Looking at the implementation, there is one bug that caught my eye:
In additional loss function, phi(t_data, θ) gives a matrix instead of a vector. Doing something like:
wr_data2 = reshape(wr_data, 1, :)
function additional_loss(phi, θ)
loss = sum(abs2, phi(t_data, θ) .- wr_data2)/size(wr_data2, 2)
return loss
end
Looking at the data, it looks very noisy, use an interpolation of it in the additional loss?
Also the time span is very large. PINNs are generally not great with large time spans. So I recommend to try it out on smaller time spans first.
If your goal is to just estimate parameters, may be doing through normal parameter estimation routines (without PINNs) would be better.