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,

@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
ΟΒ² ~ 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, ΟΒ²[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)
@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 Info: [ADVI] Should only be seen once: optimizer created for ΞΈ
β   objectid(ΞΈ) = 0x914e03f08498020d
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
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 thatβs the only thing that printed? Whereβs all of the type information?

@ChrisRackauckas

stacktrace.jl (3.0 MB)

I threw a try-catch and got the type information. Itβs quite long, so that why Iβ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 didnβ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ββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ| Time: 0:00:48
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
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_PKG_USE_CLI_GIT = true

`]st`
[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
β [7a57a42e] AbstractPPL v0.5.3
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[dce04be8] ArgCheck v2.3.0
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[cc8bc4a8] Widgets v0.6.6
[efce3f68] WoodburyMatrices v0.5.5
[700de1a5] ZygoteRules v0.2.2
β [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
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[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
β [e9f186c6] Libffi_jll v3.2.2+1
[d4300ac3] Libgcrypt_jll v1.8.7+0
[7e76a0d4] Libglvnd_jll v1.6.0+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
[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
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[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
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[2a0f44e3] Base64
[8bb1440f] DelimitedFiles
[8ba89e20] Distributed
[7b1f6079] FileWatching
[9fa8497b] Future
[b77e0a4c] InteractiveUtils
[4af54fe1] LazyArtifacts
[b27032c2] LibCURL v0.6.3
[76f85450] LibGit2
[8f399da3] Libdl
[37e2e46d] LinearAlgebra
[56ddb016] Logging
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[ca575930] NetworkOptions v1.2.0
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[1a1011a3] SharedArrays
[6462fe0b] Sockets
[2f01184e] SparseArrays
[10745b16] Statistics
[4607b0f0] SuiteSparse
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[8dfed614] Test
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[e66e0078] CompilerSupportLibraries_jll v0.5.2+0
[deac9b47] LibCURL_jll v7.84.0+0
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[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 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 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 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? Iβ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 weβ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 thatβs what weβ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.