Different gradient behaviour depending on ODE-Definition

Hi everyone,

I have started using Julia for the identification of ODE-parameters using DiffEqFlux. I noticed some strange behaviour of the “gradient” function that I cannot explain. The following code (which of course makes no sense) is the simplest example for which the behaviour occurs.

using DiffEqFlux, DifferentialEquations

function testODE(du,u,p,t)
  du[1:2] = -ones(2,2)*u[1:2]
end

function loss(x)
  u0 = [1.0, 1.0]
  tspan = (0.0,1.0)
  prob = ODEProblem(testODE,u0,tspan,rand(300))
  sim = solve(prob,Tsit5(),saveat=0.1)
  return sum(sim[end])
end

x = [1.0]

display(loss(x))

gradient(x -> loss(x),x)  

When I run this code (in Visual Studio Code) the REPL crashes while evaluating the gradient with the following error message:

The terminal process “C:\Users\eric-\AppData\Local\Programs\Julia-1.7.1\bin\julia.exe ‘-i’, ‘–banner=no’, ‘–project=C:\Users\eric-.julia\environments\v1.7’, ‘c:\Users\eric-.vscode\extensions\julialang.language-julia-1.5.10\scripts\terminalserver\terminalserver.jl’, ‘\.\pipe\vsc-jl-repl-eab064eb-17b5-44b3-9c65-518b53d97dea’, ‘\.\pipe\vsc-jl-cr-a566239a-d20f-437a-b12d-f78838a9b01a’, ‘USE_REVISE=true’, ‘USE_PLOTPANE=true’, ‘USE_PROGRESS=true’, ‘DEBUG_MODE=false’” terminated with exit code: 3.

However, if I define the testODE function as:

function testODE(du,u,p,t)
  du[1] = -1.0*u[1] - 1.0*u[2]
  du[2] = -1.0*u[1] - 1.0*u[2]
end

everything works as expected. In both cases the loss function is evaluated correctly. Can someone explain to me why this happens?

Thanks in advance!
Eric

You need to use du[1:2] .= -ones(2,2)*u[1:2]. Otherwise you aren’t modifying du.

Thank you for your reply. The error however still occurs.

Some additional information:
Apparently the problem has nothing to do with Visual Studio code, it also appears if I am starting the code from the julia.exe.
Furthermore a lot of text rushes through the terminal before the crash.

Have I missed something or is loss both independent of the input x and itself random? Additionally, for the ODE which ‘works’, it produces (nothing,) which seems odd? Sorry since that doesn’t answer the question at hand but it’s confusing and might be helpful if clarified?

Yes the loss function is independent of x and therefore the gradient (in the “working” example) produces the expected solution which is (nothing,), i.e. zero.

The random ODE parameters are an artifact from another minimal working example where the same error as described above appeared for a large number of ODE-parameters and did not appear for a low number of ODE-parameters.

I modified the MWE. The following code works out fine

using DiffEqFlux, DifferentialEquations

function testODE(du,u,p,t)
  du[1:2] = -p[1]*ones(2,2)*u[1:2]
end

function loss(x)
  u0 = [1.0, 1.0]
  tspan = (0.0,1.0)
  prob = ODEProblem(testODE,u0,tspan,ones(1))
  sim = solve(prob,Tsit5(),saveat=0.1)
  return sum(sim[end])
end

x = [1.0]

display(loss(x))

gradient(x -> loss(x),x)  

When I change the number of ODE-parameters the same error as described above appears and again I do not understand why:

using DiffEqFlux, DifferentialEquations

function testODE(du,u,p,t)
  du[1:2] = -p[1]*ones(2,2)*u[1:2]
end

function loss(x)
  u0 = [1.0, 1.0]
  tspan = (0.0,1.0)
  prob = ODEProblem(testODE,u0,tspan,ones(300))
  sim = solve(prob,Tsit5(),saveat=0.1)
  return sum(sim[end])
end

x = [1.0]

display(loss(x))

gradient(x -> loss(x),x)  

This is again just a stupid example but for my actual problem I need the high number of ODE-parameters.

Share your manifest.

Do you mean the contents of Manifest.toml? That would be the following:

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Since it is quite big, in three parts

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uuid = "a51aa0fd-4e3c-5386-b890-e753decda492"
version = "1.7.10+4"

[[deps.Xorg_libXinerama_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll"]
git-tree-sha1 = "26be8b1c342929259317d8b9f7b53bf2bb73b123"
uuid = "d1454406-59df-5ea1-beac-c340f2130bc3"
version = "1.1.4+4"

[[deps.Xorg_libXrandr_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll"]
git-tree-sha1 = "34cea83cb726fb58f325887bf0612c6b3fb17631"
uuid = "ec84b674-ba8e-5d96-8ba1-2a689ba10484"
version = "1.5.2+4"

[[deps.Xorg_libXrender_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "19560f30fd49f4d4efbe7002a1037f8c43d43b96"
uuid = "ea2f1a96-1ddc-540d-b46f-429655e07cfa"
version = "0.9.10+4"

[[deps.Xorg_libpthread_stubs_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "6783737e45d3c59a4a4c4091f5f88cdcf0908cbb"
uuid = "14d82f49-176c-5ed1-bb49-ad3f5cbd8c74"
version = "0.1.0+3"

[[deps.Xorg_libxcb_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "XSLT_jll", "Xorg_libXau_jll", "Xorg_libXdmcp_jll", "Xorg_libpthread_stubs_jll"]
git-tree-sha1 = "daf17f441228e7a3833846cd048892861cff16d6"
uuid = "c7cfdc94-dc32-55de-ac96-5a1b8d977c5b"
version = "1.13.0+3"

[[deps.Xorg_libxkbfile_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "926af861744212db0eb001d9e40b5d16292080b2"
uuid = "cc61e674-0454-545c-8b26-ed2c68acab7a"
version = "1.1.0+4"

[[deps.Xorg_xcb_util_image_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "0fab0a40349ba1cba2c1da699243396ff8e94b97"
uuid = "12413925-8142-5f55-bb0e-6d7ca50bb09b"
version = "0.4.0+1"

[[deps.Xorg_xcb_util_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll"]
git-tree-sha1 = "e7fd7b2881fa2eaa72717420894d3938177862d1"
uuid = "2def613f-5ad1-5310-b15b-b15d46f528f5"
version = "0.4.0+1"

[[deps.Xorg_xcb_util_keysyms_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "d1151e2c45a544f32441a567d1690e701ec89b00"
uuid = "975044d2-76e6-5fbe-bf08-97ce7c6574c7"
version = "0.4.0+1"

[[deps.Xorg_xcb_util_renderutil_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "dfd7a8f38d4613b6a575253b3174dd991ca6183e"
uuid = "0d47668e-0667-5a69-a72c-f761630bfb7e"
version = "0.3.9+1"

[[deps.Xorg_xcb_util_wm_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "e78d10aab01a4a154142c5006ed44fd9e8e31b67"
uuid = "c22f9ab0-d5fe-5066-847c-f4bb1cd4e361"
version = "0.4.1+1"

[[deps.Xorg_xkbcomp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxkbfile_jll"]
git-tree-sha1 = "4bcbf660f6c2e714f87e960a171b119d06ee163b"
uuid = "35661453-b289-5fab-8a00-3d9160c6a3a4"
version = "1.4.2+4"

[[deps.Xorg_xkeyboard_config_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xkbcomp_jll"]
git-tree-sha1 = "5c8424f8a67c3f2209646d4425f3d415fee5931d"
uuid = "33bec58e-1273-512f-9401-5d533626f822"
version = "2.27.0+4"

[[deps.Xorg_xtrans_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "79c31e7844f6ecf779705fbc12146eb190b7d845"
uuid = "c5fb5394-a638-5e4d-96e5-b29de1b5cf10"
version = "1.4.0+3"

[[deps.ZipFile]]
deps = ["Libdl", "Printf", "Zlib_jll"]
git-tree-sha1 = "3593e69e469d2111389a9bd06bac1f3d730ac6de"
uuid = "a5390f91-8eb1-5f08-bee0-b1d1ffed6cea"
version = "0.9.4"

[[deps.Zlib_jll]]
deps = ["Libdl"]
uuid = "83775a58-1f1d-513f-b197-d71354ab007a"

[[deps.Zstd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "cc4bf3fdde8b7e3e9fa0351bdeedba1cf3b7f6e6"
uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
version = "1.5.0+0"

[[deps.Zygote]]
deps = ["AbstractFFTs", "ChainRules", "ChainRulesCore", "DiffRules", "Distributed", "FillArrays", "ForwardDiff", "IRTools", "InteractiveUtils", "LinearAlgebra", "MacroTools", "NaNMath", "Random", "Requires", "SpecialFunctions", "Statistics", "ZygoteRules"]
git-tree-sha1 = "78da1a0a69bcc86b33f7cb07bc1566c926412de3"
uuid = "e88e6eb3-aa80-5325-afca-941959d7151f"
version = "0.6.33"

[[deps.ZygoteRules]]
deps = ["MacroTools"]
git-tree-sha1 = "8c1a8e4dfacb1fd631745552c8db35d0deb09ea0"
uuid = "700de1a5-db45-46bc-99cf-38207098b444"
version = "0.2.2"

[[deps.libass_jll]]
deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "5982a94fcba20f02f42ace44b9894ee2b140fe47"
uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0"
version = "0.15.1+0"

[[deps.libblastrampoline_jll]]
deps = ["Artifacts", "Libdl", "OpenBLAS_jll"]
uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"

[[deps.libfdk_aac_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "daacc84a041563f965be61859a36e17c4e4fcd55"
uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280"
version = "2.0.2+0"

[[deps.libpng_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "94d180a6d2b5e55e447e2d27a29ed04fe79eb30c"
uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
version = "1.6.38+0"

[[deps.libvorbis_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"]
git-tree-sha1 = "c45f4e40e7aafe9d086379e5578947ec8b95a8fb"
uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
version = "1.3.7+0"

[[deps.nghttp2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"

[[deps.p7zip_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"

[[deps.x264_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4fea590b89e6ec504593146bf8b988b2c00922b2"
uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
version = "2021.5.5+0"

[[deps.x265_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9"
uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
version = "3.5.0+0"

[[deps.xkbcommon_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"]
git-tree-sha1 = "ece2350174195bb31de1a63bea3a41ae1aa593b6"
uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd"
version = "0.9.1+5"

It looks like this is an Enzyme.jl crash. MWE:

using Enzyme

function testODE(du,u,p)
  du[1:2] = -p[1]*ones(2,2)*u[1:2]
  return nothing
end
tmp1 = [1.0, 1.0]
tmp2 = copy(tmp1)
tmp3 = copy(tmp1)
tmp4 = copy(tmp1)
p = [1.0]
Enzyme.autodiff(testODE,Enzyme.Duplicated(tmp1, tmp2),
                Enzyme.Duplicated(tmp3, tmp4),
                p)

Smaller number of parameters defaults to forward-mode AD, so it’s only when you get to large enough parameters that it’s switching to Enzyme and hitting this. Normally it would try Enzyme and when it fails it would give up and try something else, but because it’s segfaulting it can’t try/catch. Issue: Crash on multidimensional setindex · Issue #175 · wsmoses/Enzyme.jl · GitHub

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