issue with Zygote jacobian when accessing ODE solutions on the time dimension

[daviehh]

Describe the bug 🐞

Consider the example at doc, but one wishes to take the jacobian for all parameters, at a given time. The example works when taking the 1st element of the solution, at all times

solve(_prob, Tsit5(), reltol = 1e-6, abstol = 1e-6, saveat = 1)[1, :]

which does work for both ForwardDiff and Zygote. However, when one wishes to calculate the jacobian for all elements but at a given time, i.e. sol[:, i] instead of sol[i, :] as in the example, ForwardDiff gives the result but Zygote can give all zeros depending on how it's accessed: full code

using OrdinaryDiffEq
using Zygote
using SciMLSensitivity, ForwardDiff

function lotka_volterra!(du, u, p, t)
    du[1] = dx = p[1] * u[1] - p[2] * u[1] * u[2]
    du[2] = dy = -p[3] * u[2] + p[4] * u[1] * u[2]
end

p = [1.5, 1.0, 3.0, 1.0];
u0 = [1.0; 1.0];
prob = ODEProblem(lotka_volterra!, u0, (0.0, 10.0), p)
sol0 = solve(prob, Tsit5(), reltol=1e-6, abstol=1e-6)

function f_sol2(x, i)
    _prob = remake(prob, u0=x[1:2], p=x[3:end])
    sol = solve(_prob, Tsit5(), reltol=1e-6, abstol=1e-6, saveat=1)
    sol[:, i]
end

u0p = [u0; p]
df_zyg = Zygote.jacobian(x -> f_sol2(x, 6), u0p)[1]
df_fwd = ForwardDiff.jacobian(x -> f_sol2(x, 6), u0p)

in this case, df_zyg is all zero, while df_fwd works. Same if one access the interpolating sol(t) interface. However, if one access the solution at given time-step with the sol.u interface, Zygote works

function f_sol_u(x, i)
    _prob = remake(prob, u0=x[1:2], p=x[3:end])
    sol = solve(_prob, Tsit5(), reltol=1e-6, abstol=1e-6, saveat=1)
    sol.u[i]
end

df_zyg = Zygote.jacobian(x -> f_sol_u(x, 6), u0p)[1]
df_fwd = ForwardDiff.jacobian(x -> f_sol_u(x, 6), u0p)

which is a bit strange since sol.u[i] and sol[:, i] is 'hard equal ( === )', i.e. points to the same memory sol0.u[3] === sol0[:, 3] or check with pointer(sol0.u[3])

Expected behavior

Zygote.jacobian work with sol[:, i]

Minimal Reproducible Example 👇

using OrdinaryDiffEq
using Zygote
using SciMLSensitivity, ForwardDiff

function lotka_volterra!(du, u, p, t)
    du[1] = dx = p[1] * u[1] - p[2] * u[1] * u[2]
    du[2] = dy = -p[3] * u[2] + p[4] * u[1] * u[2]
end

p = [1.5, 1.0, 3.0, 1.0];
u0 = [1.0; 1.0];
prob = ODEProblem(lotka_volterra!, u0, (0.0, 10.0), p)
sol0 = solve(prob, Tsit5(), reltol=1e-6, abstol=1e-6)

function f_sol2(x, i)
    _prob = remake(prob, u0=x[1:2], p=x[3:end])
    sol = solve(_prob, Tsit5(), reltol=1e-6, abstol=1e-6, saveat=1)
    sol[:, i]
end

function f_sol_u(x, i)
    _prob = remake(prob, u0=x[1:2], p=x[3:end])
    sol = solve(_prob, Tsit5(), reltol=1e-6, abstol=1e-6, saveat=1)
    sol.u[i]
end

u0p = [u0; p]
df_zyg = Zygote.jacobian(x -> f_sol2(x, 6), u0p)[1]
df_fwd = ForwardDiff.jacobian(x -> f_sol2(x, 6), u0p)

df_zyg = Zygote.jacobian(x -> f_sol_u(x, 6), u0p)[1]
df_fwd = ForwardDiff.jacobian(x -> f_sol_u(x, 6), u0p)

sol0.u[3] === sol0[:, 3]

(added note) works when returning:

@views sol[:, i]

or

sol.u[i]

wrong Zygote.jacobian when returning

sol[:, i]

or

sol(i)

Error & Stacktrace ⚠️

N/A: error is giving 0 for non-zero results

Environment (please complete the following information):

• Output of using Pkg; Pkg.status()

Status `~/test_jl/environments/v1.10/Project.toml`
  [f6369f11] ForwardDiff v0.10.36
  [1dea7af3] OrdinaryDiffEq v6.89.0
  [1ed8b502] SciMLSensitivity v7.65.0
  [e88e6eb3] Zygote v0.6.70

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

Status `~/test_jl/environments/v1.10/Manifest.toml`
  [47edcb42] ADTypes v1.7.1
  [621f4979] AbstractFFTs v1.5.0
  [7d9f7c33] Accessors v0.1.37
  [79e6a3ab] Adapt v4.0.4
  [66dad0bd] AliasTables v1.1.3
  [ec485272] ArnoldiMethod v0.4.0
  [4fba245c] ArrayInterface v7.15.0
  [4c555306] ArrayLayouts v1.10.3
  [a9b6321e] Atomix v0.1.0
  [62783981] BitTwiddlingConvenienceFunctions v0.1.6
  [fa961155] CEnum v0.5.0
  [2a0fbf3d] CPUSummary v0.2.6
  [7057c7e9] Cassette v0.3.13
  [082447d4] ChainRules v1.69.0
  [d360d2e6] ChainRulesCore v1.24.0
  [fb6a15b2] CloseOpenIntervals v0.1.13
  [38540f10] CommonSolve v0.2.4
  [bbf7d656] CommonSubexpressions v0.3.1
  [f70d9fcc] CommonWorldInvalidations v1.0.0
  [34da2185] Compat v4.16.0
  [a33af91c] CompositionsBase v0.1.2
  [2569d6c7] ConcreteStructs v0.2.3
  [187b0558] ConstructionBase v1.5.7
  [adafc99b] CpuId v0.3.1
  [9a962f9c] DataAPI v1.16.0
  [864edb3b] DataStructures v0.18.20
  [e2d170a0] DataValueInterfaces v1.0.0
  [2b5f629d] DiffEqBase v6.154.0
  [459566f4] DiffEqCallbacks v3.8.0
  [77a26b50] DiffEqNoiseProcess v5.23.0
  [163ba53b] DiffResults v1.1.0
  [b552c78f] DiffRules v1.15.1
  [a0c0ee7d] DifferentiationInterface v0.5.15
  [b4f34e82] Distances v0.10.11
  [31c24e10] Distributions v0.25.111
  [ffbed154] DocStringExtensions v0.9.3
  [da5c29d0] EllipsisNotation v1.8.0
  [4e289a0a] EnumX v1.0.4
  [7da242da] Enzyme v0.12.33
  [f151be2c] EnzymeCore v0.7.8
  [d4d017d3] ExponentialUtilities v1.26.1
  [e2ba6199] ExprTools v0.1.10
⌅ [6b7a57c9] Expronicon v0.8.5
  [7034ab61] FastBroadcast v0.3.5
  [9aa1b823] FastClosures v0.3.2
  [29a986be] FastLapackInterface v2.0.4
  [1a297f60] FillArrays v1.13.0
  [6a86dc24] FiniteDiff v2.24.0
  [f6369f11] ForwardDiff v0.10.36
  [f62d2435] FunctionProperties v0.1.2
  [069b7b12] FunctionWrappers v1.1.3
  [77dc65aa] FunctionWrappersWrappers v0.1.3
  [d9f16b24] Functors v0.4.12
  [0c68f7d7] GPUArrays v10.3.1
  [46192b85] GPUArraysCore v0.1.6
⌃ [61eb1bfa] GPUCompiler v0.27.1
  [c145ed77] GenericSchur v0.5.4
  [86223c79] Graphs v1.11.2
  [3e5b6fbb] HostCPUFeatures v0.1.17
  [34004b35] HypergeometricFunctions v0.3.24
  [7869d1d1] IRTools v0.4.14
  [615f187c] IfElse v0.1.1
  [d25df0c9] Inflate v0.1.5
  [3587e190] InverseFunctions v0.1.16
  [92d709cd] IrrationalConstants v0.2.2
  [82899510] IteratorInterfaceExtensions v1.0.0
  [692b3bcd] JLLWrappers v1.5.0
  [ccbc3e58] JumpProcesses v9.13.4
  [ef3ab10e] KLU v0.6.0
  [63c18a36] KernelAbstractions v0.9.25
  [ba0b0d4f] Krylov v0.9.6
⌅ [929cbde3] LLVM v8.1.0
  [10f19ff3] LayoutPointers v0.1.17
  [5078a376] LazyArrays v2.2.0
  [2d8b4e74] LevyArea v1.0.0
  [d3d80556] LineSearches v7.3.0
  [7ed4a6bd] LinearSolve v2.33.0
  [2ab3a3ac] LogExpFunctions v0.3.28
  [bdcacae8] LoopVectorization v0.12.171
  [d8e11817] MLStyle v0.4.17
  [1914dd2f] MacroTools v0.5.13
  [d125e4d3] ManualMemory v0.1.8
  [bb5d69b7] MaybeInplace v0.1.4
  [e1d29d7a] Missings v1.2.0
  [46d2c3a1] MuladdMacro v0.2.4
  [d41bc354] NLSolversBase v7.8.3
  [2774e3e8] NLsolve v4.5.1
  [872c559c] NNlib v0.9.22
  [77ba4419] NaNMath v1.0.2
  [8913a72c] NonlinearSolve v3.14.0
  [d8793406] ObjectFile v0.4.2
  [6fe1bfb0] OffsetArrays v1.14.1
  [429524aa] Optim v1.9.4
  [3bd65402] Optimisers v0.3.3
  [bac558e1] OrderedCollections v1.6.3
  [1dea7af3] OrdinaryDiffEq v6.89.0
  [89bda076] OrdinaryDiffEqAdamsBashforthMoulton v1.1.0
  [6ad6398a] OrdinaryDiffEqBDF v1.1.0
  [bbf590c4] OrdinaryDiffEqCore v1.3.0
  [50262376] OrdinaryDiffEqDefault v1.1.0
  [4302a76b] OrdinaryDiffEqDifferentiation v1.1.0
  [9286f039] OrdinaryDiffEqExplicitRK v1.1.0
  [e0540318] OrdinaryDiffEqExponentialRK v1.1.0
  [becaefa8] OrdinaryDiffEqExtrapolation v1.1.0
  [5960d6e9] OrdinaryDiffEqFIRK v1.1.0
  [101fe9f7] OrdinaryDiffEqFeagin v1.1.0
  [d3585ca7] OrdinaryDiffEqFunctionMap v1.1.0
  [d28bc4f8] OrdinaryDiffEqHighOrderRK v1.1.0
  [9f002381] OrdinaryDiffEqIMEXMultistep v1.1.0
  [521117fe] OrdinaryDiffEqLinear v1.1.0
  [1344f307] OrdinaryDiffEqLowOrderRK v1.1.0
  [b0944070] OrdinaryDiffEqLowStorageRK v1.2.0
  [127b3ac7] OrdinaryDiffEqNonlinearSolve v1.1.0
  [c9986a66] OrdinaryDiffEqNordsieck v1.1.0
  [5dd0a6cf] OrdinaryDiffEqPDIRK v1.1.0
  [5b33eab2] OrdinaryDiffEqPRK v1.1.0
  [04162be5] OrdinaryDiffEqQPRK v1.1.0
  [af6ede74] OrdinaryDiffEqRKN v1.1.0
  [43230ef6] OrdinaryDiffEqRosenbrock v1.1.0
  [2d112036] OrdinaryDiffEqSDIRK v1.1.0
  [669c94d9] OrdinaryDiffEqSSPRK v1.2.0
  [e3e12d00] OrdinaryDiffEqStabilizedIRK v1.1.0
  [358294b1] OrdinaryDiffEqStabilizedRK v1.1.0
  [fa646aed] OrdinaryDiffEqSymplecticRK v1.1.0
  [b1df2697] OrdinaryDiffEqTsit5 v1.1.0
  [79d7bb75] OrdinaryDiffEqVerner v1.1.0
  [90014a1f] PDMats v0.11.31
  [65ce6f38] PackageExtensionCompat v1.0.2
  [d96e819e] Parameters v0.12.3
  [e409e4f3] PoissonRandom v0.4.4
  [f517fe37] Polyester v0.7.16
  [1d0040c9] PolyesterWeave v0.2.2
  [85a6dd25] PositiveFactorizations v0.2.4
  [d236fae5] PreallocationTools v0.4.24
  [aea7be01] PrecompileTools v1.2.1
  [21216c6a] Preferences v1.4.3
  [43287f4e] PtrArrays v1.2.1
  [1fd47b50] QuadGK v2.10.1
  [74087812] Random123 v1.7.0
  [e6cf234a] RandomNumbers v1.6.0
  [c1ae055f] RealDot v0.1.0
  [3cdcf5f2] RecipesBase v1.3.4
  [731186ca] RecursiveArrayTools v3.27.0
  [f2c3362d] RecursiveFactorization v0.2.23
  [189a3867] Reexport v1.2.2
  [ae029012] Requires v1.3.0
  [ae5879a3] ResettableStacks v1.1.1
  [37e2e3b7] ReverseDiff v1.15.3
  [79098fc4] Rmath v0.7.1
  [7e49a35a] RuntimeGeneratedFunctions v0.5.13
  [94e857df] SIMDTypes v0.1.0
  [476501e8] SLEEFPirates v0.6.43
  [0bca4576] SciMLBase v2.50.6
  [c0aeaf25] SciMLOperators v0.3.10
  [1ed8b502] SciMLSensitivity v7.65.0
  [53ae85a6] SciMLStructures v1.4.2
  [6c6a2e73] Scratch v1.2.1
  [efcf1570] Setfield v1.1.1
  [727e6d20] SimpleNonlinearSolve v1.12.0
  [699a6c99] SimpleTraits v0.9.4
  [ce78b400] SimpleUnPack v1.1.0
  [a2af1166] SortingAlgorithms v1.2.1
  [47a9eef4] SparseDiffTools v2.20.0
  [dc90abb0] SparseInverseSubset v0.1.2
  [0a514795] SparseMatrixColorings v0.4.0
  [e56a9233] Sparspak v0.3.9
  [276daf66] SpecialFunctions v2.4.0
  [aedffcd0] Static v1.1.1
  [0d7ed370] StaticArrayInterface v1.8.0
  [90137ffa] StaticArrays v1.9.7
  [1e83bf80] StaticArraysCore v1.4.3
  [82ae8749] StatsAPI v1.7.0
  [2913bbd2] StatsBase v0.34.3
  [4c63d2b9] StatsFuns v1.3.1
  [789caeaf] StochasticDiffEq v6.68.0
  [7792a7ef] StrideArraysCore v0.5.7
  [09ab397b] StructArrays v0.6.18
  [53d494c1] StructIO v0.3.1
  [2efcf032] SymbolicIndexingInterface v0.3.28
  [3783bdb8] TableTraits v1.0.1
  [bd369af6] Tables v1.12.0
  [8290d209] ThreadingUtilities v0.5.2
  [a759f4b9] TimerOutputs v0.5.24
  [9f7883ad] Tracker v0.2.35
  [d5829a12] TriangularSolve v0.2.1
  [410a4b4d] Tricks v0.1.9
  [781d530d] TruncatedStacktraces v1.4.0
  [3a884ed6] UnPack v1.0.2
  [013be700] UnsafeAtomics v0.2.1
  [d80eeb9a] UnsafeAtomicsLLVM v0.2.1
  [3d5dd08c] VectorizationBase v0.21.70
  [19fa3120] VertexSafeGraphs v0.2.0
  [e88e6eb3] Zygote v0.6.70
  [700de1a5] ZygoteRules v0.2.5
  [7cc45869] Enzyme_jll v0.0.145+0
  [1d5cc7b8] IntelOpenMP_jll v2024.2.1+0
⌅ [dad2f222] LLVMExtra_jll v0.0.31+0
  [856f044c] MKL_jll v2024.2.0+0
  [efe28fd5] OpenSpecFun_jll v0.5.5+0
⌅ [f50d1b31] Rmath_jll v0.4.3+0
  [1317d2d5] oneTBB_jll v2021.12.0+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
  [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
  [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 6f3fdf7b362 (2024-08-27 14:19 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: macOS (arm64-apple-darwin22.4.0)
  CPU: 10 × Apple M1 Pro
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-15.0.7 (ORCJIT, apple-m1)
Threads: 1 default, 0 interactive, 1 GC (on 8 virtual cores)

Additional context

Add any other context about the problem here.

[ChrisRackauckas]

@DhairyaLGandhi could you take a look?

[DhairyaLGandhi]

Yeah I'll take a look at this.