Calling reinit! makes the solver unstable

[cstjean]

Describe the bug 🐞

Calling reinit! on a freshly created integrator makes the solver unstable.

integrator = DifferentialEquations.init(prob)
step!(integrator, 0.01, true)   # succeeds

integrator = DifferentialEquations.init(prob)
reinit!(integrator)
step!(integrator, 0.01, true)   # fails

Expected behavior

The docstring

Reinitialize integrator with (optionally) different initial state u0, different integration interval from t0 to tf, and erased solution if erase_sol = true.

led me to believe that reinit!(integrator) should be a no-op on a fresh integrator. If this is the intended meaning, then there's a bug...

Minimal Reproducible Example 👇

using Revise, DifferentialEquations, ModelingToolkit
using ModelingToolkit: t_nounits as t, D_nounits as D

f(c, T) = (1 - 3 * c ^ 2)

@mtkmodel Tank begin
    @variables begin
        M1(t)
        M2(t)
        c(t)
        b(t)
    end
    @equations begin
        D(M1) ~ b + c
        D(M2) ~ (1 - b) + (1 - c)
        c ~ M1 / (M1 + M2)
        (M1 + M2) * f(c, 80) ~ 10
    end
end

@mtkbuild tank = Tank();

prob = ODEProblem(tank, [tank.c => 0.6], (0, 10.0), [],
                  guesses=[tank.M1 => 5,
                           tank.M2 => 5,
                           tank.b => 2])

integrator = DifferentialEquations.init(prob)
reinit!(integrator)   # disable to make it succeed

step!(integrator, 0.01, true)
if check_error(integrator) != ReturnCode.Success
    @error("Solver has error: $(check_error(integrator))")
end

Error & Stacktrace ⚠️

┌ Warning: At t=0.0, dt was forced below floating point epsilon 5.0e-324, and step error estimate = NaN. Aborting. There is either an error in your model specification or the true solution is unstable (or the true solution can not be represented in the precision of Float64).
└ @ SciMLBase C:\Users\\.julia\packages\SciMLBase\Pma4a\src\integrator_interface.jl:623
┌ Error: Solver has error: Unstable
└ @ Main C:\Users\\Documents\\play_env\test.jl:33

Environment (please complete the following information):

• Output of using Pkg; Pkg.status()

  [82cc6244] DataInterpolations v7.1.0
  [0c46a032] DifferentialEquations v7.15.0
  [5b8099bc] DomainSets v0.7.15
  [961ee093] ModelingToolkit v9.62.0
  [91a5bcdd] Plots v1.40.9
  [295af30f] Revise v3.7.2

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

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  [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 v1.6.46+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+2
  [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
  [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 v5.11.0+0
  [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 Version 1.10.5
Commit 6f3fdf7b36 (2024-08-27 14:19 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Windows (x86_64-w64-mingw32)
  CPU: 8 × 11th Gen Intel(R) Core(TM) i5-1135G7 @ 2.40GHz
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-15.0.7 (ORCJIT, tigerlake)
Threads: 1 default, 0 interactive, 1 GC (on 8 virtual cores)
Environment:
  JULIA_SSL_CA_ROOTS_PATH =

Additional context

Probably not related to #3370, but I used a similar MWE (except that here there is no @register_symbolic f(c, T), which fixes the problem in that issue.

This is probably a DifferentialEquations bug, but I'd be lost trying to create a MWE for that package.

[AayushSabharwal]

This happens because the integrator resets integ.u0 to integ.sol.prob.u0, but that doesn't satisfy algebraic constraints until initialization is rerun. I'll PR to OrdinaryDiffEq to fix this.