Error using pmap on autodiff ODE solver inside Turing @model function

Our group is interested in fitting unknown parameters in our multi-physics model using the variational inference package AdvancedVI. To fit the parameters, we use experimental data from multiple tests and run a dynamical simulation for each test. Since these simulations can take up to a half hour each, we would like to use the pmap function inside the Turing @model function to speed up the process.

The code below is a toy-model representation of the script we are using. A good chunk of it is borrowed from the Turing.jl webpage:

using Distributed
@everywhere using Turing, ForwardDiff, OrdinaryDiffEq, StatsPlots, 
                  AdvancedVI, LinearAlgebra, Random

@everywhere Random.seed!(1)
using Plots; plotly()

# toggle autodiff on/off in ODE solver
@everywhere autodiff = true

# toy ODE system
@everywhere function lotka_volterra(du, u, p, t)
    Ξ±, Ξ², Ξ³, Ξ΄ = p
    x, y = u
    du[1] = (Ξ± - Ξ²*y) * x
    du[2] = (Ξ΄*x - Ξ³) * y
    return nothing
end

# simulation output
@everywhere function gen_predict(p, jobid)
    @info "Started job $jobid"
    u0 = [1.0, 1.0]
    tspan = (0.0, 10.0)
    prob = ODEProblem(lotka_volterra, u0, tspan, p)
    sol = solve(prob, TRBDF2(; autodiff); saveat = 0.1)
    return vcat(sol.u...)
end

# note: ADVI requires @everywhere to be placed here 
@everywhere @model function fit_lv(data)
    # sampling
    σ² ~ filldist(truncated(Normal(0.05, 0.0125); lower = 0, upper = 1.0), 1)
    Ξ± ~ filldist(truncated(Normal(1.5, 0.5); lower = 0.5, upper = 2.5), 1)
    Ξ² ~ filldist(truncated(Normal(1.2, 0.5); lower = 0, upper = 2), 1)
    Ξ³ ~ filldist(truncated(Normal(3.0, 0.5); lower = 1, upper = 4), 1)
    Ξ΄ ~ filldist(truncated(Normal(1.0, 0.5); lower = 0, upper = 2), 1)
    p = [Ξ±[1], Ξ²[1], Ξ³[1], Ξ΄[1]]

    # distribute simulation runs over two tests
    joblist = 1:2
    predict = pmap(jobid -> gen_predict(p, jobid), joblist)
    y_sim = vcat(predict...)
    # simulation vs experiment
    data ~ MvNormal(y_sim, σ²[1] * I)
    return nothing
end

# target parameter values
p = [1.5, 1.0, 3.0, 1.0]
# generate mock data points covering two tests
u0 = [1.0, 1.0]
tspan = (0.0, 10.0)
prob = ODEProblem(lotka_volterra, u0, tspan, p)
sol = solve(prob, TRBDF2(; autodiff); saveat = 0.1)
u = vcat(sol.u...)
data = vcat(0.9.*u..., 1.1.*u...)

# configure inference model and fit parameters
model = fit_lv(data)
advi = ADVI(1, 1000)
optimizer = Turing.Variational.TruncatedADAGrad(0.01, 1.0, 10)
@time res = vi(model, advi; optimizer)
println("\ndone")

Inside the @model function fit_lv is where we want to apply pmap to distribute the simulation runs over two test days while sampling the parameters serially. In the simulation function gen_predict, we generally use the solver TRBDF2(autodiff = true) with forward-mode auto-diff since our multi-physics model is stiff.

This script works fine if you run it on the main thread via julia. However, if you run it with julia -p 2 you get the following error on the solve line once ADVI is activated (Julia version is 1.8.5)

julia> include("sample_turing.jl")
β”Œ Info: [ADVI] Should only be seen once: optimizer created for ΞΈ
β””   objectid(ΞΈ) = 0x914e03f08498020d
ERROR: LoadError: On worker 3:
First call to automatic differentiation for the Jacobian
failed. This means that the user `f` function is not compatible
with automatic differentiation. Methods to fix this include:

1. Turn off automatic differentiation (e.g. Rosenbrock23() becomes
   Rosenbrock23(autodiff=false)). More details can befound at
   https://docs.sciml.ai/DiffEqDocs/stable/features/performance_overloads/
2. Improving the compatibility of `f` with ForwardDiff.jl automatic 
   differentiation (using tools like PreallocationTools.jl). More details
   can be found at https://docs.sciml.ai/DiffEqDocs/stable/basics/faq/#Autodifferentiation-and-Dual-Numbers
3. Defining analytical Jacobians. More details can be
   found at https://docs.sciml.ai/DiffEqDocs/stable/types/ode_types/#SciMLBase.ODEFunction

Note: turning off automatic differentiation tends to have a very minimal
performance impact (for this use case, because it's forward mode for a
square Jacobian. This is different from optimization gradient scenarios).
However, one should be careful as some methods are more sensitive to
accurate gradients than others. Specifically, Rodas methods like `Rodas4`
and `Rodas5P` require accurate Jacobians in order to have good convergence,
while many other methods like BDF (`QNDF`, `FBDF`), SDIRK (`KenCarp4`),
and Rosenbrock-W (`Rosenbrock23`) do not. Thus if using an algorithm which
is sensitive to autodiff and solving at a low tolerance, please change the
algorithm as well.

"No matching function wrapper was found!"
Stacktrace:
  [1] jacobian!
    @ ~/.julia/packages/OrdinaryDiffEq/CWSFV/src/derivative_wrappers.jl:230
  [2] calc_J!
    @ ~/.julia/packages/OrdinaryDiffEq/CWSFV/src/derivative_utils.jl:144 [inlined]
  [3] calc_W!
    @ ~/.julia/packages/OrdinaryDiffEq/CWSFV/src/derivative_utils.jl:691
  [4] update_W!
    @ ~/.julia/packages/OrdinaryDiffEq/CWSFV/src/derivative_utils.jl:799 [inlined]
  [5] update_W!
    @ ~/.julia/packages/OrdinaryDiffEq/CWSFV/src/derivative_utils.jl:798 [inlined]
  [6] nlsolve!
    @ ~/.julia/packages/OrdinaryDiffEq/CWSFV/src/nlsolve/nlsolve.jl:25
  [7] perform_step!
    @ ~/.julia/packages/OrdinaryDiffEq/CWSFV/src/perform_step/sdirk_perform_step.jl:481
  [8] perform_step!
    @ ~/.julia/packages/OrdinaryDiffEq/CWSFV/src/perform_step/sdirk_perform_step.jl:458 [inlined]
  [9] solve!
    @ ~/.julia/packages/OrdinaryDiffEq/CWSFV/src/solve.jl:520
 [10] #__solve#618
    @ ~/.julia/packages/OrdinaryDiffEq/CWSFV/src/solve.jl:6
 [11] #solve_call#22
    @ ~/.julia/packages/DiffEqBase/190F1/src/solve.jl:494 [inlined]
 [12] #solve_up#29
    @ ~/.julia/packages/DiffEqBase/190F1/src/solve.jl:915
 [13] #solve#27
    @ ~/.julia/packages/DiffEqBase/190F1/src/solve.jl:825

You get the same error if you used the Bayesian inference model NUTS with MCMCSerial

res = sample(model, NUTS(0.65), MCMCSerial(), 100, 1)

On Julia 1.7.3, you get a dimension error when performing floating point operations with dual numbers (e.g. in lokta_volterra). We suspect there is a dual number configuration issue when trying to use pmap on an auto-diff compatible solver within the Turing @model. When we set autodiff = false, the above code is able to run with the distributed pmap but we lose out on solver robustness (risking simulation crashes and potentially skewing the parameter fit)

If someone knows how to fix this bug where we can use both pmap and autodiff = true, we would greatly appreciate it!

1 Like

How come that’s the only thing that printed? Where’s all of the type information?

@ChrisRackauckas

stacktrace.jl (3.0 MB)

I threw a try-catch and got the type information. It’s quite long, so that why I’m using a file upload.

The easy solution here is just ODEProblem{true, SciMLBase.FullSpecialize}(lotka_volterra, u0, tspan, p). Did that not work when you tried it?

Thanks for your suggestion. We tried it but it still didn’t work. It resolves the wrapper error but then you get the floating point operation error mentioned previously (ran with julia -p 1 and NUTS)

      From worker 2:    [ Info: Started job 1
      From worker 2:    [ Info: Started job 2
      From worker 2:    [ Info: Started job 1
Sampling (Chain 1 of 1)   0%|                                                                                                       |  ETA: N/A
Sampling (Chain 1 of 1) 100%|β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ| Time: 0:00:48
ERROR: LoadError: On worker 2:
First call to automatic differentiation for the Jacobian
failed. This means that the user `f` function is not compatible
with automatic differentiation. Methods to fix this include:

1. Turn off automatic differentiation (e.g. Rosenbrock23() becomes
   Rosenbrock23(autodiff=false)). More details can befound at
   https://docs.sciml.ai/DiffEqDocs/stable/features/performance_overloads/
2. Improving the compatibility of `f` with ForwardDiff.jl automatic 
   differentiation (using tools like PreallocationTools.jl). More details
   can be found at https://docs.sciml.ai/DiffEqDocs/stable/basics/faq/#Autodifferentiation-and-Dual-Numbers
3. Defining analytical Jacobians. More details can be
   found at https://docs.sciml.ai/DiffEqDocs/stable/types/ode_types/#SciMLBase.ODEFunction

Note: turning off automatic differentiation tends to have a very minimal
performance impact (for this use case, because it's forward mode for a
square Jacobian. This is different from optimization gradient scenarios).
However, one should be careful as some methods are more sensitive to
accurate gradients than others. Specifically, Rodas methods like `Rodas4`
and `Rodas5P` require accurate Jacobians in order to have good convergence,
while many other methods like BDF (`QNDF`, `FBDF`), SDIRK (`KenCarp4`),
and Rosenbrock-W (`Rosenbrock23`) do not. Thus if using an algorithm which
is sensitive to autodiff and solving at a low tolerance, please change the
algorithm as well.

MethodError: no method matching Float64(::ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}, ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}, 1})
Closest candidates are:
  (::Type{T})(::Real, ::RoundingMode) where T<:AbstractFloat at rounding.jl:200
  (::Type{T})(::T) where T<:Number at boot.jl:772
  (::Type{T})(::AbstractChar) where T<:Union{AbstractChar, Number} at char.jl:50
  ...
Stacktrace:
  [1] jacobian!
    @ ~/.julia/packages/OrdinaryDiffEq/4OfcV/src/derivative_wrappers.jl:230
  [2] calc_J!
    @ ~/.julia/packages/OrdinaryDiffEq/4OfcV/src/derivative_utils.jl:144 [inlined]
  [3] calc_W!
    @ ~/.julia/packages/OrdinaryDiffEq/4OfcV/src/derivative_utils.jl:691
  [4] update_W!
    @ ~/.julia/packages/OrdinaryDiffEq/4OfcV/src/derivative_utils.jl:799 [inlined]
  [5] update_W!
    @ ~/.julia/packages/OrdinaryDiffEq/4OfcV/src/derivative_utils.jl:798 [inlined]
  [6] nlsolve!
    @ ~/.julia/packages/OrdinaryDiffEq/4OfcV/src/nlsolve/nlsolve.jl:25
  [7] perform_step!
    @ ~/.julia/packages/OrdinaryDiffEq/4OfcV/src/perform_step/sdirk_perform_step.jl:481
  [8] perform_step!
    @ ~/.julia/packages/OrdinaryDiffEq/4OfcV/src/perform_step/sdirk_perform_step.jl:458 [inlined]
  [9] solve!
    @ ~/.julia/packages/OrdinaryDiffEq/4OfcV/src/solve.jl:520
 [10] #__solve#623
    @ ~/.julia/packages/OrdinaryDiffEq/4OfcV/src/solve.jl:6
 [11] #solve_call#22
    @ ~/.julia/packages/DiffEqBase/egmnd/src/solve.jl:494 [inlined]
 [12] #solve_up#29
    @ ~/.julia/packages/DiffEqBase/egmnd/src/solve.jl:915
 [13] #solve#27
    @ ~/.julia/packages/DiffEqBase/egmnd/src/solve.jl:825

I attached a more informative stack trace, which you get by running the example file with julia -p 1
stacktrace_nuts.jl (72.5 KB)
example_turing.jl (2.4 KB)
Here I used NUTS instead of ADVI since the tags are less cumbersome (the errors are similar)

I just downloaded and ran it just fine. Are you on the latest versions of the SciML stack? ]st and ]st -m?

I ran the above code with julia -p 1 --project

versioninfo()
Julia Version 1.8.3
Commit 0434deb161e (2022-11-14 20:14 UTC)
Platform Info:
OS: macOS (arm64-apple-darwin21.3.0)
CPU: 10 Γ— Apple M1 Max
WORD_SIZE: 64
LIBM: libopenlibm
LLVM: libLLVM-13.0.1 (ORCJIT, apple-m1)
Threads: 8 on 8 virtual cores
Environment:
JULIA_NUM_THREADS = auto
JULIA_PKG_USE_CLI_GIT = true

]st
βŒ… [b5ca4192] AdvancedVI v0.1.6
[f6369f11] ForwardDiff v0.10.34
[1dea7af3] OrdinaryDiffEq v6.44.0
[91a5bcdd] Plots v1.38.5
[f3b207a7] StatsPlots v0.15.4
[fce5fe82] Turing v0.24.0
[37e2e46d] LinearAlgebra
[9a3f8284] Random

]st -m
[621f4979] AbstractFFTs v1.2.1
[80f14c24] AbstractMCMC v4.4.0
βŒ… [7a57a42e] AbstractPPL v0.5.3
[1520ce14] AbstractTrees v0.4.4
[79e6a3ab] Adapt v3.5.0
[0bf59076] AdvancedHMC v0.4.2
[5b7e9947] AdvancedMH v0.7.2
[576499cb] AdvancedPS v0.4.3
βŒ… [b5ca4192] AdvancedVI v0.1.6
[dce04be8] ArgCheck v2.3.0
[ec485272] ArnoldiMethod v0.2.0
[7d9fca2a] Arpack v0.5.4
[4fba245c] ArrayInterface v6.0.25
[30b0a656] ArrayInterfaceCore v0.1.29
[6ba088a2] ArrayInterfaceGPUArrays v0.2.2
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[b0d46f97] ArrayInterfaceStaticArrays v0.1.5
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βŒ… [76274a88] Bijectors v0.10.6
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βŒ… [366bfd00] DynamicPPL v0.21.6
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βŒ… [d9f16b24] Functors v0.3.0
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[a2af1166] SortingAlgorithms v1.1.0
[47a9eef4] SparseDiffTools v1.30.0
[e56a9233] Sparspak v0.3.9
[276daf66] SpecialFunctions v2.1.7
[171d559e] SplittablesBase v0.1.15
[aedffcd0] Static v0.8.3
[90137ffa] StaticArrays v1.5.15
[1e83bf80] StaticArraysCore v1.4.0
[64bff920] StatisticalTraits v3.2.0
[82ae8749] StatsAPI v1.5.0
[2913bbd2] StatsBase v0.33.21
[4c63d2b9] StatsFuns v1.1.1
[f3b207a7] StatsPlots v0.15.4
[7792a7ef] StrideArraysCore v0.4.7
[892a3eda] StringManipulation v0.3.0
[09ab397b] StructArrays v0.6.14
[2efcf032] SymbolicIndexingInterface v0.2.1
[ab02a1b2] TableOperations v1.2.0
[3783bdb8] TableTraits v1.0.1
[bd369af6] Tables v1.10.0
[62fd8b95] TensorCore v0.1.1
[5d786b92] TerminalLoggers v0.1.6
[8290d209] ThreadingUtilities v0.5.1
[9f7883ad] Tracker v0.2.23
[3bb67fe8] TranscodingStreams v0.9.11
[28d57a85] Transducers v0.4.75
[d5829a12] TriangularSolve v0.1.19
[410a4b4d] Tricks v0.1.6
[fce5fe82] Turing v0.24.0
[5c2747f8] URIs v1.4.1
[3a884ed6] UnPack v1.0.2
[1cfade01] UnicodeFun v0.4.1
[41fe7b60] Unzip v0.2.0
[3d5dd08c] VectorizationBase v0.21.58
[19fa3120] VertexSafeGraphs v0.2.0
[cc8bc4a8] Widgets v0.6.6
[efce3f68] WoodburyMatrices v0.5.5
[700de1a5] ZygoteRules v0.2.2
βŒ… [68821587] Arpack_jll v3.5.1+1
[6e34b625] Bzip2_jll v1.0.8+0
[83423d85] Cairo_jll v1.16.1+1
[2e619515] Expat_jll v2.4.8+0
[b22a6f82] FFMPEG_jll v4.4.2+2
[f5851436] FFTW_jll v3.3.10+0
[a3f928ae] Fontconfig_jll v2.13.93+0
[d7e528f0] FreeType2_jll v2.10.4+0
[559328eb] FriBidi_jll v1.0.10+0
[0656b61e] GLFW_jll v3.3.8+0
[d2c73de3] GR_jll v0.71.7+0
[78b55507] Gettext_jll v0.21.0+0
[7746bdde] Glib_jll v2.74.0+2
[3b182d85] Graphite2_jll v1.3.14+0
[2e76f6c2] HarfBuzz_jll v2.8.1+1
[1d5cc7b8] IntelOpenMP_jll v2018.0.3+2
[aacddb02] JpegTurbo_jll v2.1.2+0
[c1c5ebd0] LAME_jll v3.100.1+0
[88015f11] LERC_jll v3.0.0+1
[dd4b983a] LZO_jll v2.10.1+0
βŒ… [e9f186c6] Libffi_jll v3.2.2+1
[d4300ac3] Libgcrypt_jll v1.8.7+0
[7e76a0d4] Libglvnd_jll v1.6.0+0
[7add5ba3] Libgpg_error_jll v1.42.0+0
[94ce4f54] Libiconv_jll v1.16.1+2
[4b2f31a3] Libmount_jll v2.35.0+0
[89763e89] Libtiff_jll v4.4.0+0
[38a345b3] Libuuid_jll v2.36.0+0
[856f044c] MKL_jll v2022.2.0+0
[e7412a2a] Ogg_jll v1.3.5+1
[458c3c95] OpenSSL_jll v1.1.20+0
[efe28fd5] OpenSpecFun_jll v0.5.5+0
[91d4177d] Opus_jll v1.3.2+0
[30392449] Pixman_jll v0.40.1+0
[ea2cea3b] Qt5Base_jll v5.15.3+2
[f50d1b31] Rmath_jll v0.4.0+0
[a2964d1f] Wayland_jll v1.21.0+0
[2381bf8a] Wayland_protocols_jll v1.25.0+0
[02c8fc9c] XML2_jll v2.10.3+0
[aed1982a] XSLT_jll v1.1.34+0
[4f6342f7] Xorg_libX11_jll v1.6.9+4
[0c0b7dd1] Xorg_libXau_jll v1.0.9+4
[935fb764] Xorg_libXcursor_jll v1.2.0+4
[a3789734] Xorg_libXdmcp_jll v1.1.3+4
[1082639a] Xorg_libXext_jll v1.3.4+4
[d091e8ba] Xorg_libXfixes_jll v5.0.3+4
[a51aa0fd] Xorg_libXi_jll v1.7.10+4
[d1454406] Xorg_libXinerama_jll v1.1.4+4
[ec84b674] Xorg_libXrandr_jll v1.5.2+4
[ea2f1a96] Xorg_libXrender_jll v0.9.10+4
[14d82f49] Xorg_libpthread_stubs_jll v0.1.0+3
[c7cfdc94] Xorg_libxcb_jll v1.13.0+3
[cc61e674] Xorg_libxkbfile_jll v1.1.0+4
[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 v1.4.2+4
[33bec58e] Xorg_xkeyboard_config_jll v2.27.0+4
[c5fb5394] Xorg_xtrans_jll v1.4.0+3
[3161d3a3] Zstd_jll v1.5.4+0
βŒ… [214eeab7] fzf_jll v0.29.0+0
[a4ae2306] libaom_jll v3.4.0+0
[0ac62f75] libass_jll v0.15.1+0
[f638f0a6] libfdk_aac_jll v2.0.2+0
[b53b4c65] libpng_jll v1.6.38+0
[f27f6e37] libvorbis_jll v1.3.7+1
[1270edf5] x264_jll v2021.5.5+0
[dfaa095f] x265_jll v3.5.0+0
[d8fb68d0] xkbcommon_jll v1.4.1+0
[0dad84c5] ArgTools v1.1.1
[56f22d72] Artifacts
[2a0f44e3] Base64
[ade2ca70] Dates
[8bb1440f] DelimitedFiles
[8ba89e20] Distributed
[f43a241f] Downloads v1.6.0
[7b1f6079] FileWatching
[9fa8497b] Future
[b77e0a4c] InteractiveUtils
[4af54fe1] LazyArtifacts
[b27032c2] LibCURL v0.6.3
[76f85450] LibGit2
[8f399da3] Libdl
[37e2e46d] LinearAlgebra
[56ddb016] Logging
[d6f4376e] Markdown
[a63ad114] Mmap
[ca575930] NetworkOptions v1.2.0
[44cfe95a] Pkg v1.8.0
[de0858da] Printf
[3fa0cd96] REPL
[9a3f8284] Random
[ea8e919c] SHA v0.7.0
[9e88b42a] Serialization
[1a1011a3] SharedArrays
[6462fe0b] Sockets
[2f01184e] SparseArrays
[10745b16] Statistics
[4607b0f0] SuiteSparse
[fa267f1f] TOML v1.0.0
[a4e569a6] Tar v1.10.1
[8dfed614] Test
[cf7118a7] UUIDs
[4ec0a83e] Unicode
[e66e0078] CompilerSupportLibraries_jll v0.5.2+0
[deac9b47] LibCURL_jll v7.84.0+0
[29816b5a] LibSSH2_jll v1.10.2+0
[c8ffd9c3] MbedTLS_jll v2.28.0+0
[14a3606d] MozillaCACerts_jll v2022.2.1
[4536629a] OpenBLAS_jll v0.3.20+0
[05823500] OpenLibm_jll v0.8.1+0
[efcefdf7] PCRE2_jll v10.40.0+0
[bea87d4a] SuiteSparse_jll v5.10.1+0
[83775a58] Zlib_jll v1.2.12+3
[8e850b90] libblastrampoline_jll v5.1.1+0
[8e850ede] nghttp2_jll v1.48.0+0
[3f19e933] p7zip_jll v17.4.0+0

This is the top of the stacktrace I get using the example_turing.jl script using julia -p 1 --project:

From worker 2: [ Info: Started job 1
From worker 2: [ Info: Started job 2
From worker 2: [ Info: Started job 1
From worker 2: β”Œ Error: MethodError(Float64, (Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}}(Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}}(0.7816855694884302,0.0,0.0,0.0,0.0,0.0),Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}}(0.7816855694884302,0.0,0.0,0.0,0.0,0.0)),), 0x000000000000820c)
From worker 2: β”” @ Main ~/example_turing.jl:27
From worker 2: β”Œ Error: Error
From worker 2: β”‚ exception =
From worker 2: β”‚ MethodError: no method matching Float64(::ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}, ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}, 1})
From worker 2: β”‚ Closest candidates are:
From worker 2: β”‚ (::Type{T})(::Real, !Matched::RoundingMode) where T<:AbstractFloat at rounding.jl:200
From worker 2: β”‚ (::Type{T})(::T) where T<:Number at boot.jl:772
From worker 2: β”‚ (::Type{T})(!Matched::AbstractChar) where T<:Union{AbstractChar, Number} at char.jl:50
From worker 2: β”‚ …
From worker 2: β”‚ Stacktrace:
From worker 2: β”‚ [1] convert
From worker 2: β”‚ @ ~/.julia/packages/ForwardDiff/QdStj/src/dual.jl:433 [inlined]
From worker 2: β”‚ [2] Dual
From worker 2: β”‚ @ ~/.julia/packages/ForwardDiff/QdStj/src/dual.jl:78 [inlined]
From worker 2: β”‚ [3] convert
From worker 2: β”‚ @ ~/.julia/packages/ForwardDiff/QdStj/src/dual.jl:435 [inlined]
From worker 2: β”‚ [4] setindex!(A::Vector{ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}, ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}, 1}}, x::ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}, ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}, 1}, 5}, i1::Int64)
From worker 2: β”‚ @ Base ./array.jl:966
From worker 2: β”‚ [5] lotka_volterra(du::Vector{ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}, ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}, 1}}, u::Vector{ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}, ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}, 1}}, p::Vector{ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}, t::Float64)
From worker 2: β”‚ @ Main ~/example_turing.jl:24
From worker 2: β”‚ [6] ODEFunction
From worker 2: β”‚ @ ~/.julia/packages/SciMLBase/hLrpl/src/scimlfunctions.jl:2096 [inlined]
From worker 2: β”‚ [7] UJacobianWrapper
From worker 2: β”‚ @ ~/.julia/packages/SciMLBase/hLrpl/src/function_wrappers.jl:15 [inlined]
From worker 2: β”‚ [8] forwarddiff_color_jacobian!(J::Matrix{ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}, f::SciMLBase.UJacobianWrapper{ODEFunction{true, SciMLBase.FullSpecialize, typeof(lotka_volterra), UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing}, Float64, Vector{ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}}, x::Vector{ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}, jac_cache::SparseDiffTools.ForwardColorJacCache{Vector{ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}, ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}, 1}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}, ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}, 1}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}, Vector{Vector{Tuple{ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}}}, UnitRange{Int64}, Nothing})
From worker 2: β”‚ @ SparseDiffTools ~/.julia/packages/SparseDiffTools/zGdIo/src/differentiation/compute_jacobian_ad.jl:377
From worker 2: β”‚ [9] jacobian!(J::Matrix{ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}, f::SciMLBase.UJacobianWrapper{ODEFunction{true, SciMLBase.FullSpecialize, typeof(lotka_volterra), UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing}, Float64, Vector{ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}}, x::Vector{ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}, fx::Vector{ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}, integrator::OrdinaryDiffEq.ODEIntegrator{TRBDF2{1, true, LinearSolve.GenericLUFactorization{RowMaximum}, NLNewton{Rational{Int64}, Rational{Int64}, Rational{Int64}, Rational{Int64}}, typeof(OrdinaryDiffEq.DEFAULT_PRECS), Val{:forward}, true, nothing}, true, Vector{ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}, Nothing, Float64, Vector{ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}, Float64, Float64, Float64, Float64, Vector{Vector{ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}}, ODESolution{ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}, 2, Vector{Vector{ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}}, Nothing, Nothing, Vector{Float64}, Vector{Vector{Vector{ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}}}, ODEProblem{Vector{ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}, Tuple{Float64, Float64}, true, Vector{ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}, ODEFunction{true, SciMLBase.FullSpecialize, typeof(lotka_volterra), UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing}, Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}, TRBDF2{1, true, LinearSolve.GenericLUFactorization{RowMaximum}, NLNewton{Rational{Int64}, Rational{Int64}, Rational{Int64}, Rational{Int64}}, typeof(OrdinaryDiffEq.DEFAULT_PRECS), Val{:forward}, true, nothing}, OrdinaryDiffEq.InterpolationData{ODEFunction{true, SciMLBase.FullSpecialize, typeof(lotka_volterra), UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing}, Vector{Vector{ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}}, Vector{Float64}, Vector{Vector{Vector{ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}}}, OrdinaryDiffEq.TRBDF2Cache{Vector{ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}, OrdinaryDiffEq.TRBDF2Tableau{Float64, Float64}, OrdinaryDiffEq.NLSolver{NLNewton{Rational{Int64}, Rational{Int64}, Rational{Int64}, Rational{Int64}}, true, Vector{ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}, Float64, Nothing, Float64, OrdinaryDiffEq.NLNewtonCache{Vector{ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}, Float64, ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}, Matrix{ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}, Matrix{ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}, SciMLBase.UJacobianWrapper{ODEFunction{true, SciMLBase.FullSpecialize, typeof(lotka_volterra), UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing}, Float64, Vector{ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}}, SparseDiffTools.ForwardColorJacCache{Vector{ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}, ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}, 1}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}, ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}, 1}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}, Vector{Vector{Tuple{ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}}}, UnitRange{Int64}, Nothing}, LinearSolve.LinearCache{Matrix{ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}, SciMLBase.NullParameters, LinearSolve.GenericLUFactorization{RowMaximum}, LU{ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}, Matrix{ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}, Vector{Int64}}, LinearSolve.InvPreconditioner{Diagonal{ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}}}, Diagonal{ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}}, Float64, true}}}}}, DiffEqBase.DEStats, Nothing}, ODEFunction{true, SciMLBase.FullSpecialize, typeof(lotka_volterra), UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing}, OrdinaryDiffEq.TRBDF2Cache{Vector{ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}, OrdinaryDiffEq.TRBDF2Tableau{Float64, Float64}, OrdinaryDiffEq.NLSolver{NLNewton{Rational{Int64}, Rational{Int64}, Rational{Int64}, Rational{Int64}}, true, Vector{ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}, Float64, Nothing, Float64, OrdinaryDiffEq.NLNewtonCache{Vector{ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}, Float64, ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}, Matrix{ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}, Matrix{ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}, SciMLBase.UJacobianWrapper{ODEFunction{true, SciMLBase.FullSpecialize, typeof(lotka_volterra), UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing}, Float64, Vector{ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}}, SparseDiffTools.ForwardColorJacCache{Vector{ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}, ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}, 1}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}, ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}, 1}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}, Vector{Vector{Tuple{ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}}}, UnitRange{Int64}, Nothing}, LinearSolve.LinearCache{Matrix{ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}, SciMLBase.NullParameters, LinearSolve.GenericLUFactorization{RowMaximum}, LU{ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}, Matrix{ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}, Vector{Int64}}, LinearSolve.InvPreconditioner{Diagonal{ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}}}, Diagonal{ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}}, Float64, true}}}}, OrdinaryDiffEq.DEOptions{Float64, ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}, Float64, Float64, PIController{Rational{Int64}}, typeof(DiffEqBase.ODE_DEFAULT_NORM), typeof(opnorm), Nothing, CallbackSet{Tuple{}, Tuple{}}, typeof(DiffEqBase.ODE_DEFAULT_ISOUTOFDOMAIN), typeof(DiffEqBase.ODE_DEFAULT_PROG_MESSAGE), typeof(DiffEqBase.ODE_DEFAULT_UNSTABLE_CHECK), DataStructures.BinaryHeap{Float64, DataStructures.FasterForward}, DataStructures.BinaryHeap{Float64, DataStructures.FasterForward}, Nothing, Nothing, Int64, Tuple{}, Float64, Tuple{}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}, ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}, Nothing, OrdinaryDiffEq.DefaultInit}, jac_config::SparseDiffTools.ForwardColorJacCache{Vector{ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}, ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}, 1}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}, ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}, 1}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}, Vector{Vector{Tuple{ForwardDiff.Dual{ForwardDiff.Tag{Turing.TuringTag, Float64}, Float64, 5}}}}, UnitRange{Int64}, Nothing})
From worker 2: β”‚ @ OrdinaryDiffEq ~/.julia/packages/OrdinaryDiffEq/4OfcV/src/derivative_wrappers.jl:228

Do you see the issue on v1.8.5? I’ve been running it on v1.9-beta3.

(remaking deleted post)

I had run the above code examples on Julia 1.8.5 to generate those error stack traces. I also installed 1.9.0-beta3 but get a similar error. This is the stack trace I get (without the extra try-catch in example_turing.jl)
stacktrace_1_9.jl (36.7 KB)
Here are my installed packages on 1.9
status.jl (11.9 KB)

I just wanted to make sure we’re on the same page with how the file is run. The script works if you run it with julia but not when you use multiple processes with julia -p <N> (at least that’s what we’re seeing). Were you running the latter?

@ChrisRackauckas yes, I still see the same issue on 1.9. I suggest you start Julia with -p 1 to get the same error as us.