Turing TypeErrror Issue

Specific Domains Probabilistic Programming
2

You’ve constructed this to have a ComplexF64 eltype, but this is incompatible with operator-overloading automatic differentiation (AD) packages like ForwardDiff, ReverseDiff, and Tracker, which use a custom numeric type to compute gradients. Instead, try

uhat = zeros(complex(eltype(ξ)),2*N);

The next issue you’ll have is that not all AD packages support complex numbers. Zygote definitely does, but it doesn’t support mutation. But if you want to differentiate an FFT, I think Zygote is your only option. So here’s a non-mutating build_field:

function build_field(ξ; α=one(eltype(ξ)))
    N = length(ξ)
    
    # construct the eigenvalues
    πk = π * (1:N);
    # NOTE we need to multiply by 2 *N for FFT scaling
    c = 2N * sqrt(2)
    umid = @. c * ξ / πk^α;
    uhat = [0; umid; zeros(N - 1)]

    # invert and get the relevant imaginary part
    u = @views imag.(ifft(uhat)[N+2:end]);
    return u
end

See https://turing.ml/dev/docs/using-turing/autodiff for details.

Also, from your simulated data, it seems γ might be intended to be a standard deviation? Note that Normal takes a standard deviation as a parameter, so perhaps you mean to use Normal(u[i], γ) as your likelihood?

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