Large memory usage proportional to time span

[ggggggggg]

Describe the bug 🐞
Unexpected large memory usage proportional to tspan[2]-tspan[1] when solving a Delay Differential Equation with an oscillatory driving function. This might not be a bug, and may actually be a feature request to specify a maximum time lag I promise to never look beyond to limit the memory used by the history function.

Expected behavior
I expect memory usage to scale close to the amount of data to be saved. In this case for each time point it saves two state variables and time, at 8 bytes each, I expect ~24 bytes per sample. Instead sol.interp.f stores ~14000 bytes/sample. The amount required by sol.interp.f scales proportional to tspan[2]-tspan[1]. Clearly some amount of memory is required to enable the history function, but this seems excessive. In this MRE the single constant lag is less than 1 part in 10,000 of tspan[2]-tspan[1], so I expect that the memory usage required for the history function should not need to grow when tspan[2]-tspan[1] is increased.

The MRE includes a delay diff eq setup, and some code to calculate the bytes/sample used by various fields of the solution object sol. I want to solve for much longer values of tspan[2]-tspan[1] and the memory usage is the primary limiting factor. The dominant contribution by at least a factor of 100 is the field sol.interp.f. I believe this field is part of the implementation of the history function for the DDE.

Minimal Reproducible Example 👇

using DifferentialEquations

function qw_dde(du,u,h,params,t)
    a,b,c,d,rt,τ = params

    hId,hIu = h(params,t-τ)              
    hdId,hdIu = h(params,t-τ,Val{1})     

    du[1] = ( 4.28e-7*(-2.51e10)*sin(2.51e10*t) + c*(hIu - u[1]) + b*hdIu ) * a
    du[2] = hdId + (rt-1.0)*(u[2] + hId)/(d)
end

const tspan = (0.0, 1e-6)
const τ = 5.6e-11
const params = (0.66, -0.5, 4.4e11, 4.0e-12, 7.8e-6, τ)
h(params,t) = zeros(2);
h(params,t,::Type{Val{1}}) = zeros(2);
u0 = [0.0,0.0];
alg = MethodOfSteps(Tsit5());
saveat = LinRange(tspan[1], tspan[2], 5000)
prob = DDEProblem(qw_dde,u0,h,tspan,params; saveat=saveat, constant_lags=[τ]);


# Run simulation:
println("solve start")
@time sol = solve(prob,alg,reltol=1e-3,abstol=1e-9,maxiters=1e9);
println("solve done")


# investigate space usage
function pretty_print2(d::Dict, pre=1)
    # https://stackoverflow.com/questions/48195775/how-to-pretty-print-nested-dicts-in-julia
    todo = Vector{Tuple}()
    for (k,v) in d
        if typeof(v) <: Dict
            push!(todo, (k,v))
        else
            println(join(fill(" ", pre)) * "$(repr(k)) => $(repr(v))")
        end
    end

    for (k,d) in todo
        s = "$(repr(k)) => "
        println(join(fill(" ", pre)) * s)
        pretty_print2(d, pre+1+length(s))
    end
    nothing
end
# define a version of summarysize that doesn't choke on Vector{Vector{Vector{Float64}}}
# and returns a dict so we can see size by property
vec_safe_summary_size(x::Vector) = sum(vec_safe_summary_size(z) for z in x)
vec_safe_summary_size(x) = Base.summarysize(x)
# vec_safe_summary_size(sol::DelayDiffEq.HistoryODEIntegrator) = Dict(prop => vec_safe_summary_size(getproperty(sol, prop)) for prop in propertynames(sol))
# vec_safe_summary_size(sol::DelayDiffEq.HistoryFunction) = Dict(prop => vec_safe_summary_size(getproperty(sol, prop)) for prop in propertynames(sol))
# vec_safe_summary_size(sol::DelayDiffEq.ODEFunctionWrapper) = Dict(prop => vec_safe_summary_size(getproperty(sol, prop)) for prop in propertynames(sol))
vec_safe_summary_size(sol::OrdinaryDiffEq.InterpolationData) = Dict(prop => vec_safe_summary_size(getproperty(sol, prop)) for prop in propertynames(sol))
vec_safe_summary_size(sol::ODESolution) = Dict(prop => vec_safe_summary_size(getproperty(sol, prop)) for prop in propertynames(sol))
v = vec_safe_summary_size(sol)
calc_per_point(x, n) = x/n
calc_per_point(d::Dict, n) = Dict(key=>calc_per_point(val, n) for (key, val) in pairs(d))
println("bytes/point by property of sol")
pretty_print2(calc_per_point(v, length(sol)))
@show length(sol);
@show tspan;

Error & Stacktrace ⚠️

Environment (please complete the following information):

• Output of using Pkg; Pkg.status()

julia> using Pkg; Pkg.status()
Status `C:\Users\oneilg\AppData\Local\Temp\jl_tkEYFY\Project.toml`
  [0c46a032] DifferentialEquations v7.13.0

• Output of using Pkg; Pkg.status(; mode = PKGMODE_MANIFEST)

julia> using Pkg; Pkg.status(; mode = PKGMODE_MANIFEST)
Status `C:\Users\oneilg\AppData\Local\Temp\jl_tkEYFY\Manifest.toml`
  [47edcb42] ADTypes v0.2.6
  [79e6a3ab] Adapt v4.0.2
⌅ [ec485272] ArnoldiMethod v0.2.0
  [4fba245c] ArrayInterface v7.8.0
  [4c555306] ArrayLayouts v1.6.1
  [aae01518] BandedMatrices v1.5.0
  [6e4b80f9] BenchmarkTools v1.5.0
  [62783981] BitTwiddlingConvenienceFunctions v0.1.5
  [764a87c0] BoundaryValueDiffEq v5.6.3
  [fa961155] CEnum v0.5.0
  [2a0fbf3d] CPUSummary v0.2.4
  [49dc2e85] Calculus v0.5.1
  [d360d2e6] ChainRulesCore v1.23.0
  [fb6a15b2] CloseOpenIntervals v0.1.12
  [523fee87] CodecBzip2 v0.8.2
  [944b1d66] CodecZlib v0.7.4
  [38540f10] CommonSolve v0.2.4
  [bbf7d656] CommonSubexpressions v0.3.0
  [34da2185] Compat v4.14.0
  [2569d6c7] ConcreteStructs v0.2.3
  [187b0558] ConstructionBase v1.5.4
  [adafc99b] CpuId v0.3.1
  [9a962f9c] DataAPI v1.16.0
  [864edb3b] DataStructures v0.18.18
  [e2d170a0] DataValueInterfaces v1.0.0
  [bcd4f6db] DelayDiffEq v5.47.1
  [2b5f629d] DiffEqBase v6.148.0
  [459566f4] DiffEqCallbacks v3.3.0
  [77a26b50] DiffEqNoiseProcess v5.21.0
  [163ba53b] DiffResults v1.1.0
  [b552c78f] DiffRules v1.15.1
  [0c46a032] DifferentialEquations v7.13.0
  [b4f34e82] Distances v0.10.11
  [31c24e10] Distributions v0.25.107
  [ffbed154] DocStringExtensions v0.9.3
  [fa6b7ba4] DualNumbers v0.6.8
  [4e289a0a] EnumX v1.0.4
⌃ [f151be2c] EnzymeCore v0.6.5
  [d4d017d3] ExponentialUtilities v1.26.1
  [e2ba6199] ExprTools v0.1.10
  [9d29842c] FastAlmostBandedMatrices v0.1.0
  [7034ab61] FastBroadcast v0.2.8
  [9aa1b823] FastClosures v0.3.2
  [29a986be] FastLapackInterface v2.0.2
  [1a297f60] FillArrays v1.9.3
  [6a86dc24] FiniteDiff v2.22.0
  [f6369f11] ForwardDiff v0.10.36
  [069b7b12] FunctionWrappers v1.1.3
  [77dc65aa] FunctionWrappersWrappers v0.1.3
  [d9f16b24] Functors v0.4.7
  [46192b85] GPUArraysCore v0.1.6
  [c145ed77] GenericSchur v0.5.3
  [86223c79] Graphs v1.9.0
  [3e5b6fbb] HostCPUFeatures v0.1.16
  [34004b35] HypergeometricFunctions v0.3.23
  [615f187c] IfElse v0.1.1
  [d25df0c9] Inflate v0.1.4
  [92d709cd] IrrationalConstants v0.2.2
  [82899510] IteratorInterfaceExtensions v1.0.0
  [692b3bcd] JLLWrappers v1.5.0
  [682c06a0] JSON v0.21.4
  [ccbc3e58] JumpProcesses v9.10.1
  [ef3ab10e] KLU v0.6.0
  [ba0b0d4f] Krylov v0.9.5
  [10f19ff3] LayoutPointers v0.1.15
  [5078a376] LazyArrays v1.8.3
  [2d8b4e74] LevyArea v1.0.0
  [d3d80556] LineSearches v7.2.0
  [7ed4a6bd] LinearSolve v2.27.0
  [2ab3a3ac] LogExpFunctions v0.3.27
  [bdcacae8] LoopVectorization v0.12.166
  [1914dd2f] MacroTools v0.5.13
  [d125e4d3] ManualMemory v0.1.8
  [b8f27783] MathOptInterface v1.27.0
  [a3b82374] MatrixFactorizations v2.1.0
  [bb5d69b7] MaybeInplace v0.1.1
  [e1d29d7a] Missings v1.1.0
  [46d2c3a1] MuladdMacro v0.2.4
  [d8a4904e] MutableArithmetics v1.4.1
  [d41bc354] NLSolversBase v7.8.3
  [2774e3e8] NLsolve v4.5.1
  [77ba4419] NaNMath v1.0.2
  [8913a72c] NonlinearSolve v3.8.0
  [6fe1bfb0] OffsetArrays v1.13.0
  [429524aa] Optim v1.9.2
  [bac558e1] OrderedCollections v1.6.3
  [1dea7af3] OrdinaryDiffEq v6.74.0
  [90014a1f] PDMats v0.11.31
  [65ce6f38] PackageExtensionCompat v1.0.2
  [d96e819e] Parameters v0.12.3
  [69de0a69] Parsers v2.8.1
  [e409e4f3] PoissonRandom v0.4.4
  [f517fe37] Polyester v0.7.9
  [1d0040c9] PolyesterWeave v0.2.1
  [85a6dd25] PositiveFactorizations v0.2.4
  [d236fae5] PreallocationTools v0.4.20
  [aea7be01] PrecompileTools v1.2.0
  [21216c6a] Preferences v1.4.3
  [1fd47b50] QuadGK v2.9.4
  [74087812] Random123 v1.7.0
  [e6cf234a] RandomNumbers v1.5.3
  [3cdcf5f2] RecipesBase v1.3.4
  [731186ca] RecursiveArrayTools v3.10.1
  [f2c3362d] RecursiveFactorization v0.2.21
  [189a3867] Reexport v1.2.2
  [ae029012] Requires v1.3.0
  [ae5879a3] ResettableStacks v1.1.1
  [79098fc4] Rmath v0.7.1
  [7e49a35a] RuntimeGeneratedFunctions v0.5.12
  [94e857df] SIMDTypes v0.1.0
  [476501e8] SLEEFPirates v0.6.42
  [0bca4576] SciMLBase v2.29.0
  [c0aeaf25] SciMLOperators v0.3.8
  [efcf1570] Setfield v1.1.1
  [727e6d20] SimpleNonlinearSolve v1.5.0
  [699a6c99] SimpleTraits v0.9.4
  [ce78b400] SimpleUnPack v1.1.0
  [a2af1166] SortingAlgorithms v1.2.1
  [47a9eef4] SparseDiffTools v2.17.0
  [e56a9233] Sparspak v0.3.9
  [276daf66] SpecialFunctions v2.3.1
  [aedffcd0] Static v0.8.10
  [0d7ed370] StaticArrayInterface v1.5.0
  [90137ffa] StaticArrays v1.9.3
  [1e83bf80] StaticArraysCore v1.4.2
  [82ae8749] StatsAPI v1.7.0
  [2913bbd2] StatsBase v0.34.2
  [4c63d2b9] StatsFuns v1.3.1
  [9672c7b4] SteadyStateDiffEq v2.1.0
  [789caeaf] StochasticDiffEq v6.65.1
  [7792a7ef] StrideArraysCore v0.5.2
  [c3572dad] Sundials v4.24.0
  [2efcf032] SymbolicIndexingInterface v0.3.8
  [3783bdb8] TableTraits v1.0.1
  [bd369af6] Tables v1.11.1
  [8290d209] ThreadingUtilities v0.5.2
  [a759f4b9] TimerOutputs v0.5.23
  [3bb67fe8] TranscodingStreams v0.10.4
  [d5829a12] TriangularSolve v0.1.20
  [410a4b4d] Tricks v0.1.8
  [781d530d] TruncatedStacktraces v1.4.0
  [3a884ed6] UnPack v1.0.2
  [3d5dd08c] VectorizationBase v0.21.65
  [19fa3120] VertexSafeGraphs v0.2.0
  [6e34b625] Bzip2_jll v1.0.8+1
  [1d5cc7b8] IntelOpenMP_jll v2024.0.2+0
  [856f044c] MKL_jll v2024.0.0+0
  [efe28fd5] OpenSpecFun_jll v0.5.5+0
  [f50d1b31] Rmath_jll v0.4.0+0
⌅ [fb77eaff] Sundials_jll v5.2.2+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 v0.6.4
  [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 v1.1.0+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
  [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`

• Output of versioninfo()

julia> versioninfo()
Julia Version 1.10.2
Commit bd47eca2c8 (2024-03-01 10:14 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Windows (x86_64-w64-mingw32)
  CPU: 8 × Intel(R) Xeon(R) W-2123 CPU @ 3.60GHz
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-15.0.7 (ORCJIT, skylake-avx512)
Threads: 1 default, 0 interactive, 1 GC (on 8 virtual cores)

Additional context

Add any other context about the problem here.