Open
Description
Describe the bug 🐞
Defining constant parameters in ODEProblem (prob.p.constant) hurt optimization time.
Expected behavior
A constant optimization time regardless the number of constant parameters.
Minimal Reproducible Example 👇
In this MWE (heat equation with source terms) I define two ODEProblem that are the same, the only difference being that in the "single" constant parameters are defined as constant, and in "generic" one using @parameters [tunable = false]. On my computer, the "generic" take twice more time for optimization. And this with only 3 sources, where I would like to define more.
###### Define PDE problem ######
using ModelingToolkit
using DifferentialEquations
using MethodOfLines
using BenchmarkTools
# Variables
using ModelingToolkit: t_nounits as t, D_nounits as ∂t
@variables x
@variables c(..)
∂²x = Differential(x)^2
## General problem info
N=3 #number of source terms
# Space and time domains
L=3.0
T=5.0
dom = [x ∈ (0, L), t ∈ (0, T)]
# Initial and boundary conditions
bcs = [
c(0,t) ~ 0.0,
c(x,0) ~ 0.0,
]
## Single case problem ##
@parameters a[1:N]
D=0.1
source(a,xᵢ,tᵢ,σₓ,σₜ)=a*exp(-(x-xᵢ)^2/(2*σₓ^2))*exp(-(t-tᵢ)^2/(2*σₜ^2))
xᵢ=[0.5,1.5,2]
tᵢ=[0.8,1,3]
σₓ=fill(0.1,N)
σₜ=fill(0.2,N)
# PDE
eqn = ∂t(c(x, t)) ~ D * ∂²x(c(x, t))+sum(source.(collect(a),xᵢ,tᵢ,σₓ,σₜ))
# Define PDE system
@named sys = PDESystem(eqn,
bcs,
dom,
[x, t],
[c(x, t)],
[a];
defaults=Dict(a => [0.0,0.5,1.0])
)
# Define ODE problem
prob_single = discretize(sys,
MOLFiniteDifference([x => 0.05],
t,
advection_scheme=scheme=UpwindScheme(2)
)
);
## Generic case problem ##
@parameters a[1:N] [tunable = true]
@parameters D=0.1 [tunable = false]
@parameters xᵢ[1:N]=[0.5,1.5,2] [tunable = false]
@parameters tᵢ[1:N]=[0.8,1,3] [tunable = false]
@parameters σₓ[1:N]=fill(0.1,N) [tunable = false]
@parameters σₜ[1:N]=fill(0.2,N) [tunable = false]
source(a,xᵢ,tᵢ,σₓ,σₜ)=a*exp(-(x-xᵢ)^2/(2*σₓ^2))*exp(-(t-tᵢ)^2/(2*σₜ^2))
# PDE
eqn = ∂t(c(x, t)) ~ D * ∂²x(c(x, t))+sum(source.(collect(a),collect(xᵢ),collect(tᵢ),collect(σₓ),collect(σₜ)))
# Define PDE system
@named sys = PDESystem(eqn,
bcs,
dom,
[x, t],
[c(x, t)],
[a,D, xᵢ, tᵢ, σₓ, σₜ];
defaults=Dict(a => [0.0,0.5,1.0])
)
# Define ODE problem
prob_generic = discretize(sys,
MOLFiniteDifference([x => 0.05],
t,
advection_scheme=scheme=UpwindScheme(2)
)
);
##### Generate synthetic data #####
@time "PDE Solve" sol = solve(prob_single, Tsit5(), saveat=0.1)
t_obs = 0:1.0:T
x_obs = [1.0]
x_idx = findall(x -> x ∈ x_obs, sol[x])
t_idx = findall(t -> t ∈ t_obs, sol[t])
idx_obs = CartesianIndex.(Iterators.product(x_idx, t_idx) |> collect)
data_obs = sol[c(x, t)][idx_obs]
##### Parameter estimation using DiffEqParamEstim ######
using Optimization
using DiffEqParamEstim
using OptimizationOptimJL
import ModelingToolkit.SciMLBase: PDETimeSeriesSolution
function (f::L2Loss)(sol::PDETimeSeriesSolution)
xidx, data = f.data
weight = f.data_weight
diff_weight = f.differ_weight
colloc_grad = f.colloc_grad
dudt = f.dudt
if sol isa DiffEqBase.AbstractEnsembleSolution
failure = any(!SciMLBase.successful_retcode(s.retcode) for s in sol)
else
failure = !SciMLBase.successful_retcode(sol.retcode)
end
failure && return Inf
sum(abs2, data - sol[c(x, t)][x_idx, :])
end
## Single problem
cost_function = build_loss_objective(prob_single,
Tsit5(),
L2Loss(t_obs, (x_idx, data_obs)),
AutoFiniteDiff(),
prob_generator=(prob, p) -> remake(prob, p=[a => p])
)
optprob = Optimization.OptimizationProblem(cost_function, fill(1.0,N))
println("Optim time single problem: ")
@btime optsol = solve(optprob, BFGS())
## Generic problem
cost_function = build_loss_objective(prob_generic,
Tsit5(),
L2Loss(t_obs, (x_idx, data_obs)),
AutoFiniteDiff(),
prob_generator=(prob, p) -> remake(prob, p=[a => p])
)
optprob = Optimization.OptimizationProblem(cost_function, fill(1.0,N))
println("Optim time generic problem: ")
@btime optsol = solve(optprob, BFGS())Error & Stacktrace
Environment (please complete the following information):
- Output of
using Pkg; Pkg.status()
[1130ab10] DiffEqParamEstim v2.2.0
[0c46a032] DifferentialEquations v7.16.1
[70703baa] JuliaSyntax v1.0.2
[94925ecb] MethodOfLines v0.11.9
[961ee093] ModelingToolkit v10.7.0
[7f7a1694] Optimization v4.4.0
[36348300] OptimizationOptimJL v0.4.3
[91a5bcdd] Plots v1.40.16- Output of
using Pkg; Pkg.status(; mode = PKGMODE_MANIFEST)
[47edcb42] ADTypes v1.15.0
[1520ce14] AbstractTrees v0.4.5
[7d9f7c33] Accessors v0.1.42
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[66dad0bd] AliasTables v1.1.3
[a95523ee] AlmostBlockDiagonals v0.1.10
[ec485272] ArnoldiMethod v0.4.0
[4fba245c] ArrayInterface v7.19.0
[4c555306] ArrayLayouts v1.11.1
[13072b0f] AxisAlgorithms v1.1.0
[aae01518] BandedMatrices v1.9.4
[e2ed5e7c] Bijections v0.2.2
[d1d4a3ce] BitFlags v0.1.9
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[764a87c0] BoundaryValueDiffEq v5.18.0
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[85d9eb09] BoundaryValueDiffEqFIRK v1.9.0
[1a22d4ce] BoundaryValueDiffEqMIRK v1.9.0
[9255f1d6] BoundaryValueDiffEqMIRKN v1.8.0
[ed55bfe0] BoundaryValueDiffEqShooting v1.9.0
[70df07ce] BracketingNonlinearSolve v1.3.0
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⌅ [f6369f11] ForwardDiff v0.10.38
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[34004b35] HypergeometricFunctions v0.3.28
[615f187c] IfElse v0.1.1
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⌃ [98e50ef6] JuliaFormatter v1.0.62
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[442fdcdd] Measures v0.3.2
[94925ecb] MethodOfLines v0.11.9
[e1d29d7a] Missings v1.2.0
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[102ac46a] MultivariatePolynomials v0.5.9
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[04162be5] OrdinaryDiffEqQPRK v1.1.0
[af6ede74] OrdinaryDiffEqRKN v1.1.0
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[2d112036] OrdinaryDiffEqSDIRK v1.3.0
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[e3e12d00] OrdinaryDiffEqStabilizedIRK v1.3.0
[358294b1] OrdinaryDiffEqStabilizedRK v1.1.0
[fa646aed] OrdinaryDiffEqSymplecticRK v1.3.0
[b1df2697] OrdinaryDiffEqTsit5 v1.1.0
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[a7812802] PDEBase v0.1.19
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[91a5bcdd] Plots v1.40.16
[e409e4f3] PoissonRandom v0.4.4
[f517fe37] Polyester v0.7.18
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[27ebfcd6] Primes v0.5.7
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[c0aeaf25] SciMLOperators v1.3.1
[431bcebd] SciMLPublic v1.0.0
[53ae85a6] SciMLStructures v1.7.0
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[efcf1570] Setfield v1.1.2
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⌅ [fb77eaff] Sundials_jll v5.2.3+0
[a44049a8] Vulkan_Loader_jll v1.3.243+0
[a2964d1f] Wayland_jll v1.23.1+1
⌅ [02c8fc9c] XML2_jll v2.13.6+1
[ffd25f8a] XZ_jll v5.8.1+0
[f67eecfb] Xorg_libICE_jll v1.1.2+0
[c834827a] Xorg_libSM_jll v1.2.6+0
[4f6342f7] Xorg_libX11_jll v1.8.12+0
[0c0b7dd1] Xorg_libXau_jll v1.0.13+0
[935fb764] Xorg_libXcursor_jll v1.2.4+0
[a3789734] Xorg_libXdmcp_jll v1.1.6+0
[1082639a] Xorg_libXext_jll v1.3.7+0
[d091e8ba] Xorg_libXfixes_jll v6.0.1+0
[a51aa0fd] Xorg_libXi_jll v1.8.3+0
[d1454406] Xorg_libXinerama_jll v1.1.6+0
[ec84b674] Xorg_libXrandr_jll v1.5.5+0
[ea2f1a96] Xorg_libXrender_jll v0.9.12+0
[c7cfdc94] Xorg_libxcb_jll v1.17.1+0
[cc61e674] Xorg_libxkbfile_jll v1.1.3+0
[e920d4aa] Xorg_xcb_util_cursor_jll v0.1.5+0
[12413925] Xorg_xcb_util_image_jll v0.4.1+0
[2def613f] Xorg_xcb_util_jll v0.4.1+0
[975044d2] Xorg_xcb_util_keysyms_jll v0.4.1+0
[0d47668e] Xorg_xcb_util_renderutil_jll v0.3.10+0
[c22f9ab0] Xorg_xcb_util_wm_jll v0.4.2+0
[35661453] Xorg_xkbcomp_jll v1.4.7+0
[33bec58e] Xorg_xkeyboard_config_jll v2.44.0+0
[c5fb5394] Xorg_xtrans_jll v1.6.0+0
[3161d3a3] Zstd_jll v1.5.7+1
[35ca27e7] eudev_jll v3.2.14+0
[214eeab7] fzf_jll v0.61.1+0
[a4ae2306] libaom_jll v3.11.0+0
⌅ [0ac62f75] libass_jll v0.15.2+0
[1183f4f0] libdecor_jll v0.2.2+0
[2db6ffa8] libevdev_jll v1.13.4+0
[f638f0a6] libfdk_aac_jll v2.0.4+0
[36db933b] libinput_jll v1.28.1+0
[b53b4c65] libpng_jll v1.6.50+0
[f27f6e37] libvorbis_jll v1.3.7+2
[009596ad] mtdev_jll v1.1.7+0
[1317d2d5] oneTBB_jll v2022.0.0+0
⌅ [1270edf5] x264_jll v2021.5.5+0
⌅ [dfaa095f] x265_jll v3.5.0+0
[d8fb68d0] xkbcommon_jll v1.9.2+0
[0dad84c5] ArgTools v1.1.2
[56f22d72] Artifacts v1.11.0
[2a0f44e3] Base64 v1.11.0
[ade2ca70] Dates v1.11.0
[8ba89e20] Distributed v1.11.0
[f43a241f] Downloads v1.6.0
[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
[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- Output of
versioninfo()
Julia Version 1.11.5
Commit 760b2e5b73 (2025-04-14 06:53 UTC)
Build Info:
Official https://julialang.org/ release
Platform Info:
OS: Windows (x86_64-w64-mingw32)
CPU: 12 × 13th Gen Intel(R) Core(TM) i7-1365U
WORD_SIZE: 64
LLVM: libLLVM-16.0.6 (ORCJIT, goldmont)
Threads: 6 default, 0 interactive, 3 GC (on 12 virtual cores)
Environment:
JULIA_EDITOR = code
JULIA_VSCODE_REPL = 1
JULIA_NUM_THREADS = 6Additional context
I'm trying to create a "generic" ODEProblem, in the sense that it is very tunable thanks to an important number of parameters. The objective is it perform inverse modeling on this ODEProblem, so doing optimization. In my case there a two kinds of parameters: the "constants" (constant per experiment, not provided to cost function), and the "tunables" (to be optimized, so varying throughout the experiment). The good thing with a "generic" ODEProblem is that we pay the discretization time once (since we can save the ODEProblem using Serialization for instance). The drawback so far (after some benchmark) is that the "constant" parameters hurt the optimization time.