Errors when trying to include the calculation of eigenvalues (in the neuralFMU -simulation and -training)

[juguma]

Problem description and MWE

The attached script is a reduced and modified variant of simple_hybrid_ME.ipynb.
Removed has been anything unnecessary to reproduce the error.
Modifications are:

• inclusion of recordEigenvaluesSensitivity=:ForwardDiff, recordEigenvalues = true in the loss function (lossSum)
• renaming of train! to _train! *, only one iteration, removal of some arguments, adding of gradient =:ForwardDiff

# imports
using FMI
using FMIFlux
using FMIFlux.Flux
using FMIZoo
using DifferentialEquations: Tsit5
import Plots

# set seed
import Random
Random.seed!(42);

tStart = 0.0
tStep = 0.01
tStop = 5.0
tSave = collect(tStart:tStep:tStop)

realFMU = fmiLoad("SpringFrictionPendulum1D", "Dymola", "2022x")
fmiInfo(realFMU)

initStates = ["s0", "v0"]
x₀ = [0.5, 0.0]
params = Dict(zip(initStates, x₀))
vrs = ["mass.s", "mass.v", "mass.a", "mass.f"]

realSimData = fmiSimulate(realFMU, (tStart, tStop); parameters=params, recordValues=vrs, saveat=tSave)
posReal = fmi2GetSolutionValue(realSimData, "mass.s")
fmiUnload(realFMU)

simpleFMU = fmiLoad("SpringPendulum1D", "Dymola", "2022x")

# loss function for training
function lossSum(p)
    global posReal
    solution = neuralFMU(x₀; p=p,recordEigenvaluesSensitivity=:ForwardDiff, recordEigenvalues = true)
    posNet = fmi2GetSolutionState(solution, 1; isIndex=true)   
    FMIFlux.Losses.mse(posReal, posNet) 
end

# NeuralFMU setup
numStates = fmiGetNumberOfStates(simpleFMU)
net = Chain(x -> simpleFMU(x=x, dx_refs=:all),
            Dense(numStates, 16, tanh),
            Dense(16, 16, tanh),
            Dense(16, numStates))
neuralFMU = ME_NeuralFMU(simpleFMU, net, (tStart, tStop), Tsit5(); saveat=tSave);

# train
paramsNet = FMIFlux.params(neuralFMU)
optim = Adam()
FMIFlux._train!(lossSum, paramsNet, Iterators.repeated((), 1), optim; gradient =:ForwardDiff) 

Reported error

MethodError: no method matching Float64(::ForwardDiff.Dual{ForwardDiff.Tag{typeof(lossSum), Float64}, Float64, 32})

Closest candidates are:
(::Type{T})(::Real, ::RoundingMode) where T<:AbstractFloat
@ Base rounding.jl:207
(::Type{T})(::T) where T<:Number
@ Core boot.jl:792
Float64(::IrrationalConstants.Fourπ)
@ IrrationalConstants C:\Users\JUR.julia\packages\IrrationalConstants\vp5v4\src\macro.jl:112
...

Stacktrace:
[1] convert(::Type{Float64}, x::ForwardDiff.Dual{ForwardDiff.Tag{typeof(lossSum), Float64}, Float64, 32})
@ Base .\number.jl:7
[2] setindex!(A::Vector{Float64}, x::ForwardDiff.Dual{ForwardDiff.Tag{typeof(lossSum), Float64}, Float64, 32}, i1::Int64)
@ Base .\array.jl:1021
[3] _generic_matvecmul!(C::Vector{…}, tA::Char, A::Matrix{…}, B::Vector{…}, _add::LinearAlgebra.MulAddMul{…})
@ LinearAlgebra C:\Users\JUR\AppData\Local\Programs\julia-1.10.0\share\julia\stdlib\v1.10\LinearAlgebra\src\matmul.jl:743
[4] generic_matvecmul!
@ LinearAlgebra C:\Users\JUR\AppData\Local\Programs\julia-1.10.0\share\julia\stdlib\v1.10\LinearAlgebra\src\matmul.jl:687 [inlined]
[5] mul!
@ LinearAlgebra C:\Users\JUR\AppData\Local\Programs\julia-1.10.0\share\julia\stdlib\v1.10\LinearAlgebra\src\matmul.jl:66 [inlined]
[6] mul!
@ LinearAlgebra C:\Users\JUR\AppData\Local\Programs\julia-1.10.0\share\julia\stdlib\v1.10\LinearAlgebra\src\matmul.jl:237 [inlined]
[7] jvp!(jac::FMISensitivity.FMU2Jacobian{…}, x::Vector{…}, v::Vector{…})
@ FMISensitivity C:\Users\JUR.julia\packages\FMISensitivity\Yt2rV\src\FMI2.jl:1323
[...]

Remarks

• The same happens if you use recordEigenvaluesSensitivity=:none in the lossSum.
• You can replace the gradient with :ReverseDiff (in the lossSum and in _train!), and end up with another error. So that doesn't work either.
• The combination :none (in lossSum) and :ReverseDiff (in _train!) works, however, if one wants to include the eigenvalues in the senstitivity calculation, this is not an option, is it?
• I haven't tried with Zygote, I don't care about Zygote ;-)

*this is actually a bug that this is not updated, but _train! is probably not the preferred resolution, rather train! with the neuralFMU instead of params as the second argument