KiB)
0.015297 seconds (10.37 k allocations: 526.766 KiB)
5.087436 seconds (3.20 M allocations: 200.980 MiB, 99.88% compilation tim
e)
0.001595 seconds (2.00 k allocations: 324.484 KiB)
15.515276 seconds (8.28 M allocations: 529.283 MiB, 0.77% gc time, 98.51%
compilation time)
(n, ts) = (3, [0.077477232, 0.010391377, 0.00287147, 0.015230795, 0.0031954
78, 0.00143379])
0.749471 seconds (171.07 k allocations: 14.870 MiB, 18.78% gc time)
10.576737 seconds (4.80 M allocations: 306.695 MiB, 4.84% gc time, 99.59%
compilation time)
0.007085 seconds (1.34 k allocations: 644.125 KiB)
0.107159 seconds (25.35 k allocations: 1.129 MiB)
6.200717 seconds (3.21 M allocations: 201.309 MiB, 0.98% gc time, 99.80%
compilation time)
0.003002 seconds (2.01 k allocations: 476.203 KiB)
18.419813 seconds (8.44 M allocations: 544.822 MiB, 3.87% gc time, 90.78%
compilation time)
(n, ts) = (4, [0.606777145, 0.04025794, 0.006594484, 0.106412101, 0.0090626
77, 0.002733501])
2.152670 seconds (258.31 k allocations: 22.838 MiB)
10.396875 seconds (3.95 M allocations: 251.192 MiB, 0.77% gc time, 98.02%
compilation time)
0.012790 seconds (1.37 k allocations: 1.187 MiB)
0.396995 seconds (39.99 k allocations: 1.873 MiB)
5.699005 seconds (3.20 M allocations: 201.442 MiB, 1.05% gc time, 99.42%
compilation time)
0.004575 seconds (2.02 k allocations: 713.219 KiB)
21.466795 seconds (7.80 M allocations: 510.007 MiB, 0.65% gc time, 73.86%
compilation time)
(n, ts) = (5, [2.15065258, 0.204010212, 0.012562743, 0.397636547, 0.0297650
33, 0.004376809])
9.270526 seconds (550.87 k allocations: 48.491 MiB, 0.33% gc time)
12.552918 seconds (3.89 M allocations: 248.157 MiB, 0.53% gc time, 96.87%
compilation time)
0.023914 seconds (1.38 k allocations: 2.126 MiB)
1.275194 seconds (63.10 k allocations: 3.091 MiB)
6.639549 seconds (3.21 M allocations: 202.175 MiB, 0.70% gc time, 98.75%
compilation time)
0.007726 seconds (2.02 k allocations: 1005.625 KiB)
40.907454 seconds (8.39 M allocations: 566.465 MiB, 0.53% gc time, 45.75%
compilation time)
(n, ts) = (6, [9.284921131, 0.38863154, 0.099835936, 1.269570858, 0.0825042
66, 0.007336899])
20.124514 seconds (645.69 k allocations: 58.354 MiB, 0.25% gc time)
11.167647 seconds (2.79 M allocations: 177.335 MiB, 0.42% gc time, 91.65%
compilation time)
0.048843 seconds (1.38 k allocations: 3.629 MiB)
3.792469 seconds (101.24 k allocations: 4.883 MiB)
1.352034 seconds (491.21 k allocations: 33.446 MiB, 89.14% compilation ti
me)
0.012571 seconds (2.02 k allocations: 1.348 MiB)
61.604998 seconds (4.86 M allocations: 357.518 MiB, 0.23% gc time, 18.57%
compilation time)
(n, ts) = (7, [20.135846071, 0.973571613, 0.048526323, 3.785443886, 0.14602
9285, 0.012207415])
47.442937 seconds (900.95 k allocations: 82.711 MiB, 0.15% gc time)
2.234558 seconds (87.09 k allocations: 11.261 MiB)
0.085793 seconds (1.38 k allocations: 5.840 MiB)
7.873646 seconds (124.44 k allocations: 6.799 MiB)
0.406437 seconds (15.28 k allocations: 4.193 MiB)
0.019976 seconds (2.02 k allocations: 1.853 MiB)
116.172770 seconds (2.26 M allocations: 225.530 MiB, 0.13% gc time)
(n, ts) = (8, [47.422160116, 2.237167129, 0.159052304, 7.857108393, 0.40682
329, 0.019724213])
111.777519 seconds (1.32 M allocations: 122.362 MiB, 0.03% gc time)
5.296111 seconds (129.01 k allocations: 17.277 MiB)
0.163487 seconds (1.38 k allocations: 9.038 MiB)
18.470475 seconds (181.83 k allocations: 10.563 MiB)
0.802975 seconds (18.54 k allocations: 6.093 MiB)
0.031869 seconds (2.02 k allocations: 2.484 MiB)
273.069550 seconds (3.32 M allocations: 335.848 MiB, 0.02% gc time)
(n, ts) = (9, [111.715681861, 5.306513574, 0.162672147, 18.497250955, 0.806
047714, 0.031245442])
185.193861 seconds (1.43 M allocations: 137.566 MiB, 0.02% gc time)
8.894672 seconds (138.58 k allocations: 23.825 MiB, 0.42% gc time)
0.339395 seconds (1.39 k allocations: 13.525 MiB)
36.685963 seconds (234.78 k allocations: 14.327 MiB)
1.472124 seconds (22.19 k allocations: 8.639 MiB)
0.047012 seconds (2.02 k allocations: 3.280 MiB)
465.395810 seconds (3.67 M allocations: 402.537 MiB, 0.02% gc time)
(n, ts) = (10, [185.551388911, 8.852969261, 0.3697326, 36.460622379, 1.4722
80712, 0.046464586])
742.318148 seconds (2.81 M allocations: 271.145 MiB, 0.01% gc time)
28.147586 seconds (204.72 k allocations: 45.189 MiB, 0.12% gc time)
0.660222 seconds (1.39 k allocations: 27.085 MiB)
101.110014 seconds (315.80 k allocations: 23.681 MiB)
4.460541 seconds (30.64 k allocations: 16.156 MiB)
0.106267 seconds (2.02 k allocations: 5.388 MiB)
1753.644824 seconds (6.73 M allocations: 777.501 MiB, 0.01% gc time)
(n, ts) = (12, [742.444633045, 28.099931445, 0.671871089, 101.09180542, 4.4
18762558, 0.105724637])
3271.076194 seconds (5.14 M allocations: 516.645 MiB, 0.00% gc time)
111.907911 seconds (328.37 k allocations: 102.016 MiB, 0.03% gc time)
1.445180 seconds (1.40 k allocations: 64.528 MiB, 1.56% gc time)
453.846594 seconds (586.28 k allocations: 50.502 MiB)
16.798161 seconds (46.19 k allocations: 36.239 MiB)
0.298806 seconds (2.02 k allocations: 10.569 MiB)
7721.814233 seconds (12.20 M allocations: 1.525 GiB, 0.01% gc time)
(n, ts) = (15, [3280.945699767, 111.68386331, 1.440597037, 455.258098403, 1
6.803721564, 0.297667147])
7859.525245 seconds (7.45 M allocations: 766.079 MiB, 0.00% gc time)
219.411070 seconds (392.62 k allocations: 161.462 MiB, 0.02% gc time)
2.693095 seconds (1.41 k allocations: 105.404 MiB)
1113.745588 seconds (872.20 k allocations: 80.006 MiB)
35.337037 seconds (58.48 k allocations: 57.750 MiB)
0.804299 seconds (2.03 k allocations: 15.774 MiB)
18425.563637 seconds (17.55 M allocations: 2.318 GiB, 0.01% gc time)
(n, ts) = (17, [7818.776738086, 219.183847673, 2.940070303, 1116.980391667,
35.291632917, 0.862468663])
12-element Vector{Vector{Float64}}:
[0.00574782, 0.002653532, 0.001610379, 0.002345503, 0.001183512, 0.0010866
02]
[0.077477232, 0.010391377, 0.00287147, 0.015230795, 0.003195478, 0.0014337
9]
[0.606777145, 0.04025794, 0.006594484, 0.106412101, 0.009062677, 0.0027335
01]
[2.15065258, 0.204010212, 0.012562743, 0.397636547, 0.029765033, 0.0043768
09]
[9.284921131, 0.38863154, 0.099835936, 1.269570858, 0.082504266, 0.0073368
99]
[20.135846071, 0.973571613, 0.048526323, 3.785443886, 0.146029285, 0.01220
7415]
[47.422160116, 2.237167129, 0.159052304, 7.857108393, 0.40682329, 0.019724
213]
[111.715681861, 5.306513574, 0.162672147, 18.497250955, 0.806047714, 0.031
245442]
[185.551388911, 8.852969261, 0.3697326, 36.460622379, 1.472280712, 0.04646
4586]
[742.444633045, 28.099931445, 0.671871089, 101.09180542, 4.418762558, 0.10
5724637]
[3280.945699767, 111.68386331, 1.440597037, 455.258098403, 16.803721564, 0
.297667147]
[7818.776738086, 219.183847673, 2.940070303, 1116.980391667, 35.291632917,
0.862468663]n_to_param(n) = 4n^2
lw = 2
ms = 0.5
plt1 = plot(title="Sensitivity Scaling on Brusselator");
plot!(plt1, n_to_param.(forwarddiffn), forwarddiff, lab="Forward-Mode DSAAD", lw=lw, marksize=ms, linestyle=:auto, marker=:auto);
#plot!(plt1, n_to_param.(reversediffn), reversediff, lab="Reverse-Mode DSAAD", lw=lw, marksize=ms, linestyle=:auto, marker=:auto);
csadata = [[csa[j][i] for j in eachindex(csa)] for i in eachindex(csa[1])]
plot!(plt1, n_to_param.(csan), csadata[1], lab="Interpolating CASA user-Jacobian", lw=lw, marksize=ms, linestyle=:auto, marker=:auto);
plot!(plt1, n_to_param.(csan), csadata[2], lab="Interpolating CASA AD-Jacobian", lw=lw, marksize=ms, linestyle=:auto, marker=:auto);
plot!(plt1, n_to_param.(csan), csadata[3], lab=raw"Interpolating CASA AD-$v^{T}J$ seeding", lw=lw, marksize=ms, linestyle=:auto, marker=:auto);
plot!(plt1, n_to_param.(csan), csadata[1+3], lab="Quadrature CASA user-Jacobian", lw=lw, marksize=ms, linestyle=:auto, marker=:auto);
plot!(plt1, n_to_param.(csan), csadata[2+3], lab="Quadrature CASA AD-Jacobian", lw=lw, marksize=ms, linestyle=:auto, marker=:auto);
plot!(plt1, n_to_param.(csan), csadata[3+3], lab=raw"Quadrature CASA AD-$v^{T}J$ seeding", lw=lw, marksize=ms, linestyle=:auto, marker=:auto);
plot!(plt1, n_to_param.(numdiffn), numdiff, lab="Numerical Differentiation", lw=lw, marksize=ms, linestyle=:auto, marker=:auto);
xaxis!(plt1, "Number of Parameters", :log10);
yaxis!(plt1, "Runtime (s)", :log10);
plot!(plt1, legend=:outertopleft, size=(1200, 600))
VJP Choice Benchmarks
bt = 0:0.1:1
tspan = (0.0, 1.0)
csan = vcat(2:10,12,15,17)
tols = (abstol=1e-5, reltol=1e-7)
_adjoint_methods = ntuple(2) do ii
Alg = (InterpolatingAdjoint, QuadratureAdjoint)[ii]
(
advj1 = Alg(autodiff=true,autojacvec=EnzymeVJP()), # AD vJ
advj2 = Alg(autodiff=true,autojacvec=ReverseDiffVJP(false)), # AD vJ
advj3 = Alg(autodiff=true,autojacvec=ReverseDiffVJP(true)), # AD vJ
)
end |> NamedTuple{(:interp, :quad)}
adjoint_methods = mapreduce(collect, vcat, _adjoint_methods)
csavjp = map(csan) do n
bfun, b_u0, b_p, brusselator_jac, brusselator_comp = makebrusselator!(PROBS, n)
@time ts = map(adjoint_methods) do alg
@info "Running $alg"
f = SciMLSensitivity.alg_autodiff(alg) ? bfun : ODEFunction(bfun, jac=brusselator_jac)
solver = Rodas5(autodiff=false)
@time diffeq_sen_l2(bfun, b_u0, tspan, b_p, bt, solver; sensalg=alg, tols...)
t = @elapsed diffeq_sen_l2(bfun, b_u0, tspan, b_p, bt, solver; sensalg=alg, tols...)
return t
end
@show n,ts
ts
end0.001674 seconds (1.27 k allocations: 190.828 KiB)
5.627629 seconds (9.27 M allocations: 585.102 MiB, 3.14% gc time, 99.10%
compilation time)
4.743868 seconds (6.92 M allocations: 449.769 MiB, 1.45% gc time, 99.78%
compilation time)
0.001107 seconds (2.02 k allocations: 216.688 KiB)
4.725973 seconds (7.07 M allocations: 450.189 MiB, 2.10% gc time, 99.33%
compilation time)
4.937058 seconds (6.72 M allocations: 434.261 MiB, 2.80% gc time, 99.86%
compilation time)
20.490427 seconds (31.24 M allocations: 1.935 GiB, 2.36% gc time, 99.04% c
ompilation time)
(n, ts) = (2, [0.001380201, 0.047034978, 0.00576743, 0.000852244, 0.0291420
7, 0.003891103])
0.003143 seconds (1.33 k allocations: 335.484 KiB)
0.147500 seconds (2.09 M allocations: 95.600 MiB)
0.016374 seconds (5.41 k allocations: 549.000 KiB)
0.001664 seconds (2.00 k allocations: 324.484 KiB)
0.084741 seconds (1.10 M allocations: 50.154 MiB)
0.010036 seconds (7.24 k allocations: 600.453 KiB)
0.569108 seconds (6.41 M allocations: 295.261 MiB, 6.46% gc time)
(n, ts) = (3, [0.00290209, 0.185125713, 0.01606502, 0.00144243, 0.086602187
, 0.009833563])
0.006557 seconds (1.34 k allocations: 644.125 KiB)
0.485419 seconds (6.23 M allocations: 268.498 MiB, 9.08% gc time)
0.045718 seconds (8.54 k allocations: 1017.906 KiB)
0.002831 seconds (2.01 k allocations: 476.203 KiB)
0.236269 seconds (2.94 M allocations: 126.581 MiB, 6.53% gc time)
0.024090 seconds (11.63 k allocations: 957.094 KiB)
1.574224 seconds (18.39 M allocations: 796.423 MiB, 5.75% gc time)
(n, ts) = (4, [0.006263807, 0.453176076, 0.045560519, 0.002588972, 0.238510
376, 0.024099925])
0.012760 seconds (1.37 k allocations: 1.187 MiB)
1.053909 seconds (14.51 M allocations: 666.822 MiB, 4.06% gc time)
0.108306 seconds (12.50 k allocations: 1.762 MiB)
0.004577 seconds (2.02 k allocations: 713.219 KiB)
0.511037 seconds (6.63 M allocations: 304.667 MiB, 5.57% gc time)
0.050829 seconds (17.30 k allocations: 1.453 MiB)
3.490396 seconds (42.35 M allocations: 1.908 GiB, 4.08% gc time)
(n, ts) = (5, [0.012620284, 1.073973985, 0.111278388, 0.00437521, 0.4932506
72, 0.050328516])
0.023628 seconds (1.38 k allocations: 2.126 MiB)
2.155795 seconds (29.30 M allocations: 1.260 GiB, 4.83% gc time)
0.218484 seconds (17.32 k allocations: 2.941 MiB)
0.007535 seconds (2.02 k allocations: 1005.625 KiB)
0.974699 seconds (12.88 M allocations: 567.154 MiB, 4.64% gc time)
0.096779 seconds (24.17 k allocations: 2.051 MiB)
6.971019 seconds (84.44 M allocations: 3.643 GiB, 4.32% gc time)
(n, ts) = (6, [0.023554749, 2.166941769, 0.214909488, 0.007555998, 0.980109
647, 0.09775679])
0.048713 seconds (1.38 k allocations: 3.629 MiB)
4.116842 seconds (55.53 M allocations: 2.326 GiB, 4.61% gc time)
0.421294 seconds (23.32 k allocations: 4.747 MiB)
0.012361 seconds (2.02 k allocations: 1.348 MiB)
1.724237 seconds (22.90 M allocations: 981.691 MiB, 4.58% gc time)
0.172259 seconds (32.28 k allocations: 2.785 MiB)
13.064482 seconds (156.98 M allocations: 6.593 GiB, 4.41% gc time)
(n, ts) = (7, [0.063678084, 4.168345153, 0.422831064, 0.011953048, 1.726615
745, 0.171250857])
0.084330 seconds (1.38 k allocations: 5.840 MiB)
6.966717 seconds (93.69 M allocations: 4.182 GiB, 5.09% gc time)
0.735917 seconds (29.97 k allocations: 7.322 MiB)
0.020017 seconds (2.02 k allocations: 1.853 MiB)
2.951111 seconds (39.29 M allocations: 1.753 GiB, 4.74% gc time)
0.291788 seconds (41.80 k allocations: 3.789 MiB)
22.100934 seconds (266.11 M allocations: 11.907 GiB, 4.41% gc time)
(n, ts) = (8, [0.08767775, 6.967770223, 0.73303425, 0.019527596, 2.94286716
7, 0.294625593])
0.162136 seconds (1.38 k allocations: 9.038 MiB)
13.608983 seconds (181.84 M allocations: 7.891 GiB, 4.90% gc time)
1.399365 seconds (40.48 k allocations: 11.079 MiB)
0.031553 seconds (2.02 k allocations: 2.484 MiB)
4.681993 seconds (61.70 M allocations: 2.677 GiB, 4.87% gc time)
0.457698 seconds (52.44 k allocations: 4.905 MiB)
40.758462 seconds (487.28 M allocations: 21.190 GiB, 4.40% gc time)
(n, ts) = (9, [0.162991154, 13.6734323, 1.409581638, 0.031286955, 4.6745888
41, 0.459775642])
0.295712 seconds (1.39 k allocations: 13.525 MiB)
18.057280 seconds (233.92 M allocations: 9.952 GiB, 6.76% gc time)
1.906566 seconds (46.53 k allocations: 15.842 MiB)
0.047371 seconds (2.02 k allocations: 3.280 MiB)
7.203526 seconds (92.71 M allocations: 3.942 GiB, 6.73% gc time)
0.704683 seconds (64.33 k allocations: 6.243 MiB)
56.637095 seconds (653.49 M allocations: 27.864 GiB, 6.15% gc time)
(n, ts) = (10, [0.304005488, 18.194288198, 1.996499481, 0.046063255, 7.1690
73109, 0.705133973])
0.631983 seconds (1.39 k allocations: 27.085 MiB)
38.895426 seconds (498.79 M allocations: 22.283 GiB, 7.34% gc time)
4.026101 seconds (67.17 k allocations: 30.513 MiB)
0.110545 seconds (2.02 k allocations: 5.388 MiB)
15.241586 seconds (188.66 M allocations: 8.423 GiB, 9.54% gc time)
1.412087 seconds (91.88 k allocations: 9.739 MiB)
120.363438 seconds (1.38 G allocations: 61.554 GiB, 6.82% gc time)
(n, ts) = (12, [0.651621359, 39.216584284, 4.020643019, 0.108589037, 14.624
936001, 1.413266997])
1.521636 seconds (1.40 k allocations: 64.528 MiB)
109.695003 seconds (1.25 G allocations: 53.273 GiB, 16.43% gc time)
10.417667 seconds (105.39 k allocations: 69.894 MiB)
0.303129 seconds (2.02 k allocations: 10.569 MiB)
40.133131 seconds (453.40 M allocations: 19.275 GiB, 16.66% gc time)
3.478531 seconds (142.59 k allocations: 17.231 MiB)
320.744496 seconds (3.41 G allocations: 145.412 GiB, 12.66% gc time)
(n, ts) = (15, [1.833535673, 104.759119693, 10.41737647, 0.300402495, 34.35
544778, 3.512935485])
2.947193 seconds (1.41 k allocations: 105.404 MiB)
136.989007 seconds (1.92 G allocations: 80.231 GiB, 4.86% gc time)
16.017779 seconds (131.41 k allocations: 112.046 MiB, 0.09% gc time)
0.692477 seconds (2.03 k allocations: 15.774 MiB)
53.181394 seconds (743.36 M allocations: 30.973 GiB, 4.94% gc time)
6.211243 seconds (182.65 k allocations: 24.263 MiB)
434.722626 seconds (5.34 G allocations: 222.910 GiB, 4.51% gc time)
(n, ts) = (17, [2.881048936, 137.684989378, 16.980809029, 0.817746656, 53.8
31269179, 6.474921106])
12-element Vector{Vector{Float64}}:
[0.001380201, 0.047034978, 0.00576743, 0.000852244, 0.02914207, 0.00389110
3]
[0.00290209, 0.185125713, 0.01606502, 0.00144243, 0.086602187, 0.009833563
]
[0.006263807, 0.453176076, 0.045560519, 0.002588972, 0.238510376, 0.024099
925]
[0.012620284, 1.073973985, 0.111278388, 0.00437521, 0.493250672, 0.0503285
16]
[0.023554749, 2.166941769, 0.214909488, 0.007555998, 0.980109647, 0.097756
79]
[0.063678084, 4.168345153, 0.422831064, 0.011953048, 1.726615745, 0.171250
857]
[0.08767775, 6.967770223, 0.73303425, 0.019527596, 2.942867167, 0.29462559
3]
[0.162991154, 13.6734323, 1.409581638, 0.031286955, 4.674588841, 0.4597756
42]
[0.304005488, 18.194288198, 1.996499481, 0.046063255, 7.169073109, 0.70513
3973]
[0.651621359, 39.216584284, 4.020643019, 0.108589037, 14.624936001, 1.4132
66997]
[1.833535673, 104.759119693, 10.41737647, 0.300402495, 34.35544778, 3.5129
35485]
[2.881048936, 137.684989378, 16.980809029, 0.817746656, 53.831269179, 6.47
4921106]plt2 = plot(title="Brusselator quadrature adjoint scaling");
csacompare = [[csavjp[j][i] for j in eachindex(csavjp)] for i in eachindex(csavjp[1])]
plot!(plt2, n_to_param.(csan), csadata[2+3], lab="AD-Jacobian", lw=lw, marksize=ms, linestyle=:auto, marker=:auto);
plot!(plt2, n_to_param.(csan), csacompare[1+3], lab=raw"EnzymeVJP", lw=lw, marksize=ms, linestyle=:auto, marker=:auto);
plot!(plt2, n_to_param.(csan), csacompare[2+3], lab=raw"ReverseDiffVJP", lw=lw, marksize=ms, linestyle=:auto, marker=:auto);
plot!(plt2, n_to_param.(csan), csacompare[3+3], lab=raw"Compiled ReverseDiffVJP", lw=lw, marksize=ms, linestyle=:auto, marker=:auto);
xaxis!(plt2, "Number of Parameters", :log10);
yaxis!(plt2, "Runtime (s)", :log10);
plot!(plt2, legend=:outertopleft, size=(1200, 600))
Appendix
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/AutomaticDifferentiation","BrussScaling.jmd")Computer Information:
Julia Version 1.10.4
Commit 48d4fd48430 (2024-06-04 10:41 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/AutomaticDifferentiation/Project.toml`
[6e4b80f9] BenchmarkTools v1.5.0
[a93c6f00] DataFrames v1.6.1
[1313f7d8] DataFramesMeta v0.15.3
[a0c0ee7d] DifferentiationInterface v0.5.9
[a82114a7] DifferentiationInterfaceTest v0.5.0
[7da242da] Enzyme v0.12.25
[6a86dc24] FiniteDiff v2.23.1
[f6369f11] ForwardDiff v0.10.36
[1dea7af3] OrdinaryDiffEq v6.86.0
[65888b18] ParameterizedFunctions v5.17.0
[91a5bcdd] Plots v1.40.5
[08abe8d2] PrettyTables v2.3.2
[37e2e3b7] ReverseDiff v1.15.3
[31c91b34] SciMLBenchmarks v0.1.3
[1ed8b502] SciMLSensitivity v7.64.0
[90137ffa] StaticArrays v1.9.7
[07d77754] Tapir v0.2.26
[9f7883ad] Tracker v0.2.34
[e88e6eb3] Zygote v0.6.70
[37e2e46d] LinearAlgebra
[d6f4376e] Markdown
[de0858da] Printf
[8dfed614] TestAnd the full manifest:
Status `/cache/build/exclusive-amdci3-0/julialang/scimlbenchmarks-dot-jl/benchmarks/AutomaticDifferentiation/Manifest.toml`
[47edcb42] ADTypes v1.6.1
[621f4979] AbstractFFTs v1.5.0
[1520ce14] AbstractTrees v0.4.5
[7d9f7c33] Accessors v0.1.37
[79e6a3ab] Adapt v4.0.4
[66dad0bd] AliasTables v1.1.3
[ec485272] ArnoldiMethod v0.4.0
[4fba245c] ArrayInterface v7.12.0
[4c555306] ArrayLayouts v1.10.2
[a9b6321e] Atomix v0.1.0
[6e4b80f9] BenchmarkTools v1.5.0
[e2ed5e7c] Bijections v0.1.7
[d1d4a3ce] BitFlags v0.1.9
[62783981] BitTwiddlingConvenienceFunctions v0.1.6
[fa961155] CEnum v0.5.0
[2a0fbf3d] CPUSummary v0.2.6
[00ebfdb7] CSTParser v3.4.3
[49dc2e85] Calculus v0.5.1
[7057c7e9] Cassette v0.3.13
[8be319e6] Chain v0.6.0
[082447d4] ChainRules v1.69.0
[d360d2e6] ChainRulesCore v1.24.0
[0ca39b1e] Chairmarks v1.2.1
[fb6a15b2] CloseOpenIntervals v0.1.13
[da1fd8a2] CodeTracking v1.3.5
[944b1d66] CodecZlib v0.7.5
[35d6a980] ColorSchemes v3.26.0
[3da002f7] ColorTypes v0.11.5
[c3611d14] ColorVectorSpace v0.10.0
[5ae59095] Colors v0.12.11
[861a8166] Combinatorics v1.0.2
[a80b9123] CommonMark v0.8.12
[38540f10] CommonSolve v0.2.4
[bbf7d656] CommonSubexpressions v0.3.0
[f70d9fcc] CommonWorldInvalidations v1.0.0
[34da2185] Compat v4.15.0
[b0b7db55] ComponentArrays v0.15.14
[b152e2b5] CompositeTypes v0.1.4
[a33af91c] CompositionsBase v0.1.2
[2569d6c7] ConcreteStructs v0.2.3
[f0e56b4a] ConcurrentUtilities v2.4.2
[8f4d0f93] Conda v1.10.2
[187b0558] ConstructionBase v1.5.6
[d38c429a] Contour v0.6.3
[adafc99b] CpuId v0.3.1
[a8cc5b0e] Crayons v4.1.1
[9a962f9c] DataAPI v1.16.0
[a93c6f00] DataFrames v1.6.1
[1313f7d8] DataFramesMeta v0.15.3
[864edb3b] DataStructures v0.18.20
[e2d170a0] DataValueInterfaces v1.0.0
[8bb1440f] DelimitedFiles v1.9.1
[2b5f629d] DiffEqBase v6.151.5
[459566f4] DiffEqCallbacks v3.6.2
[77a26b50] DiffEqNoiseProcess v5.22.0
[163ba53b] DiffResults v1.1.0
[b552c78f] DiffRules v1.15.1
[de460e47] DiffTests v0.1.2
[a0c0ee7d] DifferentiationInterface v0.5.9
[a82114a7] DifferentiationInterfaceTest v0.5.0
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[31c24e10] Distributions v0.25.109
[ffbed154] DocStringExtensions v0.9.3
[5b8099bc] DomainSets v0.7.14
[fa6b7ba4] DualNumbers v0.6.8
⌅ [7c1d4256] DynamicPolynomials v0.5.7
⌅ [06fc5a27] DynamicQuantities v0.13.2
[da5c29d0] EllipsisNotation v1.8.0
[4e289a0a] EnumX v1.0.4
[7da242da] Enzyme v0.12.25
[f151be2c] EnzymeCore v0.7.7
[460bff9d] ExceptionUnwrapping v0.1.10
[d4d017d3] ExponentialUtilities v1.26.1
[e2ba6199] ExprTools v0.1.10
[c87230d0] FFMPEG v0.4.1
⌃ [7034ab61] FastBroadcast v0.3.4
[9aa1b823] FastClosures v0.3.2
[29a986be] FastLapackInterface v2.0.4
[1a297f60] FillArrays v1.11.0
[64ca27bc] FindFirstFunctions v1.2.0
[6a86dc24] FiniteDiff v2.23.1
[53c48c17] FixedPointNumbers v0.8.5
[1fa38f19] Format v1.3.7
[f6369f11] ForwardDiff v0.10.36
[f62d2435] FunctionProperties v0.1.2
[069b7b12] FunctionWrappers v1.1.3
[77dc65aa] FunctionWrappersWrappers v0.1.3
[d9f16b24] Functors v0.4.11
[0c68f7d7] GPUArrays v10.3.0
[46192b85] GPUArraysCore v0.1.6
[61eb1bfa] GPUCompiler v0.26.7
[28b8d3ca] GR v0.73.7
[c145ed77] GenericSchur v0.5.4
[d7ba0133] Git v1.3.1
[c27321d9] Glob v1.3.1
[86223c79] Graphs v1.11.2
[42e2da0e] Grisu v1.0.2
[cd3eb016] HTTP v1.10.8
[eafb193a] Highlights v0.5.3
[3e5b6fbb] HostCPUFeatures v0.1.17
[34004b35] HypergeometricFunctions v0.3.23
[7073ff75] IJulia v1.25.0
[7869d1d1] IRTools v0.4.14
[615f187c] IfElse v0.1.1
[d25df0c9] Inflate v0.1.5
[842dd82b] InlineStrings v1.4.2
[8197267c] IntervalSets v0.7.10
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[41ab1584] InvertedIndices v1.3.0
[92d709cd] IrrationalConstants v0.2.2
[82899510] IteratorInterfaceExtensions v1.0.0
[c3a54625] JET v0.9.6
[27aeb0d3] JLArrays v0.1.5
[1019f520] JLFzf v0.1.7
[692b3bcd] JLLWrappers v1.5.0
[682c06a0] JSON v0.21.4
[98e50ef6] JuliaFormatter v1.0.58
⌃ [aa1ae85d] JuliaInterpreter v0.9.32
[ccbc3e58] JumpProcesses v9.11.1
[ef3ab10e] KLU v0.6.0
[63c18a36] KernelAbstractions v0.9.22
[ba0b0d4f] Krylov v0.9.6
[929cbde3] LLVM v8.0.0
[b964fa9f] LaTeXStrings v1.3.1
[2ee39098] LabelledArrays v1.16.0
[984bce1d] LambertW v0.4.6
[23fbe1c1] Latexify v0.16.4
[10f19ff3] LayoutPointers v0.1.17
[5078a376] LazyArrays v2.1.9
[2d8b4e74] LevyArea v1.0.0
[d3d80556] LineSearches v7.2.0
[7ed4a6bd] LinearSolve v2.30.2
[2ab3a3ac] LogExpFunctions v0.3.28
[e6f89c97] LoggingExtras v1.0.3
[bdcacae8] LoopVectorization v0.12.171
⌅ [6f1432cf] LoweredCodeUtils v2.4.8
[d8e11817] MLStyle v0.4.17
[1914dd2f] MacroTools v0.5.13
[d125e4d3] ManualMemory v0.1.8
[bb5d69b7] MaybeInplace v0.1.3
[739be429] MbedTLS v1.1.9
[442fdcdd] Measures v0.3.2
[e1d29d7a] Missings v1.2.0
[dbe65cb8] MistyClosures v1.0.1
[961ee093] ModelingToolkit v9.26.0
[46d2c3a1] MuladdMacro v0.2.4
[102ac46a] MultivariatePolynomials v0.5.6
[ffc61752] Mustache v1.0.19
[d8a4904e] MutableArithmetics v1.4.5
[d41bc354] NLSolversBase v7.8.3
[2774e3e8] NLsolve v4.5.1
[872c559c] NNlib v0.9.21
[77ba4419] NaNMath v1.0.2
[8913a72c] NonlinearSolve v3.13.1
[d8793406] ObjectFile v0.4.1
[6fe1bfb0] OffsetArrays v1.14.1
[4d8831e6] OpenSSL v1.4.3
[429524aa] Optim v1.9.4
[3bd65402] Optimisers v0.3.3
[bac558e1] OrderedCollections v1.6.3
[1dea7af3] OrdinaryDiffEq v6.86.0
[90014a1f] PDMats v0.11.31
[65ce6f38] PackageExtensionCompat v1.0.2
[65888b18] ParameterizedFunctions v5.17.0
[d96e819e] Parameters v0.12.3
[69de0a69] Parsers v2.8.1
[b98c9c47] Pipe v1.3.0
[ccf2f8ad] PlotThemes v3.2.0
[995b91a9] PlotUtils v1.4.1
[91a5bcdd] Plots v1.40.5
[e409e4f3] PoissonRandom v0.4.4
[f517fe37] Polyester v0.7.15
[1d0040c9] PolyesterWeave v0.2.2
[2dfb63ee] PooledArrays v1.4.3
[85a6dd25] PositiveFactorizations v0.2.4
[d236fae5] PreallocationTools v0.4.22
[aea7be01] PrecompileTools v1.2.1
[21216c6a] Preferences v1.4.3
[08abe8d2] PrettyTables v2.3.2
[92933f4c] ProgressMeter v1.10.2
[43287f4e] PtrArrays v1.2.0
[1fd47b50] QuadGK v2.9.4
[74087812] Random123 v1.7.0
[e6cf234a] RandomNumbers v1.5.3
[c1ae055f] RealDot v0.1.0
[3cdcf5f2] RecipesBase v1.3.4
[01d81517] RecipesPipeline v0.6.12
[731186ca] RecursiveArrayTools v3.26.0
[f2c3362d] RecursiveFactorization v0.2.23
[189a3867] Reexport v1.2.2
[05181044] RelocatableFolders v1.0.1
[ae029012] Requires v1.3.0
[ae5879a3] ResettableStacks v1.1.1
[37e2e3b7] ReverseDiff v1.15.3
[79098fc4] Rmath v0.7.1
[7e49a35a] RuntimeGeneratedFunctions v0.5.13
[94e857df] SIMDTypes v0.1.0
[476501e8] SLEEFPirates v0.6.43
⌃ [0bca4576] SciMLBase v2.44.0
[31c91b34] SciMLBenchmarks v0.1.3
[c0aeaf25] SciMLOperators v0.3.8
[1ed8b502] SciMLSensitivity v7.64.0
[53ae85a6] SciMLStructures v1.4.1
[6c6a2e73] Scratch v1.2.1
[91c51154] SentinelArrays v1.4.5
[efcf1570] Setfield v1.1.1
[992d4aef] Showoff v1.0.3
[777ac1f9] SimpleBufferStream v1.1.0
[727e6d20] SimpleNonlinearSolve v1.11.0
[699a6c99] SimpleTraits v0.9.4
[ce78b400] SimpleUnPack v1.1.0
[b85f4697] SoftGlobalScope v1.1.0
[a2af1166] SortingAlgorithms v1.2.1
[47a9eef4] SparseDiffTools v2.19.0
[dc90abb0] SparseInverseSubset v0.1.2
[0a514795] SparseMatrixColorings v0.3.5
[e56a9233] Sparspak v0.3.9
[276daf66] SpecialFunctions v2.4.0
[aedffcd0] Static v1.1.1
[0d7ed370] StaticArrayInterface v1.5.1
[90137ffa] StaticArrays v1.9.7
[1e83bf80] StaticArraysCore v1.4.3
[82ae8749] StatsAPI v1.7.0
[2913bbd2] StatsBase v0.34.3
[4c63d2b9] StatsFuns v1.3.1
[789caeaf] StochasticDiffEq v6.66.0
[7792a7ef] StrideArraysCore v0.5.7
[69024149] StringEncodings v0.3.7
[892a3eda] StringManipulation v0.3.4
[09ab397b] StructArrays v0.6.18
[53d494c1] StructIO v0.3.0
[2efcf032] SymbolicIndexingInterface v0.3.26
[19f23fe9] SymbolicLimits v0.2.1
[d1185830] SymbolicUtils v2.1.2
[0c5d862f] Symbolics v5.34.0
[9ce81f87] TableMetadataTools v0.1.0
[3783bdb8] TableTraits v1.0.1
[bd369af6] Tables v1.12.0
[07d77754] Tapir v0.2.26
[62fd8b95] TensorCore v0.1.1
⌅ [8ea1fca8] TermInterface v0.4.1
[8290d209] ThreadingUtilities v0.5.2
[a759f4b9] TimerOutputs v0.5.24
[0796e94c] Tokenize v0.5.29
[9f7883ad] Tracker v0.2.34
[3bb67fe8] TranscodingStreams v0.11.1
[d5829a12] TriangularSolve v0.2.1
[410a4b4d] Tricks v0.1.8
[781d530d] TruncatedStacktraces v1.4.0
[5c2747f8] URIs v1.5.1
[3a884ed6] UnPack v1.0.2
[1cfade01] UnicodeFun v0.4.1
[1986cc42] Unitful v1.21.0
[45397f5d] UnitfulLatexify v1.6.4
[a7c27f48] Unityper v0.1.6
[013be700] UnsafeAtomics v0.2.1
[d80eeb9a] UnsafeAtomicsLLVM v0.1.5
[41fe7b60] Unzip v0.2.0
[3d5dd08c] VectorizationBase v0.21.70
[81def892] VersionParsing v1.3.0
[19fa3120] VertexSafeGraphs v0.2.0
[44d3d7a6] Weave v0.10.12
[ddb6d928] YAML v0.4.11
[c2297ded] ZMQ v1.2.6
[e88e6eb3] Zygote v0.6.70
[700de1a5] ZygoteRules v0.2.5
[6e34b625] Bzip2_jll v1.0.8+1
[83423d85] Cairo_jll v1.18.0+2
⌅ [7cc45869] Enzyme_jll v0.0.137+0
[2702e6a9] EpollShim_jll v0.0.20230411+0
[2e619515] Expat_jll v2.6.2+0
⌅ [b22a6f82] FFMPEG_jll v4.4.4+1
[a3f928ae] Fontconfig_jll v2.13.96+0
[d7e528f0] FreeType2_jll v2.13.2+0
[559328eb] FriBidi_jll v1.0.14+0
[0656b61e] GLFW_jll v3.4.0+0
[d2c73de3] GR_jll v0.73.7+0
[78b55507] Gettext_jll v0.21.0+0
[f8c6e375] Git_jll v2.44.0+2
[7746bdde] Glib_jll v2.80.2+0
[3b182d85] Graphite2_jll v1.3.14+0
[2e76f6c2] HarfBuzz_jll v2.8.1+1
[1d5cc7b8] IntelOpenMP_jll v2024.2.0+0
[aacddb02] JpegTurbo_jll v3.0.3+0
[c1c5ebd0] LAME_jll v3.100.2+0
⌅ [88015f11] LERC_jll v3.0.0+1
[dad2f222] LLVMExtra_jll v0.0.30+0
[1d63c593] LLVMOpenMP_jll v15.0.7+0
[dd4b983a] LZO_jll v2.10.2+0
⌅ [e9f186c6] Libffi_jll v3.2.2+1
[d4300ac3] Libgcrypt_jll v1.8.11+0
[7e76a0d4] Libglvnd_jll v1.6.0+0
[7add5ba3] Libgpg_error_jll v1.49.0+0
[94ce4f54] Libiconv_jll v1.17.0+0
[4b2f31a3] Libmount_jll v2.40.1+0
⌅ [89763e89] Libtiff_jll v4.5.1+1
[38a345b3] Libuuid_jll v2.40.1+0
[856f044c] MKL_jll v2024.2.0+0
[e7412a2a] Ogg_jll v1.3.5+1
[458c3c95] OpenSSL_jll v3.0.14+0
[efe28fd5] OpenSpecFun_jll v0.5.5+0
[91d4177d] Opus_jll v1.3.2+0
[30392449] Pixman_jll v0.43.4+0
[c0090381] Qt6Base_jll v6.7.1+1
[629bc702] Qt6Declarative_jll v6.7.1+2
[ce943373] Qt6ShaderTools_jll v6.7.1+1
[e99dba38] Qt6Wayland_jll v6.7.1+1
[f50d1b31] Rmath_jll v0.4.2+0
[a44049a8] Vulkan_Loader_jll v1.3.243+0
[a2964d1f] Wayland_jll v1.21.0+1
[2381bf8a] Wayland_protocols_jll v1.31.0+0
[02c8fc9c] XML2_jll v2.13.1+0
[aed1982a] XSLT_jll v1.1.41+0
[ffd25f8a] XZ_jll v5.4.6+0
[f67eecfb] Xorg_libICE_jll v1.1.1+0
[c834827a] Xorg_libSM_jll v1.2.4+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 v1.3.6+0
[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 v0.9.11+0
[14d82f49] Xorg_libpthread_stubs_jll v0.1.1+0
[c7cfdc94] Xorg_libxcb_jll v1.17.0+0
[cc61e674] Xorg_libxkbfile_jll v1.1.2+0
[e920d4aa] Xorg_xcb_util_cursor_jll v0.1.4+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 v4.3.5+0
[3161d3a3] Zstd_jll v1.5.6+0
[35ca27e7] eudev_jll v3.2.9+0
⌅ [214eeab7] fzf_jll v0.43.0+0
[1a1c6b14] gperf_jll v3.1.1+0
[a4ae2306] libaom_jll v3.9.0+0
[0ac62f75] libass_jll v0.15.1+0
[2db6ffa8] libevdev_jll v1.11.0+0
[f638f0a6] libfdk_aac_jll v2.0.2+0
[36db933b] libinput_jll v1.18.0+0
[b53b4c65] libpng_jll v1.6.43+1
[a9144af2] libsodium_jll v1.0.20+0
⌃ [f27f6e37] libvorbis_jll v1.3.7+1
[009596ad] mtdev_jll v1.1.6+0
[1317d2d5] oneTBB_jll v2021.12.0+0
[1270edf5] x264_jll v2021.5.5+0
[dfaa095f] x265_jll v3.5.0+0
[d8fb68d0] xkbcommon_jll v1.4.1+1
[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 v0.6.4
[76f85450] LibGit2
[8f399da3] Libdl
[37e2e46d] LinearAlgebra
[56ddb016] Logging
[d6f4376e] Markdown
[a63ad114] Mmap
[ca575930] NetworkOptions v1.2.0
[44cfe95a] Pkg v1.10.0
[de0858da] Printf
[9abbd945] Profile
[3fa0cd96] REPL
[9a3f8284] Random
[ea8e919c] SHA v0.7.0
[9e88b42a] Serialization
[1a1011a3] SharedArrays
[6462fe0b] Sockets
[2f01184e] SparseArrays v1.10.0
[10745b16] Statistics v1.10.0
[4607b0f0] SuiteSparse
[fa267f1f] TOML v1.0.3
[a4e569a6] Tar v1.10.0
[8dfed614] Test
[cf7118a7] UUIDs
[4ec0a83e] Unicode
[e66e0078] CompilerSupportLibraries_jll v1.1.1+0
[deac9b47] LibCURL_jll v8.4.0+0
[e37daf67] LibGit2_jll v1.6.4+0
[29816b5a] LibSSH2_jll v1.11.0+1
[c8ffd9c3] MbedTLS_jll v2.28.2+1
[14a3606d] MozillaCACerts_jll v2023.1.10
[4536629a] OpenBLAS_jll v0.3.23+4
[05823500] OpenLibm_jll v0.8.1+2
[efcefdf7] PCRE2_jll v10.42.0+1
[bea87d4a] SuiteSparse_jll v7.2.1+1
[83775a58] Zlib_jll v1.2.13+1
[8e850b90] libblastrampoline_jll v5.8.0+1
[8e850ede] nghttp2_jll v1.52.0+1
[3f19e933] p7zip_jll v17.4.0+2
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`