# TypeError in Julia/Turing when sampling for a forced differential equation

**URL:** <https://discourse.julialang.org/t/typeerror-in-julia-turing-when-sampling-for-a-forced-differential-equation/82937>\
**Category:** General Usage\
**Tags:** turing\
**Created:** [June 17, 2022, 8:07pm UTC](https://discourse.julialang.org/t/typeerror-in-julia-turing-when-sampling-for-a-forced-differential-equation/82937 "2022-06-17T20:07:58Z")\
**Posts on this page:** 7\
**Page:** 1

<div class="post-metadata">

**Author:** ![Duo\_Chan](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/duo_chan/32/37251_2.png) [@Duo\_Chan](https://discourse.julialang.org/u/Duo_Chan)\
**Post date:** [June 17, 2022, 8:07pm UTC](https://discourse.julialang.org/t/typeerror-in-julia-turing-when-sampling-for-a-forced-differential-equation/82937/1 "2022-06-17T20:07:58Z")

</div>

Hi

I am new to Julia and Turing and am trying to fit a forced 0-D box ODE to data, but I get type error when doing sampling.

The tutorial ([Bayesian Estimation of Differential Equations](https://turing.ml/dev/tutorials/10-bayesian-differential-equations/)) gives an example for unforced LV model. Following this page ([julia - solve system of ODEs with read in external forcing - Stack Overflow](https://stackoverflow.com/questions/49428939/solve-system-of-odes-with-read-in-external-forcing)), I added an interpolation handle of the forcing as a parameter of the ODE, and the ODE solver runs without problems.

When I combine the forced ODE with Turing, however, I get a type error during HMC’s gradient calculation, quoting ”TypeError: in typeassert, expected Float64, got a value of type ForwardDiff.Dual{Nothing, Float64, 3}”.

Below are my codes that should reproduce the error I got.

I appreciate any help, Thanks.

Below are my codes:

```julia
using Interpolations, DifferentialEquations, Plots, Turing, LinearAlgebra

# Define ODE
function f(du,u,p,t)
      α, β, F = p
      du[1] = α * u[1] + β * F(t) # Interpolations.jl interpolates via ()
end

# Define initial value problem
begin
    # Define forcing 
    time_forcing = -1.:9.
    data_forcing = [10,0,0,0,0,0,0,0,0, 0, 0]
    F = Interpolations.scale(interpolate(data_forcing, BSpline(Linear())), time_forcing)
    α = -0.5
    β = 1
    p_lin = (α, β, F) 

    # Define u0 and tspan
    u0 = [0.]
    tspan = (-1.,9.) # Note, that we would need to extrapolate beyond 
    ode_lin = ODEProblem(f,u0,tspan,p_lin)
end

# Generate data
sol = solve(ode_lin, Tsit5(); saveat=1)
data = Array(sol) + 0.2 * randn(size(Array(sol)))

@model function fit_simple_box(data, F, ode_lin)
    # Prior distributions.
    σ ~ InverseGamma(2, 3)
    α ~ Normal(0, 3)
    β ~ Normal(0, 3)

    # Simulate Lotka-Volterra model. 
    p = (α, β, F)
    predicted = solve(ode_lin, Tsit5(); p=p, saveat=1)

    # Observations.
    for i in 1:length(predicted)
        data ~ Normal(predicted[i][1], σ^2)
    end

    return nothing
end

model = fit_simple_box(data, F, ode_lin)
chain = sample(model, NUTS(0.65), MCMCSerial(), 1000, 2)

```

---

<div class="post-metadata">

**Author:** ![Christopher\_Fisher](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/christopher_fisher/32/26132_2.png) [@Christopher\_Fisher](https://discourse.julialang.org/u/Christopher_Fisher)\
**Post date:** [June 18, 2022, 12:47am UTC](https://discourse.julialang.org/t/typeerror-in-julia-turing-when-sampling-for-a-forced-differential-equation/82937/2 "2022-06-18T00:47:55Z")

</div>

I tried to run your code, but I received the following error:

```julia
ERROR: UndefVarError: g1_lin not defined
Stacktrace:
 [1] top-level scope
   @ Untitled-2:47

```

I might be able to provide more guidance if given g1\_lin or the full error message.

Automatic differentiation uses the Dual type to compute gradients from your code. The error you found typically happens when the type of an array is not generic. In this case, it is forced to be Float64, making a Dual type impossible. One possible culprit is

```julia
    data_forcing = [10,0,0,0,0,0,0,0,0, 0, 0]
    F = Interpolations.scale(interpolate(data_forcing, BSpline(Linear())), time_forcing)

```

If F always returns a Float64 regardless of the input type, this might be the cause of your problem.

---

<div class="post-metadata">

**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [June 18, 2022, 3:45am UTC](https://discourse.julialang.org/t/typeerror-in-julia-turing-when-sampling-for-a-forced-differential-equation/82937/3 "2022-06-18T03:45:42Z")

</div>

> [@Duo\_Chan](#):
>
> `predicted = solve(ode_lin, Tsit5(); p=p, saveat=1)`

You need to do `u0 = typeof(α).(ode_lin.u0)` to promote it to dual. But I have an idea for how to automate this promotion, so I’ll instead respond with a PR in a second.

---

<div class="post-metadata">

**Author:** ![Duo\_Chan](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/duo_chan/32/37251_2.png) [@Duo\_Chan](https://discourse.julialang.org/u/Duo_Chan)\
**Post date:** [June 18, 2022, 4:12pm UTC](https://discourse.julialang.org/t/typeerror-in-julia-turing-when-sampling-for-a-forced-differential-equation/82937/4 "2022-06-18T16:12:31Z")

</div>

Hi Christopher, Thanks for your quick response. the g1\_lin was a bug, which I have fixed by replacing them with F, which stands for forcing. That said, I still get the same error message regarding type errors. The error message is quite long, copy the entire message goes beyond the length limit, but I will copy until [4] in the stack trace, so that it would help you to confirm if the error I got is reproduced.

If interpolation is the problem, is there any way to walk around? I can realize the same Bayesian model in Stan, but Julia has such a powerful differential equation tool box, which makes it much favorable in a long run.

```julia
ERROR: TypeError: in typeassert, expected Float64, got a value of type ForwardDiff.Dual{Nothing, Float64, 3}
Stacktrace:
  [1] setindex!(A::Vector{Float64}, x::ForwardDiff.Dual{ForwardDiff.Tag{Turing.Essential.var"#f#4"{DynamicPPL.TypedVarInfo{NamedTuple{(:σ, :α, :β), Tuple{DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:σ, Setfield.IdentityLens}, Int64}, Vector{InverseGamma{Float64}}, Vector{AbstractPPL.VarName{:σ, Setfield.IdentityLens}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:α, Setfield.IdentityLens}, Int64}, Vector{Normal{Float64}}, Vector{AbstractPPL.VarName{:α, Setfield.IdentityLens}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:β, Setfield.IdentityLens}, Int64}, Vector{Normal{Float64}}, Vector{AbstractPPL.VarName{:β, Setfield.IdentityLens}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}}}, Float64}, DynamicPPL.Model{typeof(fit_simple_box), (:data, :F, :ode_lin), (), (), Tuple{Matrix{Float64}, ScaledInterpolation{Float64, 1, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}, BSpline{Linear{Throw{OnGrid}}}, Tuple{StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}}}, ODEProblem{Vector{Float64}, Tuple{Float64, Float64}, true, Tuple{Float64, Int64, ScaledInterpolation{Float64, 1, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}, BSpline{Linear{Throw{OnGrid}}}, Tuple{StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}}}}, ODEFunction{true, typeof(f), UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}}, Tuple{}, DynamicPPL.DefaultContext}, DynamicPPL.Sampler{NUTS{Turing.Essential.ForwardDiffAD{0}, (), AdvancedHMC.DiagEuclideanMetric}}, DynamicPPL.DefaultContext}, Float64}, Float64, 3}, i1::Int64)
    @ Base ./array.jl:903
  [2] f(du::Vector{Float64}, u::Vector{Float64}, p::Tuple{ForwardDiff.Dual{ForwardDiff.Tag{Turing.Essential.var"#f#4"{DynamicPPL.TypedVarInfo{NamedTuple{(:σ, :α, :β), Tuple{DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:σ, Setfield.IdentityLens}, Int64}, Vector{InverseGamma{Float64}}, Vector{AbstractPPL.VarName{:σ, Setfield.IdentityLens}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:α, Setfield.IdentityLens}, Int64}, Vector{Normal{Float64}}, Vector{AbstractPPL.VarName{:α, Setfield.IdentityLens}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:β, Setfield.IdentityLens}, Int64}, Vector{Normal{Float64}}, Vector{AbstractPPL.VarName{:β, Setfield.IdentityLens}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}}}, Float64}, DynamicPPL.Model{typeof(fit_simple_box), (:data, :F, :ode_lin), (), (), Tuple{Matrix{Float64}, ScaledInterpolation{Float64, 1, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}, BSpline{Linear{Throw{OnGrid}}}, Tuple{StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}}}, ODEProblem{Vector{Float64}, Tuple{Float64, Float64}, true, Tuple{Float64, Int64, ScaledInterpolation{Float64, 1, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}, BSpline{Linear{Throw{OnGrid}}}, Tuple{StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}}}}, ODEFunction{true, typeof(f), UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}}, Tuple{}, DynamicPPL.DefaultContext}, DynamicPPL.Sampler{NUTS{Turing.Essential.ForwardDiffAD{0}, (), AdvancedHMC.DiagEuclideanMetric}}, DynamicPPL.DefaultContext}, Float64}, Float64, 3}, ForwardDiff.Dual{ForwardDiff.Tag{Turing.Essential.var"#f#4"{DynamicPPL.TypedVarInfo{NamedTuple{(:σ, :α, :β), Tuple{DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:σ, Setfield.IdentityLens}, Int64}, Vector{InverseGamma{Float64}}, Vector{AbstractPPL.VarName{:σ, Setfield.IdentityLens}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:α, Setfield.IdentityLens}, Int64}, Vector{Normal{Float64}}, Vector{AbstractPPL.VarName{:α, Setfield.IdentityLens}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:β, Setfield.IdentityLens}, Int64}, Vector{Normal{Float64}}, Vector{AbstractPPL.VarName{:β, Setfield.IdentityLens}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}}}, Float64}, DynamicPPL.Model{typeof(fit_simple_box), (:data, :F, :ode_lin), (), (), Tuple{Matrix{Float64}, ScaledInterpolation{Float64, 1, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}, BSpline{Linear{Throw{OnGrid}}}, Tuple{StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}}}, ODEProblem{Vector{Float64}, Tuple{Float64, Float64}, true, Tuple{Float64, Int64, ScaledInterpolation{Float64, 1, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}, BSpline{Linear{Throw{OnGrid}}}, Tuple{StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}}}}, ODEFunction{true, typeof(f), UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}}, Tuple{}, DynamicPPL.DefaultContext}, DynamicPPL.Sampler{NUTS{Turing.Essential.ForwardDiffAD{0}, (), AdvancedHMC.DiagEuclideanMetric}}, DynamicPPL.DefaultContext}, Float64}, Float64, 3}, ScaledInterpolation{Float64, 1, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}, BSpline{Linear{Throw{OnGrid}}}, Tuple{StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}}}}, t::Float64)
    @ Main ~/Dropbox/Git_code/Deglacial_PowerLaw/scripts/Run_ODE_with_forcing.jl:6
  [3] (::ODEFunction{true, typeof(f), UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing})(::Vector{Float64}, ::Vararg{Any})
    @ SciMLBase ~/.julia/packages/SciMLBase/t5VdI/src/scimlfunctions.jl:1613
  [4] initialize!(integrator::OrdinaryDiffEq.ODEIntegrator{Tsit5{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!), Static.False}, true, Vector{Float64}, Nothing, Float64, Tuple{ForwardDiff.Dual{ForwardDiff.Tag{Turing.Essential.var"#f#4"{DynamicPPL.TypedVarInfo{NamedTuple{(:σ, :α, :β), Tuple{DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:σ, Setfield.IdentityLens}, Int64}, Vector{InverseGamma{Float64}}, Vector{AbstractPPL.VarName{:σ, Setfield.IdentityLens}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:α, Setfield.IdentityLens}, Int64}, Vector{Normal{Float64}}, Vector{AbstractPPL.VarName{:α, Setfield.IdentityLens}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:β, Setfield.IdentityLens}, Int64}, Vector{Normal{Float64}}, Vector{AbstractPPL.VarName{:β, Setfield.IdentityLens}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}}}, Float64}, DynamicPPL.Model{typeof(fit_simple_box), (:data, :F, :ode_lin), (), (), Tuple{Matrix{Float64}, ScaledInterpolation{Float64, 1, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}, BSpline{Linear{Throw{OnGrid}}}, Tuple{StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}}}, ODEProblem{Vector{Float64}, Tuple{Float64, Float64}, true, Tuple{Float64, Int64, ScaledInterpolation{Float64, 1, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}, BSpline{Linear{Throw{OnGrid}}}, Tuple{StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}}}}, ODEFunction{true, typeof(f), UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}}, Tuple{}, DynamicPPL.DefaultContext}, DynamicPPL.Sampler{NUTS{Turing.Essential.ForwardDiffAD{0}, (), AdvancedHMC.DiagEuclideanMetric}}, DynamicPPL.DefaultContext}, Float64}, Float64, 3}, ForwardDiff.Dual{ForwardDiff.Tag{Turing.Essential.var"#f#4"{DynamicPPL.TypedVarInfo{NamedTuple{(:σ, :α, :β), Tuple{DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:σ, Setfield.IdentityLens}, Int64}, Vector{InverseGamma{Float64}}, Vector{AbstractPPL.VarName{:σ, Setfield.IdentityLens}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:α, Setfield.IdentityLens}, Int64}, Vector{Normal{Float64}}, Vector{AbstractPPL.VarName{:α, Setfield.IdentityLens}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:β, Setfield.IdentityLens}, Int64}, Vector{Normal{Float64}}, Vector{AbstractPPL.VarName{:β, Setfield.IdentityLens}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}}}, Float64}, DynamicPPL.Model{typeof(fit_simple_box), (:data, :F, :ode_lin), (), (), Tuple{Matrix{Float64}, ScaledInterpolation{Float64, 1, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}, BSpline{Linear{Throw{OnGrid}}}, Tuple{StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}}}, ODEProblem{Vector{Float64}, Tuple{Float64, Float64}, true, Tuple{Float64, Int64, ScaledInterpolation{Float64, 1, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}, BSpline{Linear{Throw{OnGrid}}}, Tuple{StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}}}}, ODEFunction{true, typeof(f), UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}}, Tuple{}, DynamicPPL.DefaultContext}, DynamicPPL.Sampler{NUTS{Turing.Essential.ForwardDiffAD{0}, (), AdvancedHMC.DiagEuclideanMetric}}, DynamicPPL.DefaultContext}, Float64}, Float64, 3}, ScaledInterpolation{Float64, 1, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}, BSpline{Linear{Throw{OnGrid}}}, Tuple{StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}}}}, Float64, Float64, Float64, Float64, Vector{Vector{Float64}}, ODESolution{Float64, 2, Vector{Vector{Float64}}, Nothing, Nothing, Vector{Float64}, Vector{Vector{Vector{Float64}}}, ODEProblem{Vector{Float64}, Tuple{Float64, Float64}, true, Tuple{ForwardDiff.Dual{ForwardDiff.Tag{Turing.Essential.var"#f#4"{DynamicPPL.TypedVarInfo{NamedTuple{(:σ, :α, :β), Tuple{DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:σ, Setfield.IdentityLens}, Int64}, Vector{InverseGamma{Float64}}, Vector{AbstractPPL.VarName{:σ, Setfield.IdentityLens}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:α, Setfield.IdentityLens}, Int64}, Vector{Normal{Float64}}, Vector{AbstractPPL.VarName{:α, Setfield.IdentityLens}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:β, Setfield.IdentityLens}, Int64}, Vector{Normal{Float64}}, Vector{AbstractPPL.VarName{:β, Setfield.IdentityLens}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}}}, Float64}, DynamicPPL.Model{typeof(fit_simple_box), (:data, :F, :ode_lin), (), (), Tuple{Matrix{Float64}, ScaledInterpolation{Float64, 1, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}, BSpline{Linear{Throw{OnGrid}}}, Tuple{StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}}}, ODEProblem{Vector{Float64}, Tuple{Float64, Float64}, true, Tuple{Float64, Int64, ScaledInterpolation{Float64, 1, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}, BSpline{Linear{Throw{OnGrid}}}, Tuple{StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}}}}, ODEFunction{true, typeof(f), UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}}, Tuple{}, DynamicPPL.DefaultContext}, DynamicPPL.Sampler{NUTS{Turing.Essential.ForwardDiffAD{0}, (), AdvancedHMC.DiagEuclideanMetric}}, DynamicPPL.DefaultContext}, Float64}, Float64, 3}, ForwardDiff.Dual{ForwardDiff.Tag{Turing.Essential.var"#f#4"{DynamicPPL.TypedVarInfo{NamedTuple{(:σ, :α, :β), Tuple{DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:σ, Setfield.IdentityLens}, Int64}, Vector{InverseGamma{Float64}}, Vector{AbstractPPL.VarName{:σ, Setfield.IdentityLens}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:α, Setfield.IdentityLens}, Int64}, Vector{Normal{Float64}}, Vector{AbstractPPL.VarName{:α, Setfield.IdentityLens}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:β, Setfield.IdentityLens}, Int64}, Vector{Normal{Float64}}, Vector{AbstractPPL.VarName{:β, Setfield.IdentityLens}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}}}, Float64}, DynamicPPL.Model{typeof(fit_simple_box), (:data, :F, :ode_lin), (), (), Tuple{Matrix{Float64}, ScaledInterpolation{Float64, 1, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}, BSpline{Linear{Throw{OnGrid}}}, Tuple{StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}}}, ODEProblem{Vector{Float64}, Tuple{Float64, Float64}, true, Tuple{Float64, Int64, ScaledInterpolation{Float64, 1, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}, BSpline{Linear{Throw{OnGrid}}}, Tuple{StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}}}}, ODEFunction{true, typeof(f), UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}}, Tuple{}, DynamicPPL.DefaultContext}, DynamicPPL.Sampler{NUTS{Turing.Essential.ForwardDiffAD{0}, (), AdvancedHMC.DiagEuclideanMetric}}, DynamicPPL.DefaultContext}, Float64}, Float64, 3}, ScaledInterpolation{Float64, 1, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}, BSpline{Linear{Throw{OnGrid}}}, Tuple{StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}}}}, ODEFunction{true, typeof(f), UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}, Tsit5{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!), Static.False}, OrdinaryDiffEq.InterpolationData{ODEFunction{true, typeof(f), UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Vector{Vector{Float64}}, Vector{Float64}, Vector{Vector{Vector{Float64}}}, OrdinaryDiffEq.Tsit5Cache{Vector{Float64}, Vector{Float64}, Vector{Float64}, OrdinaryDiffEq.Tsit5ConstantCache{Float64, Float64}, typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!), Static.False}}, DiffEqBase.DEStats}, ODEFunction{true, typeof(f), UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, OrdinaryDiffEq.Tsit5Cache{Vector{Float64}, Vector{Float64}, Vector{Float64}, OrdinaryDiffEq.Tsit5ConstantCache{Float64, Float64}, typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!), Static.False}, OrdinaryDiffEq.DEOptions{Float64, Float64, 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{}, Int64, Tuple{}}, Vector{Float64}, Float64, Nothing, OrdinaryDiffEq.DefaultInit}, cache::OrdinaryDiffEq.Tsit5Cache{Vector{Float64}, Vector{Float64}, Vector{Float64}, OrdinaryDiffEq.Tsit5ConstantCache{Float64, Float64}, typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!), Static.False})
    @ OrdinaryDiffEq ~/.julia/packages/OrdinaryDiffEq/nrmdG/src/perform_step/low_order_rk_perform_step.jl:627

```

---

<div class="post-metadata">

**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [June 18, 2022, 4:16pm UTC](https://discourse.julialang.org/t/typeerror-in-julia-turing-when-sampling-for-a-forced-differential-equation/82937/5 "2022-06-18T16:16:37Z")

</div>

> [@Duo\_Chan](#):
>
> If interpolation is the problem, is there any way to walk around?

Yes, just do what I mentioned. Though there’s a fix coming soon as well.

---

<div class="post-metadata">

**Author:** ![Duo\_Chan](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/duo_chan/32/37251_2.png) [@Duo\_Chan](https://discourse.julialang.org/u/Duo_Chan)\
**Post date:** [June 18, 2022, 9:24pm UTC](https://discourse.julialang.org/t/typeerror-in-julia-turing-when-sampling-for-a-forced-differential-equation/82937/6 "2022-06-18T21:24:28Z")

</div>

Yes, that solves the problem! Thanks!

---

<div class="post-metadata">

**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [June 18, 2022, 9:50pm UTC](https://discourse.julialang.org/t/typeerror-in-julia-turing-when-sampling-for-a-forced-differential-equation/82937/7 "2022-06-18T21:50:03Z")

</div>

Awesome, so then this PR will do that automatically behind the scenes in the future:

[https://github.com/SciML/DiffEqBase.jl/pull/773](https://github.com/SciML/DiffEqBase.jl/pull/773)

That should be released in a few hours, but it’s just a helper to do the same thing.