Thermal Fluid ODE Compilation and Perf
This is a 1D advection-diffusion-source PDE that uses a second order upwind scheme.
using Pkg
# Rev fixes precompilation https://github.com/hzgzh/XSteam.jl/pull/2
Pkg.add(Pkg.PackageSpec(; name = "XSteam", rev = "f2a1c589054cfd6bba307985a3a534b6f5a1863b"))
using ModelingToolkit, Symbolics, XSteam, Polynomials, BenchmarkTools,
CairoMakie, OrdinaryDiffEq
using ModelingToolkit: t_nounits as t, D_nounits as D
using SciMLBase: NoInit
using OMJuliaSetup Julia Code
# o o o o o o o < heat capacitors
# | | | | | | | < heat conductors
# o o o o o o o
# | | | | | | |
#Source -> o--o--o--o--o--o--o -> Sink
# advection diff source PDE
m_flow_source(t) = 2.75
T_source(t) = (t > 12 * 3600) * 56.0 + 12.0
# @register_symbolic m_flow_source(t)
# @register_symbolic T_source(t)
#build polynomial liquid-water property only dependent on Temperature
p_l = 5 #bar
T_vec = collect(1:1:150);
@generated kin_visc_T(t) = :(Base.evalpoly(
t, $(fit(T_vec, my_pT.(p_l, T_vec) ./ rho_pT.(p_l, T_vec), 5).coeffs...,)))
@generated lambda_T(t) = :(Base.evalpoly(t, $(fit(T_vec, tc_pT.(p_l, T_vec), 3).coeffs...,)))
@generated Pr_T(t) = :(Base.evalpoly(t,
$(fit(T_vec, 1e3 * Cp_pT.(p_l, T_vec) .* my_pT.(p_l, T_vec) ./ tc_pT.(p_l, T_vec), 5).coeffs...,)))
@generated rho_T(t) = :(Base.evalpoly(t, $(fit(T_vec, rho_pT.(p_l, T_vec), 4).coeffs...,)))
@generated rhocp_T(t) = :(Base.evalpoly(
t, $(fit(T_vec, 1000 * rho_pT.(p_l, T_vec) .* Cp_pT.(p_l, T_vec), 5).coeffs...,)))
# @register_symbolic kin_visc_T(t)
# @register_symbolic lambda_T(t)
# @register_symbolic Pr_T(t)
# @register_symbolic rho_T(t)
# @register_symbolic rhocp_T(t)
@connector function FluidPort(; name, p = 101325.0, m = 0.0, T = 0.0)
sts = @variables p(t)=p m(t)=m [connect=Flow] T(t)=T [connect=Stream]
ODESystem(Equation[], t, sts, []; name = name)
end
@connector function VectorHeatPort(; name, N = 100, T0 = 0.0, Q0 = 0.0)
sts = @variables (T(t))[1:N]=fill(T0, N) (Q(t))[1:N]=fill(Q0, N) [connect=Flow]
ODESystem(Equation[], t, [T; Q], []; name = name)
end
@register_symbolic Dxx_coeff(u, d, T)
#Taylor-aris dispersion model
function Dxx_coeff(u, d, T)
Re = abs(u) * d / kin_visc_T(T) + 0.1
if Re < 1000.0
(d^2 / 4) * u^2 / 48 / 0.14e-6
else
d * u * (1.17e9 * Re^(-2.5) + 0.41)
end
end
@register_symbolic Nusselt(Re, Pr, f)
#Nusselt number model
function Nusselt(Re, Pr, f)
if Re <= 2300.0
3.66
elseif Re <= 3100.0
3.5239 * (Re / 1000)^4 - 45.158 * (Re / 1000)^3 + 212.13 * (Re / 1000)^2 -
427.45 * (Re / 1000) + 316.08
else
f / 8 * ((Re - 1000) * Pr) / (1 + 12.7 * (f / 8)^(1 / 2) * (Pr^(2 / 3) - 1))
end
end
@register_symbolic Churchill_f(Re, epsilon, d)
#Darcy weisbach friction factor
function Churchill_f(Re, epsilon, d)
theta_1 = (-2.457 * log(((7 / Re)^0.9) + (0.27 * (epsilon / d))))^16
theta_2 = (37530 / Re)^16
8 * ((((8 / Re)^12) + (1 / ((theta_1 + theta_2)^1.5)))^(1 / 12))
end
function FluidRegion(; name, L = 1.0, dn = 0.05, N = 100, T0 = 0.0,
lumped_T = 50, diffusion = true, e = 1e-4)
@named inlet = FluidPort()
@named outlet = FluidPort()
@named heatport = VectorHeatPort(N = N)
dx = L / N
c = [-1 / 8, -3 / 8, -3 / 8] # advection stencil coefficients
A = pi * dn^2 / 4
p = @parameters C_shift=0.0 Rw=0.0 # stuff for latter
@variables begin
(T(t))[1:N] = fill(T0, N)
Twall(t)[1:N] = fill(T0, N)
(S(t))[1:N] = fill(T0, N)
(C(t))[1:N] = fill(1.0, N)
u(t) = 1e-6
Re(t) = 1000.0
Dxx(t) = 0.0
Pr(t) = 1.0
alpha(t) = 1.0
f(t) = 1.0
end
sts = vcat(T, Twall, S, C, Num[u], Num[Re], Num[Dxx], Num[Pr], Num[alpha], Num[f])
eqs = Equation[Re ~ 0.1 + dn * abs(u) / kin_visc_T(lumped_T)
Pr ~ Pr_T(lumped_T)
f ~ Churchill_f(Re, e, dn) #Darcy-weisbach
alpha ~ Nusselt(Re, Pr, f) * lambda_T(lumped_T) / dn
Dxx ~ diffusion * Dxx_coeff(u, dn, lumped_T)
inlet.m ~ -outlet.m
inlet.p ~ outlet.p
inlet.T ~ instream(inlet.T)
outlet.T ~ T[N]
u ~ inlet.m / rho_T(inlet.T) / A
[C[i] ~ dx * A * rhocp_T(T[i]) for i in 1:N]
[S[i] ~ heatport.Q[i] for i in 1:N]
[Twall[i] ~ heatport.T[i] for i in 1:N]
#source term
[S[i] ~
(1 / (1 / (alpha * dn * pi * dx) + abs(Rw / 1000))) * (Twall[i] - T[i])
for i in 1:N]
#second order upwind + diffusion + source
D(T[1]) ~
u / dx * (inlet.T - T[1]) + Dxx * (T[2] - T[1]) / dx^2 +
S[1] / (C[1] - C_shift)
D(T[2]) ~
u / dx * (c[1] * inlet.T - sum(c) * T[1] + c[2] * T[2] + c[3] * T[3]) +
Dxx * (T[1] - 2 * T[2] + T[3]) / dx^2 + S[2] / (C[2] - C_shift)
[D(T[i]) ~
u / dx *
(c[1] * T[i - 2] - sum(c) * T[i - 1] + c[2] * T[i] + c[3] * T[i + 1]) +
Dxx * (T[i - 1] - 2 * T[i] + T[i + 1]) / dx^2 + S[i] / (C[i] - C_shift)
for i in 3:(N - 1)]
D(T[N]) ~
u / dx * (T[N - 1] - T[N]) + Dxx * (T[N - 1] - T[N]) / dx^2 +
S[N] / (C[N] - C_shift)]
ODESystem(eqs, t, sts, p; systems = [inlet, outlet, heatport], name = name)
end
@register_symbolic Cn_circular_wall_inner(d, D, cp, ρ)
function Cn_circular_wall_inner(d, D, cp, ρ)
C = pi / 4 * (D^2 - d^2) * cp * ρ
return C / 2
end
@register_symbolic Cn_circular_wall_outer(d, D, cp, ρ)
function Cn_circular_wall_outer(d, D, cp, ρ)
C = pi / 4 * (D^2 - d^2) * cp * ρ
return C / 2
end
@register_symbolic Ke_circular_wall(d, D, λ)
function Ke_circular_wall(d, D, λ)
2 * pi * λ / log(D / d)
end
function CircularWallFEM(; name, L = 100, N = 10, d = 0.05, t_layer = [0.002],
λ = [50], cp = [500], ρ = [7850], T0 = 0.0)
@named inner_heatport = VectorHeatPort(N = N)
@named outer_heatport = VectorHeatPort(N = N)
dx = L / N
Ne = length(t_layer)
Nn = Ne + 1
dn = vcat(d, d .+ 2.0 .* cumsum(t_layer))
Cn = zeros(Nn)
Cn[1:Ne] += Cn_circular_wall_inner.(dn[1:Ne], dn[2:Nn], cp, ρ) .* dx
Cn[2:Nn] += Cn_circular_wall_outer.(dn[1:Ne], dn[2:Nn], cp, ρ) .* dx
p = @parameters C_shift = 0.0
Ke = Ke_circular_wall.(dn[1:Ne], dn[2:Nn], λ) .* dx
@variables begin
(Tn(t))[1:N, 1:Nn] = fill(T0, N, Nn)
(Qe(t))[1:N, 1:Ne] = fill(T0, N, Ne)
end
sts = [vec(Tn); vec(Qe)]
e0 = Equation[inner_heatport.T[i] ~ Tn[i, 1] for i in 1:N]
e1 = Equation[outer_heatport.T[i] ~ Tn[i, Nn] for i in 1:N]
e2 = Equation[Qe[i, j] ~ Ke[j] * (-Tn[i, j + 1] + Tn[i, j]) for i in 1:N for j in 1:Ne]
e3 = Equation[D(Tn[i, 1]) * (Cn[1] + C_shift) ~ inner_heatport.Q[i] - Qe[i, 1]
for i in 1:N]
e4 = Equation[D(Tn[i, j]) * Cn[j] ~ Qe[i, j - 1] - Qe[i, j] for i in 1:N
for j in 2:(Nn - 1)]
e5 = Equation[D(Tn[i, Nn]) * Cn[Nn] ~ Qe[i, Ne] + outer_heatport.Q[i] for i in 1:N]
eqs = vcat(e0, e1, e2, e3, e4, e5)
ODESystem(eqs, t, sts, p; systems = [inner_heatport, outer_heatport], name = name)
end
function CylindricalSurfaceConvection(; name, L = 100, N = 100, d = 1.0, α = 5.0)
dx = L / N
S = pi * d * dx
@named heatport = VectorHeatPort(N = N)
sts = @variables Tenv(t) = 0.0
eqs = [Tenv ~ 18.0
[heatport.Q[i] ~ α * S * (heatport.T[i] - Tenv) for i in 1:N]]
ODESystem(eqs, t, sts, []; systems = [heatport], name = name)
end
function PreinsulatedPipe(;
name, L = 100.0, N = 100.0, dn = 0.05, T0 = 0.0, t_layer = [0.004, 0.013],
λ = [50, 0.04], cp = [500, 1200], ρ = [7800, 40], α = 5.0,
e = 1e-4, lumped_T = 50, diffusion = true)
@named inlet = FluidPort()
@named outlet = FluidPort()
@named fluid_region = FluidRegion(
L = L, N = N, dn = dn, e = e, lumped_T = lumped_T, diffusion = diffusion)
@named shell = CircularWallFEM(
L = L, N = N, d = dn, t_layer = t_layer, λ = λ, cp = cp, ρ = ρ)
@named surfconv = CylindricalSurfaceConvection(L = L, N = N, d = dn +
2.0 * sum(t_layer), α = α)
systems = [fluid_region, shell, inlet, outlet, surfconv]
eqs = [connect(fluid_region.inlet, inlet)
connect(fluid_region.outlet, outlet)
connect(fluid_region.heatport, shell.inner_heatport)
connect(shell.outer_heatport, surfconv.heatport)]
ODESystem(eqs, t, [], []; systems = systems, name = name)
end
function Source(; name, p_feed = 100000)
@named outlet = FluidPort()
sts = @variables m_flow(t) = 1e-6
eqs = [m_flow ~ m_flow_source(t)
outlet.m ~ -m_flow
outlet.p ~ p_feed
outlet.T ~ T_source(t)]
compose(ODESystem(eqs, t, sts, []; name = name), [outlet])
end
function Sink(; name)
@named inlet = FluidPort()
eqs = [
inlet.T ~ instream(inlet.T)
]
compose(ODESystem(eqs, t, [], []; name = name), [inlet])
end
function TestBenchPreinsulated(; name, L = 1.0, dn = 0.05, t_layer = [0.0056, 0.013],
N = 100, diffusion = true, lumped_T = 20)
@named pipe = PreinsulatedPipe(L = L, dn = dn, N = N, diffusion = diffusion,
t_layer = t_layer, lumped_T = lumped_T)
@named source = Source()
@named sink = Sink()
subs = [source, pipe, sink]
eqs = [connect(source.outlet, pipe.inlet)
connect(pipe.outlet, sink.inlet)]
compose(ODESystem(eqs, t, [], []; name = name), subs)
end
function compile_run_problem(sys;
solver = FBDF(; autodiff = AutoForwardDiff()),
duref = nothing)
tspan = (0.0, 19 * 3600.0)
t0 = time()
u0map = [v => 12.0 for v in unknowns(sys)]
prob = ODEProblem(sys, u0map, tspan; sparse = true,
warn_initialize_determined = false, initializealg = NoInit())
(; f, u0, p) = prob
ff = f.f
du = similar(u0)
ff(du, u0, p, 0.0)
t_fode = time() - t0
duref === nothing || @assert duref ≈ du
t_run = @belapsed $ff($du, $u0, $p, 0.0)
t_solve = @elapsed sol = solve(prob, solver; reltol = 1e-6, abstol = 1e-6, saveat = 100)
@assert SciMLBase.successful_retcode(sol)
(t_fode, t_run, t_solve), du
end
function run_and_time_julia!(ss_times, times, total_times, i, N)
@named testbench = TestBenchPreinsulated(L = 470, N = N, dn = 0.3127, t_layer = [
0.0056, 0.058])
ss_times[i] = @elapsed sys_mtk = mtkcompile(testbench)
times[i], _ = compile_run_problem(sys_mtk)
t_fode, t_run, t_solve = times[i]
total_times[i, 1] = ss_times[i] + t_fode + t_solve
endrun_and_time_julia! (generic function with 1 method)N = [5, 10, 20, 40, 60, 80, 160, 320, 480, 640, 800, 960, 1280];
N_states = 4 .* N; # x-axis for plots
# max size we run per method, including OpenModelica
max_sizes = [last(N), last(N)];
# NaN-initialize so Makie will ignore incomplete
ss_times = fill(NaN, length(N));
# more indepth Julia-times
times = fill((NaN, NaN, NaN), length(N));
# all times: MTK, OpenModelica, Dymola
total_times = fill(NaN, length(N), 3);Julia Timings
@time run_and_time_julia!(ss_times, times, total_times, 1, 4); # precompile
for (i, n) in enumerate(N)
@time run_and_time_julia!(ss_times, times, total_times, i, n)
end160.859643 seconds (177.49 M allocations: 9.315 GiB, 2.40% gc time, 99.04%
compilation time: 36% of which was recompilation)
4.054184 seconds (3.30 M allocations: 176.679 MiB, 65.98% compilation tim
e)
4.335669 seconds (4.06 M allocations: 208.519 MiB, 2.84% gc time, 64.99%
compilation time)
5.199944 seconds (5.70 M allocations: 275.836 MiB, 2.19% gc time, 61.03%
compilation time)
7.199618 seconds (10.38 M allocations: 478.369 MiB, 1.46% gc time, 63.38%
compilation time)
9.264826 seconds (14.67 M allocations: 646.983 MiB, 2.54% gc time, 60.20%
compilation time)
13.510870 seconds (20.30 M allocations: 871.027 MiB, 4.86% gc time, 51.49%
compilation time)
41.120423 seconds (50.41 M allocations: 2.040 GiB, 2.12% gc time, 37.21% c
ompilation time)
92.887831 seconds (148.06 M allocations: 5.961 GiB, 4.34% gc time, 40.72%
compilation time)
182.200596 seconds (293.29 M allocations: 11.626 GiB, 4.13% gc time, 34.48%
compilation time)
302.990004 seconds (517.69 M allocations: 19.858 GiB, 4.38% gc time, 31.49%
compilation time)
469.808688 seconds (795.19 M allocations: 30.186 GiB, 4.10% gc time, 30.13%
compilation time)
677.146576 seconds (1.13 G allocations: 42.226 GiB, 3.97% gc time, 27.32% c
ompilation time)
1167.685159 seconds (1.99 G allocations: 72.644 GiB, 4.26% gc time, 26.27%
compilation time)Time OpenModelica
using OMJulia, CSV, DataFrames
mod = OMJulia.OMCSession();
OMJulia.sendExpression(mod, "getVersion()")
OMJulia.sendExpression(mod, "installPackage(Modelica)")
modelicafile = "../../benchmarks/ModelingToolkit/DhnControl.mo"
resultfile = "modelica_res.csv"
@show "Start OpenModelica Timings"
for i in eachindex(N)
n = N[i]
n > max_sizes[end] && break
@show n
totaltime = @elapsed res = begin
@sync ModelicaSystem(mod, modelicafile, "DhnControl.Test.test_preinsulated_470_$n")
sendExpression(mod, "simulate(DhnControl.Test.test_preinsulated_470_$n)")
end
#runtime = res["timeTotal"]
@assert res["messages"][1:11] == "LOG_SUCCESS"
total_times[i, 2] = totaltime
end
OMJulia.quit(mod)
total_times[:, 2]"Start OpenModelica Timings" = "Start OpenModelica Timings"
n = 5
n = 10
n = 20
n = 40
n = 60
n = 80
n = 160
n = 320
n = 480
n = 640
n = 800
n = 960
n = 1280
13-element Vector{Float64}:
4.677776716
3.716024314
5.958861806
10.752853246
15.544922506
20.660293004
41.020119178
85.255619972
132.521331867
183.881996847
237.487050874
290.464767294
434.45636033Time Dymola
Dymola requires a license server and thus cannot be hosted. This was run locally for the following times:
translation_and_total_times = [1.802 1.921
1.78 1.846
1.84 1.877
2.028 2.075
2.221 2.283
2.409 2.496
3.189 3.427
4.758 5.577
6.39 8.128
8.052 11.026
9.707 14.393
11.411 17.752
15.094 27.268]
total_times[:, 3] = translation_and_total_times[1:length(N), 2]13-element Vector{Float64}:
1.921
1.846
1.877
2.075
2.283
2.496
3.427
5.577
8.128
11.026
14.393
17.752
27.268Generate Final Plots
f = Figure(size = (800, 800));
let ax = Axis(f[1, 1]; yscale = log10, xscale = log10, title = "Structural Simplify Time")
lines!(N, ss_times)
end
for (i, timecat) in enumerate(("ODEProblem + f!", "Run", "Solve"))
title = timecat * " Time"
ax = Axis(f[i + 1, 1]; yscale = log10, xscale = log10, title)
lines!(N, getindex.(times, i))
end
f
f2 = Figure(size = (800, 400));
title = "Total Time: Thermal Fluid Benchmark"
ax = Axis(f2[1, 1]; yscale = log10, xscale = log10, title)
names = ["MTK", "OpenModelica", "Dymola"]
_lines = map(enumerate(names)) do (j, label)
ts = @view(total_times[:, j])
lines!(N_states, ts)
end
Legend(f2[1, 2], _lines, names)
f2
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/ModelingToolkit","ThermalFluid.jmd")Computer Information:
Julia Version 1.11.9
Commit 53a02c0720c (2026-02-06 00:27 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-16.0.6 (ORCJIT, znver2)
Threads: 128 default, 0 interactive, 64 GC (on 128 virtual cores)
Environment:
JULIA_NUM_THREADS = auto
Package Information:
Status `/julia/github-runners/amdci1-1/_work/SciMLBenchmarks.jl/SciMLBenchmarks.jl/benchmarks/ModelingToolkit/Project.toml`
[6e4b80f9] BenchmarkTools v1.8.0
[336ed68f] CSV v0.10.17
[13f3f980] CairoMakie v0.15.14
[a93c6f00] DataFrames v1.8.2
⌃ [7ed4a6bd] LinearSolve v5.17.3
[961ee093] ModelingToolkit v11.43.1
[16a59e39] ModelingToolkitStandardLibrary v2.29.8
⌅ [0f4fe800] OMJulia v0.3.3
[1dea7af3] OrdinaryDiffEq v7.8.1
[43230ef6] OrdinaryDiffEqRosenbrock v2.7.3
[f27b6e38] Polynomials v4.1.3
[0bca4576] SciMLBase v3.54.0
[31c91b34] SciMLBenchmarks v0.2.1
[0c5d862f] Symbolics v7.39.2
[95ff35a0] XSteam v0.3.0 `https://github.com/hzgzh/XSteam.jl.git#f2a1c58`
[de0858da] Printf v1.11.0
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`And the full manifest:
Status `/julia/github-runners/amdci1-1/_work/SciMLBenchmarks.jl/SciMLBenchmarks.jl/benchmarks/ModelingToolkit/Manifest.toml`
[47edcb42] ADTypes v1.24.0
[14f7f29c] AMD v0.5.4
[621f4979] AbstractFFTs v1.5.0
[6e696c72] AbstractPlutoDingetjes v1.4.1
[1520ce14] AbstractTrees v0.4.5
[7d9f7c33] Accessors v0.1.45
[79e6a3ab] Adapt v4.7.0
[35492f91] AdaptivePredicates v1.2.0
[66dad0bd] AliasTables v1.1.3
[27a7e980] Animations v0.4.2
[ec485272] ArnoldiMethod v0.4.0
[4fba245c] ArrayInterface v7.30.2
[4c555306] ArrayLayouts v1.12.2
[67c07d97] Automa v1.2.0
[13072b0f] AxisAlgorithms v1.1.0
[39de3d68] AxisArrays v0.4.8
[aae01518] BandedMatrices v1.12.0
[18cc8868] BaseDirs v1.4.0
[6e4b80f9] BenchmarkTools v1.8.0
[e2ed5e7c] Bijections v0.2.2
[b2a6c25c] BinaryHeaps v1.1.0
[caf10ac8] BipartiteGraphs v0.1.14
[8e7c35d0] BlockArrays v1.10.0
[70df07ce] BracketingNonlinearSolve v1.12.7
[fa961155] CEnum v0.5.0
[96374032] CRlibm v1.0.2
[336ed68f] CSV v0.10.17
[159f3aea] Cairo v1.1.1
[13f3f980] CairoMakie v0.15.14
[d360d2e6] ChainRulesCore v1.26.1
[944b1d66] CodecZlib v0.7.9
[6b39b394] CodecZstd v0.8.7
[a2cac450] ColorBrewer v0.4.2
[35d6a980] ColorSchemes v3.31.0
[3da002f7] ColorTypes v0.12.1
[c3611d14] ColorVectorSpace v0.11.0
[5ae59095] Colors v0.13.1
⌅ [861a8166] Combinatorics v1.0.2
[38540f10] CommonSolve v0.2.14
[bbf7d656] CommonSubexpressions v0.3.1
[f70d9fcc] CommonWorldInvalidations v1.2.2
[34da2185] Compat v4.18.1
[b152e2b5] CompositeTypes v0.1.4
[a33af91c] CompositionsBase v0.1.2
[95dc2771] ComputePipeline v0.1.8
[2569d6c7] ConcreteStructs v0.2.8
[187b0558] ConstructionBase v1.6.0
[d38c429a] Contour v0.6.3
[b7a15901] CoreMath v0.1.0
[a8cc5b0e] Crayons v4.2.0
[9a962f9c] DataAPI v1.16.0
[a93c6f00] DataFrames v1.8.2
[864edb3b] DataStructures v0.19.6
[e2d170a0] DataValueInterfaces v1.0.0
[927a84f5] DelaunayTriangulation v1.6.7
[2b5f629d] DiffEqBase v7.21.1
[459566f4] DiffEqCallbacks v4.19.4
[163ba53b] DiffResults v1.1.0
[b552c78f] DiffRules v1.16.0
[a0c0ee7d] DifferentiationInterface v0.7.21
[31c24e10] Distributions v0.25.131
[ffbed154] DocStringExtensions v0.9.5
[5b8099bc] DomainSets v0.8.1
[7c1d4256] DynamicPolynomials v0.6.8
[4e289a0a] EnumX v1.0.7
[f151be2c] EnzymeCore v0.8.21
[429591f6] ExactPredicates v2.2.9
[e2ba6199] ExprTools v0.1.11
[55351af7] ExproniconLite v0.10.14
[b86e33f2] FFTA v0.3.1
[7034ab61] FastBroadcast v1.4.0
[9aa1b823] FastClosures v0.3.2
[a4df4552] FastPower v1.5.0
[5789e2e9] FileIO v1.20.0
[8fc22ac5] FilePaths v0.9.0
[48062228] FilePathsBase v0.9.24
[1a297f60] FillArrays v1.17.0
[64ca27bc] FindFirstFunctions v3.2.1
[6a86dc24] FiniteDiff v2.33.0
⌅ [53c48c17] FixedPointNumbers v0.8.6
[1fa38f19] Format v1.3.7
[f6369f11] ForwardDiff v1.4.6
[b38be410] FreeType v4.1.1
[663a7486] FreeTypeAbstraction v0.10.8
[a85aefff] FunctionMaps v0.1.2
[069b7b12] FunctionWrappers v1.1.3
[77dc65aa] FunctionWrappersWrappers v1.13.0
[46192b85] GPUArraysCore v0.2.0
[a0844989] Gamma v1.2.0
[5c1252a2] GeometryBasics v0.5.12
[a2bd30eb] Graphics v1.1.3
[86223c79] Graphs v1.15.0
[3955a311] GridLayoutBase v0.11.3
⌅ [eafb193a] Highlights v0.5.3
[34004b35] HypergeometricFunctions v0.3.30
[2803e5a7] ImageAxes v0.6.12
[c817782e] ImageBase v0.1.7
[a09fc81d] ImageCore v0.10.5
[82e4d734] ImageIO v0.6.10
[bc367c6b] ImageMetadata v0.9.10
[3263718b] ImplicitDiscreteSolve v2.3.0
[9b13fd28] IndirectArrays v1.0.0
[d25df0c9] Inflate v0.1.5
⌅ [842dd82b] InlineStrings v1.4.6
[18e54dd8] IntegerMathUtils v0.1.4
[a98d9a8b] Interpolations v0.16.3
[d1acc4aa] IntervalArithmetic v1.0.12
[8197267c] IntervalSets v0.7.14
[3587e190] InverseFunctions v0.1.17
[41ab1584] InvertedIndices v1.3.1
[92d709cd] IrrationalConstants v0.2.6
[f1662d9f] Isoband v0.1.1
[c8e1da08] IterTools v1.10.0
[82899510] IteratorInterfaceExtensions v1.0.0
[692b3bcd] JLLWrappers v1.8.0
⌅ [682c06a0] JSON v0.21.4
[ae98c720] Jieko v0.2.1
[b835a17e] JpegTurbo v0.1.6
⌃ [ccbc3e58] JumpProcesses v9.32.3
[5ab0869b] KernelDensity v0.6.12
[ba0b0d4f] Krylov v0.10.10
[2faa5264] LHLFactorization v2.2.2
[b964fa9f] LaTeXStrings v1.4.1
[8cdb02fc] LazyModules v0.3.1
[9c8b4983] LightXML v0.9.3
[87fe0de2] LineSearch v0.1.18
⌃ [7ed4a6bd] LinearSolve v5.17.3
[2ab3a3ac] LogExpFunctions v1.0.1
[e6f89c97] LoggingExtras v1.2.0
[1914dd2f] MacroTools v0.5.16
[ee78f7c6] Makie v0.24.14
[dbb5928d] MappedArrays v0.4.3
[0a4f8689] MathTeXEngine v0.6.9
[bb5d69b7] MaybeInplace v0.1.8
[e1d29d7a] Missings v1.2.0
[961ee093] ModelingToolkit v11.43.1
⌃ [7771a370] ModelingToolkitBase v1.71.2
[16a59e39] ModelingToolkitStandardLibrary v2.29.8
[6bb917b9] ModelingToolkitTearing v1.20.6
[e94cdb99] MosaicViews v0.3.4
⌅ [2e0e35c7] Moshi v0.3.9
[46d2c3a1] MuladdMacro v0.2.7
[102ac46a] MultivariatePolynomials v0.5.19
[ffc61752] Mustache v1.0.21
[d8a4904e] MutableArithmetics v1.8.0
[77ba4419] NaNMath v1.1.4
[f09324ee] Netpbm v1.1.1
⌃ [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
⌅ [0f4fe800] OMJulia v0.3.3
[510215fc] Observables v0.5.5
[6fe1bfb0] OffsetArrays v1.17.0
[52e1d378] OpenEXR v0.3.3
[bac558e1] OrderedCollections v2.0.1
[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
[f57f5aa1] PNGFiles v0.4.5
[19eb6ba3] Packing v0.5.1
[5432bcbf] PaddedViews v0.5.12
⌅ [69de0a69] Parsers v2.8.8
[eebad327] PkgVersion v0.3.3
[995b91a9] PlotUtils v1.4.4
[e409e4f3] PoissonRandom v0.4.13
[647866c9] PolygonOps v0.1.2
[f27b6e38] Polynomials v4.1.3
[2dfb63ee] PooledArrays v1.4.3
[d236fae5] PreallocationTools v1.7.1
⌅ [aea7be01] PrecompileTools v1.2.1
[21216c6a] Preferences v1.6.0
[08abe8d2] PrettyTables v3.4.8
[27ebfcd6] Primes v0.5.7
[92933f4c] ProgressMeter v1.11.0
[43287f4e] PtrArrays v1.4.0
[0c0d3e7f] PureKLU v1.5.0
[4b34888f] QOI v1.0.2
[1fd47b50] QuadGK v2.11.3
[b3c3ace0] RangeArrays v0.3.2
[c84ed2f1] Ratios v0.4.5
[988b38a3] ReadOnlyArrays v0.2.0
[795d4caa] ReadOnlyDicts v1.0.1
[3cdcf5f2] RecipesBase v1.3.4
[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
[5eaf0fd0] RoundingEmulator v0.2.1
[7e49a35a] RuntimeGeneratedFunctions v0.5.26
[9dfe8606] SCCNonlinearSolve v1.15.3
[fdea26ae] SIMD v3.7.2
[0bca4576] SciMLBase v3.54.0
[31c91b34] SciMLBenchmarks 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
[6c6a2e73] Scratch v1.3.0
[91c51154] SentinelArrays v1.4.10
[efcf1570] Setfield v1.1.2
[65257c39] ShaderAbstractions v0.5.0
[73760f76] SignedDistanceFields v0.4.1
[727e6d20] SimpleNonlinearSolve v2.14.5
[699a6c99] SimpleTraits v0.9.6
[45858cf5] Sixel v0.1.5
[a2af1166] SortingAlgorithms v1.2.3
[a57abbd0] SparseColumnPivotedQR v2.1.8
[0a514795] SparseMatrixColorings v0.4.28
[276daf66] SpecialFunctions v2.9.0
[860ef19b] StableRNGs v1.0.4
[cae243ae] StackViews v0.1.2
[0c0c59c1] StarAlgebras v0.3.0
[64909d44] StateSelection v1.11.1
[90137ffa] StaticArrays v1.9.20
[1e83bf80] StaticArraysCore v1.4.4
[10745b16] Statistics v1.11.5
[82ae8749] StatsAPI v1.8.0
[2913bbd2] StatsBase v0.34.13
[4c63d2b9] StatsFuns v2.2.1
[69024149] StringEncodings v0.3.7
⌅ [892a3eda] StringManipulation v0.5.0
[09ab397b] StructArrays v0.7.3
[2efcf032] SymbolicIndexingInterface v0.3.55
[19f23fe9] SymbolicLimits v1.2.1
[d1185830] SymbolicUtils v4.46.6
[0c5d862f] Symbolics v7.39.2
[3783bdb8] TableTraits v1.0.1
[bd369af6] Tables v1.14.0
[ed4db957] TaskLocalValues v0.1.3
[62fd8b95] TensorCore v0.1.1
[8ea1fca8] TermInterface v2.0.0
[731e570b] TiffImages v0.11.9
[a759f4b9] TimerOutputs v1.2.1
[3bb67fe8] TranscodingStreams v0.11.3
[981d1d27] TriplotBase v0.1.0
[781d530d] TruncatedStacktraces v1.4.0
[3a884ed6] UnPack v1.0.2
[1cfade01] UnicodeFun v0.4.1
[1986cc42] Unitful v1.29.0
[d30d5f5c] WeakCacheSets v0.1.0
[ea10d353] WeakRefStrings v1.4.3
[44d3d7a6] Weave v0.10.12
[e3aaa7dc] WebP v0.1.3
[efce3f68] WoodburyMatrices v1.1.0
[76eceee3] WorkerUtilities v1.6.1
[95ff35a0] XSteam v0.3.0 `https://github.com/hzgzh/XSteam.jl.git#f2a1c58`
[ddb6d928] YAML v0.4.16
[c2297ded] ZMQ v1.5.1
[6e34b625] Bzip2_jll v1.0.9+0
[4e9b3aee] CRlibm_jll v1.0.1+0
[83423d85] Cairo_jll v1.18.7+0
[a38c48d9] CoreMath_jll v0.1.0+0
⌅ [5ae413db] EarCut_jll v2.2.4+0
[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
⌅ [b0724c58] GettextRuntime_jll v0.22.4+0
⌅ [59f7168a] Giflib_jll v5.2.3+0
[7746bdde] Glib_jll v2.88.3+0
[3b182d85] Graphite2_jll v1.3.16+0
[2e76f6c2] HarfBuzz_jll v100.14004.0+0
[905a6f67] Imath_jll v3.2.2+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
[6cdc7f73] OpenBLASConsistentFPCSR_jll v0.3.34+0
[18a262bb] OpenEXR_jll v3.4.15+0
[458c3c95] OpenSSL_jll v3.5.8+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
[f50d1b31] Rmath_jll v0.5.2+0
[02c8fc9c] XML2_jll v2.15.3+0
[ffd25f8a] XZ_jll v5.8.4+0
[4f6342f7] Xorg_libX11_jll v1.8.13+0
[0c0b7dd1] Xorg_libXau_jll v1.0.13+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
[ea2f1a96] Xorg_libXrender_jll v0.9.12+0
[a65dc6b1] Xorg_libpciaccess_jll v0.19.0+0
[c7cfdc94] Xorg_libxcb_jll v1.17.1+0
[c5fb5394] Xorg_xtrans_jll v1.6.0+0
[8f1865be] ZeroMQ_jll v4.3.6+0
[3161d3a3] Zstd_jll v1.5.7+1
[9a68df92] isoband_jll v0.2.3+0
[a4ae2306] libaom_jll v3.14.1+0
[0ac62f75] libass_jll v0.17.5+0
[8e53e030] libdrm_jll v2.4.134+0
[f638f0a6] libfdk_aac_jll v2.0.4+0
[b53b4c65] libpng_jll v1.6.58+0
[075b6546] libsixel_jll v1.10.5+0
[a9144af2] libsodium_jll v1.0.21+0
[9a156e7d] libva_jll v2.23.0+0
[f27f6e37] libvorbis_jll v1.3.8+0
[c5f90fcd] libwebp_jll v1.6.0+0
[1317d2d5] oneTBB_jll v2022.3.0+0
⌅ [1270edf5] x264_jll v10164.0.1+0
[dfaa095f] x265_jll v4.1.0+0
[0dad84c5] ArgTools v1.1.2
[56f22d72] Artifacts v1.11.0
[2a0f44e3] Base64 v1.11.0
[8bf52ea8] CRC32c v1.11.0
[ade2ca70] Dates v1.11.0
[8ba89e20] Distributed v1.11.0
[f43a241f] Downloads v1.6.0
[7b1f6079] FileWatching v1.11.0
[9fa8497b] Future v1.11.0
[b77e0a4c] InteractiveUtils v1.11.0
[4af54fe1] LazyArtifacts v1.11.0
[b27032c2] LibCURL v0.6.4
[76f85450] LibGit2 v1.11.0
[8f399da3] Libdl v1.11.0
[37e2e46d] LinearAlgebra v1.11.0
[56ddb016] Logging v1.11.0
[d6f4376e] Markdown v1.11.0
[a63ad114] Mmap v1.11.0
[ca575930] NetworkOptions v1.2.0
[44cfe95a] Pkg v1.11.0
[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
[1a1011a3] SharedArrays v1.11.0
[6462fe0b] Sockets v1.11.0
[2f01184e] SparseArrays v1.11.0
[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 v1.1.1+0
[deac9b47] LibCURL_jll v8.6.0+0
[e37daf67] LibGit2_jll v1.7.2+0
[29816b5a] LibSSH2_jll v1.11.0+1
[c8ffd9c3] MbedTLS_jll v2.28.6+0
[14a3606d] MozillaCACerts_jll v2023.12.12
[4536629a] OpenBLAS_jll v0.3.27+1
[05823500] OpenLibm_jll v0.8.5+0
[efcefdf7] PCRE2_jll v10.42.0+1
[bea87d4a] SuiteSparse_jll v7.7.0+0
[83775a58] Zlib_jll v1.2.13+1
[8e850b90] libblastrampoline_jll v5.11.0+0
[8e850ede] nghttp2_jll v1.59.0+0
[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`