Incorrect solution.stats.nf in implicit methods on SecondOrderODEProblems

[nathanaelbosch]

Describe the bug 🐞

On SecondOrderODEProblems, the reported number of function evaluations in sol.stats.nf is incorrect for some implicit methods. This is probably linked to the Jacobian computation, as setting autodiff=false fixes this.

Minimal Reproducible Example 👇

Here is a small test function to evaluate a given algorithm

using Test
using OrdinaryDiffEq

function test_nf(alg)
    f_counter = [0]
    function f(ddu, du, u, p, t; f_counter=f_counter)
        f_counter .+= 1
        ddu .= p .* u
        return nothing
    end
    u0 = [1.0]
    du0 = [0.0]
    p = [-1.0]
    tspan = (0.0, 1.0)
    prob = SecondOrderODEProblem(f, du0, u0, tspan, p)
    sol = solve(prob, alg, save_everystep=false, dense=false)
    @test sol.stats.nf == f_counter[1]
end

We can then try a bunch of different solvers:

julia> test_nf(Tsit5())
Test Passed

julia> test_nf(RadauIIA5())
Test Failed at REPL[55]:14
  Expression: sol.stats.nf == f_counter[1]
   Evaluated: 28 == 27

ERROR: There was an error during testing

julia> test_nf(RadauIIA5(autodiff=false))
Test Passed

julia> test_nf(Rosenbrock23())
Test Failed at REPL[55]:14
  Expression: sol.stats.nf == f_counter[1]
   Evaluated: 73 == 59

ERROR: There was an error during testing

julia> test_nf(Rosenbrock23(autodiff=false))
Test Passed

So since only the two implicit methods fail, and autodiff=false fixes this, this issue is most likely linked to the Jacobian computation.

Environment:

• Output of using Pkg; Pkg.status()

Status `~/.julia/dev/ProbNumDiffEq/test/Project.toml`
  [4c88cf16] Aqua v0.8.9
  [8e7c35d0] BlockArrays v1.1.1
  [f3b72e0c] DiffEqDevTools v2.45.1
  [1a297f60] FillArrays v1.13.0
  [6a86dc24] FiniteDiff v2.26.0
  [26cc04aa] FiniteDifferences v0.12.32
  [b59a298d] FiniteHorizonGramians v0.2.1
  [f6369f11] ForwardDiff v0.10.38
  [c3a54625] JET v0.9.12
  [2c470bb0] Kronecker v0.5.5
  [92481ed7] LinearRegression v0.2.1
  [961ee093] ModelingToolkit v9.51.0
  [fdc4e326] ODEProblemLibrary v0.1.8
  [1dea7af3] OrdinaryDiffEq v6.90.1
  [65888b18] ParameterizedFunctions v5.17.0
  [91a5bcdd] Plots v1.40.9
  [bf3e78b0] ProbNumDiffEq v0.16.2 `~/.julia/dev/ProbNumDiffEq`
  [1bc83da4] SafeTestsets v0.1.0
  [ce78b400] SimpleUnPack v1.1.0
  [10745b16] Statistics v1.11.1
  [98d24dd4] TestSetExtensions v3.0.0
  [a759f4b9] TimerOutputs v0.5.25
  [37e2e46d] LinearAlgebra v1.11.0
  [9a3f8284] Random v1.11.0
  [8dfed614] Test v1.11.0

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

Status `~/.julia/dev/ProbNumDiffEq/test/Manifest.toml`
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  [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
  [3161d3a3] Zstd_jll v1.5.6+1
  [35ca27e7] eudev_jll v3.2.9+0
  [214eeab7] fzf_jll v0.53.0+0
  [1a1c6b14] gperf_jll v3.1.1+0
  [a4ae2306] libaom_jll v3.9.0+0
  [0ac62f75] libass_jll v0.15.2+0
  [1183f4f0] libdecor_jll v0.2.2+0
  [2db6ffa8] libevdev_jll v1.11.0+0
  [f638f0a6] libfdk_aac_jll v2.0.3+0
  [36db933b] libinput_jll v1.18.0+0
  [b53b4c65] libpng_jll v1.6.44+0
  [f27f6e37] libvorbis_jll v1.3.7+2
  [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 v1.1.2
  [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 v0.8.1+2
  [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 ⌅ have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated -m`

• Output of versioninfo()

Julia Version 1.11.1
Commit 8f5b7ca12ad (2024-10-16 10:53 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 6 × 13th Gen Intel(R) Core(TM) i9-13900K
  WORD_SIZE: 64
  LLVM: libLLVM-16.0.6 (ORCJIT, alderlake)
Threads: 6 default, 0 interactive, 3 GC (on 6 virtual cores)
Environment:
  JULIA_NUM_THREADS = auto

[ChrisRackauckas]

So since only the two implicit methods fail, and autodiff=false fixes this, this issue is most likely linked to the Jacobian computation.

Maybe we just make sure it's corrected with the change to DI?